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Radioactivity measurements principles and practice
Appl.
Radiat.
Isot. Vo1.39,
Int. J. Radiat. Printed
in Great
Appl.
No.8,
Instrum.
pp.717-937,
1988
0883-'2889/88 $3.00+0.00 Pergamon
Part A.
Press plc
Britain
RADIOACTIVITY
PRINCIPLES
MEASUREMENTS
AND PRACTICE
1. INTRODUCTION
1.1. ORGANIZATION
OF LABORATORIES
FOR RADIONUCLIDE
METROLOGY
This report, which was prepared initially at the request of the International Atomic as a guide to laboratories engaged in, or about to become Energy Agency, was written engaged in radionuclide metrology. These may be national laboratories specialized either in measurements of radioactivity or dosimetry of ionizing radiations, or both, which are recognized by national law or international agreement, or they may be newly entering the field in regions of the world that are developing the uses of radioactive materials in the natural sciences or in medicine. These laboratories may collaborate with or be members of the Network of SecondaryStandard Dosimetry Laboratories (SSDL's) established and supported by the International Atomic Energy Agency (IAEA) and the World Health Organization (WHO) (see Eisenlohr, 1978, 1984; IAEA 1978a, 1979b, 1981, 1985,; IAEA/WHO, 1976, 1984). This international collaborative project, which includes top-level basic standardization laboratories as affiliated members (Fig. l-l), maintains a high level of quality of dosimetry work. The worldwide SSDL network consists at present of more than 50 laboratories of very different character, some of them being large national laboratories. The creation of this network was brought about by the basic need for an internationally consistent standard of absorbed dose for use by radiotherapy centres operating increasingly available cobalt-60 teletherapy units for the treatment of malignant turnours, in countries where the understanding of the principles of radiation measurements had not kept pace with the developments in medical methods. In view of the increasing use of radioactive materials, it was realized, as early as 1951, that international cooperation was needed to assure the conformity of international measurements of activity. Accordingly representatives of Canada, the United Kingdom and the United Stateb agreed, at that time, to exchange suitable samples of carbon-14,
Fig.
l-l.
The IAEA/WHO Network of Secondary-Standard Dosimetry Laboratories: AFF.PsoL'~: Affiliated Primary-standard Dosimetry L.bo=.tOTie.; IAEA:InternationaL AtmnlcEnergyAgency; WHO:WorldHealthorganization;
sodium-24, phosphorus-32, cobalt-60, bromine-82, strontium-90-yttrium-90, iodine-131, thallium-204 and gold-198 for intercomparative measurements (Mann and Seliger, 1958). These beginnings have since developed under the aegis, first, of the International Commission on Radiological Units and Measurements (ICRU) and then of the Bureau International des Poids et Mesures (BIPM) into a system of intercomparative activity measurements involving all of the leading national standardizing laboratories (ICRU, 1963; Rytz, 1983). But, as in the case of dosimetric measurements, the progress in radionuclide metrology has not, in some countries, kept pace with the developing technological, biological and medical applications.
717
Radioactivity
718
measurements:
principles
and practice
It is, especially, the aim of this report to provide guidance to any laboratory that is called upon to provide radioactivity standards and calibrations that are in agreement with the international standards, where such services are presently deficient or lacking. The work of the SSDL's, both in radiation dosimetry and in radioactivity, must clearly be continuously adapted to current and future needs, and must conform with different national laws and regulations, and with the precepts of the international hierarchy of standards laboratories (see Fig. 1-Z). It is to be hoped that the radioactivity-measuring laboratories, be they linked to the SSDL network or to some other metrological chain, will also establish firmly recognized transfer channels between the workers in the field and the national and international standards laboratories (Eisenlohr et al., 1981). 1.2. TASKS
OF LABORATORIES
ENGAGED
IN RADIONUCLIDE
METROLOGY
The first "classical" task of the radionuclide-metrology laboratories is to maintain with appropriate limits of uncertainty, and provide standards, for the calibration of Their second task is to maintain consistency of their activity-measuring instruments. activity measurements with other established laboratories, national and international, by means of direct or indirect international comparisons of their measuring competence (see, for example, L.M. Cavallo et al., HN*, 1973, p. 5; Rytz, 1983; NCRP, 1985). By means of such intercomparisons an international hierarchical system of measurements consistency and traceability has been established (Mann et al., 1981). This system that applies both to dosimetry and radioactivity measurements is illustrated in Fig. 1-2: f3lPM (IAEA,
International t
I~RM)
National
I laboratories
Qualitycontrotand I regulatory bodies
State
health
Government
Fig.
1-2.
laboratories, agencies,
Universities
lndustrlal
groups
,
Hospitals,
and
others
Hierarchy of radioactivity-standardization laboratories and organizations (the "Traceability Tree")
calibration services can also provide Laboratories that radioactivity SUPPlY This is indLs.pensible support in most, if not all, applications of radioactive materials. agriculture, archeology, biology, the a very large domain that includes, for example, the building industry, chemistry and the chemical industry, cosmology, energy production, medicine, meteorology, the metal fusion, geology and hydrology, environmental sciences, and the textile industry, mining and cokery. physics, reactor technology and safeguards, scope of industry (including leather, paper, and plastics). But, despite the extensive mo.st radioactivity measurements in these fields can be performed by these applications, very similar procedures, most of which are described or referenced in the following pages. 1.3. PURPOSE
AND SCOPE OF THIS REPORT
This report is written as a concise introduction to the field of radionuclide metrolproblems that may be encountered in ogy. Emphasis is given to the basic and practical although an attempt has been made to cover the whole field at measuring radioactivity, least by the inclusion of recent references.
Radioactivity measurements: principles and practice
719
The report therefore comprises this introductory chapter and six more. Following this introduction. the second chapter gives a brief survey of the basic concepts, definitions, quantities and units, and some useful data and constants used in the treatment and The third chapter treats the most important general problems measurement of radioactivity. in radioactivity measurements, such as radiation protection, source preparation, and the The fourth chapter describes the various treatment of experimental uncertainties. interactions of radiation with matter and detectors based on such interactions. The fifth chapter describes different methods of measuring activity. The sixth chapter gives a brief account of the basic principles of electronic instrumentation as applied to the processing The seventh chapter and recording of electrical pulses generated in radiation detectors. attempts to estimate the possible requirements for staff, space and equipment needed for Extensive references laboratories designed to make routine measurements of radioactivity. A principal reference is the are given in order to facilitate the use of this report. second edition of the U.S. National Council on Radiation Protection and Measurements (NCRP) "A Handbook of Radioactivity Measurements Procedures" (NCRP, 1985). The Report No. 58 present report largely complements NCRP, 1985, that is directed more towards applications in biology and medicine. 1.4. SI UNITS The Syst&me International d'Unit6.s created by BIPM (SI units: BIPM, 1985; NBS, 1986), has been adopted by IAEA and most countries, but as the greater part of the present literature is difficult to understand without any knowledge of the old system of units, both systems are generally used here in parallel (the old mostly within brackets). The SI unit for the quantity activity of a radionuclide, which is one measure of the The term phenomenon or property of radioactivity, is one reciprocal second, s -1 radionuclide metrology covers all aspects of radioactivity measurements, such as those of activity, half life, the atomic energy available and necessary for a nuclear transition to take place, probabilities of different modes of decay, and so forth
The following SI prefixes and symbols are used throughout:
Factor
Prefix
Symbol
Factor
Prefix
Symbol
1018
exa
E
10-l
deci
d
1015
peta
P
10-X
centi
1012
tera
T
10-j
milli
109
giga
G
10-6
micro
106
mega
M
10-9
Ilall0
103
kilo
k
10-12
pica
102
hecto
h
10-15
femto
101
deka
da
10-18
atto
2. DEFINITIONS,
OUANTITIES.
SOME USEFUL
CONSTANTS
SYMBOLS
AND UNITS;
AND REIATIONS
2.1, INTRODUCTION "Radioactivitb" was the name coined by Marie Curie to describe the phenomenon of radiation, atomic transformation, with the emission of corpuscular and, or, electromagnetic A detailed treatment of the phenomenon, or discovered by Antoine Henri Becquerel in 1896. and the underlying principles of atomic and nuclear physics is property, of radioactivity far beyond the scope of this report. Therefore this Chapter 2 seeks only to supply the reader briefly with the essential information needed for the successful performance of in particular. But for this radionuclide metrology, in general, and activity measurements purpose, it is also necessary here to consider the most basic attributes of radioactivity, the law of radioactive decay, the types of such as the statistical nature of radioactivity, their probabilities of emission, and other nuclear data. Further radiations emitted, detailed information may be obtained from several appropriate texts (see, for example, Evans, 1955; Siegbahn, 1965; Herceg Novi, 1973; Knoll, 1979: Mann et al., 1980; NCRP, 1985). 2.2. BASIC
CONCEPTS
2.2.1. Measurement,
AND
PARAMETERS
standardization
USED
IN THE MEASUREMENT
OF RADIOACTIVITY
and calibration
"Measurement" is a set of experimental operations, the purpose of which is to assign magnitude to a physical property, or to quantify it, in terms of a number and a unit.
a
Any physical quantity, such as mass, length or time, is measured in terms of a unit that may be defined in terms of a standard such as the kilogram, just as commercial transactions are measured in terms of one or more basic currencies that are related to one Indeed it is not just by chance that many national standards laboratories have another. the framework of governmental departments of commerce or developed, or remain, within trade. (See, for example, L.M. Cavallo et al., HN, 1973, p. 5.) Following the industrial revolution and the growth of international scientific cooperto tighten up a system that had developed quite randomly in ation, it became necessary of eighteen countries met different parts of the world. Therefore, in 1875 representatives des Poids et and signed the Convention du HBtre that established the Bureau International Mesures at S&vres as the custodian of the international standards of mass and length (and and dissemination (BIPM, later, time), and charged this Bureau with their preservation 1985). All three standards were defined standards, although those of length and time have The standard of mass, been redefined in terms of precisely measurable physical quantities. held in the kilogram, is, however, still the original cylindrical mass of platinum-iridium are measured by careful and precise experimental S&vres. Replicate national kilograms methods relative to the international standard at BIPM, and domestic standards are, in In terms of this hierarchical turn, measured in terms of their own national standard. system a mass of, say, 25 kilograms is a shorthand way of saying that the quantity "mass" system, is, Q of a certain object, in any part of the world using this international within an uncertaintv that can be estimated and should be stated, twenty-five times that of the international kilogram in S&vres. In 1960, the llth Conf&rence Gdnerale des Poids et Mesa-es (CGPM) extended the international system to include base (i.e. defined) units, derived units, and supplementary units, comprising L.e Syst&me International d'Unit8s (SI). The seven base units (and their names and symbols) for the followjng auantities are presently (BIPM, 1985; NBS, 1986): mass (kilogram, kg), length (meter, m), time (second, s), electric current (ampere, A), and luminous thermodynamic temperature (kelvin, K), amount of substance (mole, mol) intensity (candela., cd). standard has often been In the past the accepted standard or the best available defined as the primary standard. National-laboratory standards, although secondary international standards also frequently designated as primary standards. are Such ambiguity can be avoided if standards are designated according to the hierarchical system shown in Fig. 1-2, simply as international, national, laboratory working standard, hospital standard and so forth (NCRP, 1985). Basically, however, the only statements of importance in specifying a standard are its value and a realistic estimate of the uncertainty of that value (see 13.4). In many cases the national standard of a short-lived radionuclide such as, for example, Ia11 is in fact a secondary, or even tertiary standard calibrated very precisely by means of an ionization chamber maintained in the national laboratory or nt BIPM (set? 74.5.1.1.2).
721
Radioactivity
722
measurements:
principles
and practice
Another misused term is "absolute" and every effort should be made to use it unambiguously. Only the defined standards are absolute, in the sense that they have no error. K.F. Gauss has referred to measurements made "in absolute measure", meaning in terms of the defined, and therefore "absolute", standards. But such measurements have varying degrees of uncertainty. Nowadays "absolute" usually means "direct" as opposed to "relative" measurements. Thus the direct method of coincidence counting will give a value in terms of the absolute standard of time without the use of another standard, whereas an ionization chamber gives only a relative measurement, but nonetheless 8, in absolute measure". An "absolute neutron cross section" with an uncertainty attached to it is often a relative measurement, but is probably "in absolute measure" in the sense used by Gauss. In this report, every effort will be made to conform with the statement referring to "Electrical quantities", in BIPM (1985, Appendix 11.4), that "So-called 'absolute' electrical measurements, i.e. those that realize the unit according to its definition, can be undertaken only by laboratories enjoying exceptional facilities." The term calibration normally refers to the relative, or indirect, measurement physical quantity by comparison with a standard that embodies that quantity. 2.2.2. Radioactivity
standards.
reference
and calibration
of a
sources
A standard is, quite generally, a very well characterized sample, instrument, or procedure intended to define, represent, conserve or reproduce the measure (unit) of a physical quantity, in our case activity. There exiqts a great variety of types of calibrated sources of radioactivity, International standards are, in general, maintained by the BIPM; in the case of activity standards chiefly through the "international reference system," known as SIR (72.2.3). National standards are normally recognized by law as the basis for the calibration of all other standards of a quantity in one country. Ideally they should be "traceable" ((2.2.3) International standards to international standards. are of the highest metrological quality and are, in general, checked by intercomparisons betweeen national and international standardization laboratories. A complete hierarchy of national, laboratory, field or calibration standards is derived from, and, in the case of radioactivity, traceable to, the international standards, within stated limits of uncertainty (72.2.3). All activity standards of every kind must be fully documented; that is, they must be accompanied by a certificate issued by the standardizing laboratory that fully describes their preparation, characteristics, and calibration, and, most importantly, states the estimated uncertainties in the certified value, both random and non-random. For a discussion of statements of estimated uncertainty reference may be made to 73.4.1.2, er seq. Field standards, the last level in the hierachical system of standards, should be available for every field instrument. There is no better way to check efficiently and reliably the functioning of field instruments than by using suitable calibration standards; these are often called "reference sources". International cooperation in radionuclide metrology would be greatly facilitated if the forms of standards and sources could themselves be standardized. This has indeed already been done in the SIR program (72.2.3) where standard glass ampoules (for filling with a specified volume of solution) can be obtained from BIPM. Into most European languages the word "standardization" is translated as "normalisation". 2.2.3. Traceability
and aualitv
assurance
Because of all the problems and hazards connected with radioactivity, its measurement should always be extremely reliable. This can be achieved to a considerable extent by measurements-assurance programs and so-called traceability exercises (Mann et al.. 1981; NCRP, 1985, Ch. 8.3). The term "traceability" is not yet fully recognized officially, but within the restraints imposed by the transitory nature of radioactivity, it aims to achieve either exulicit or implicit (NCRP, 1985, Ch. 8.3) measurements assurance within the hierarchical systems (Fig. 1-2). The necessary credibility of measurements and standards of radioactivity is not easy to achieve because of the multitude of radioactive substances used and their different and, frequently short, half lives. Direct verification by special organizations of every standard issued (quality assurance) is not possible for radioactivity standards. Therefore, continuing international, and many national, quality-assurance, or traceability, radioactivity-measurements programs have been established, which allow the achievement of a high degree of reliability of radioactivity standards and measurements at all levels of the hierarchical system (Fig. l-2).
Radioactivity
measurements:
principles
and practice
723
The international system of radioactivity-measurements traceability comprises a close collaboration between many of the outstanding radioactivity-standardization laboratories around the world. It involves two principal activities organized by BIPM, namely (i) frequent interlaboratory comparative measurements of the activity concentrations of radioactive solutions, encapsulated in standard glass ampoules and all prepared from the same master solution (see, for example, Rytz, 1985), and (ii) an international reference system (SIR, Syst&me International de RBfbrence) that allows national laboratories to submit standard glass ampoules containing radioactive solutions with stated activity concentration to BIPM for verification and registration (Rytz, 1983). The SIR program complements and extends the program of international comparisons of activity measurements organized by the BIPM. The participants are, as a rule, national and international laboratories of radionuclide metrology. They are invited to submit samples of solutions of gamma-ray-emitting nuclides, which they have prepared and standardized Two very stable, pressurized wellthemselves, in sealed, and standard, glass ampoules. type ionization chambers have been installed at the BIPM (Rytz, 1983) and used for comparing the current produced by a submitted sample with that produced by a BIPM reference source of very pure radium. From this ratio the activity concentration is calculated. This international traceability and new ideas may still be expected.
program
(SIR)
is still
developing,
so
that
changes
At the national level many standardizing laboratories conduct internal traceability exercises between themselves and the principal domestic radioactivity-measuring laboratories, and especially with those involved in regulation. Such exercises are very similar to those conducted at the international level, except that solid sources of alpha-particle-emitting nuclides may often be included. The national laboratory will usually distribute calibrated radioactive solutions, or solid samples, in the form of "blinds". These are sources of known but undisclosed activity concentration, or activity, and it is incumbent upon the receiving laboratory to measure the activity, and perhaps even identify it, and to return its results to the national laboratory or, in some cases, to the next higher laboratory in the hierarchy. The tested laboratory may then receive a cetificate of traceability stating its achievement in terms of its percentage divergence of its value from that of the national or monitoring laboratory. But this kind of traceability "is usually imulicit, insofar as it only establishes the ability of a laboratory to assay any radionuclide at any given time. In the long term it is the competence and reliability of a laboratory and the skill of its staff that comprise its traceability" (NCRP, 1985, Ch. 8.3). And it is the purpose of any traceability or quality-assurance program, relating to any production process, to provide the necessary assurance that, within certain well-specified limits, that process shall remain in control. Essentially this is also the aim of the SSDL network. With the many uses of radionuclides, especially in medicine, this task can be formidable. And it is interesting to note that in the United Kingdom the National Physical Laboratory has to some extent circumvented the problem of distributing calibrated sources of photon emitters by sponsoring the manufacture of calibrated ionization chambers. These can then be maintained "in control" by monitoring with a few standards calibrated for photon-emission rate over an appropriate range of energy. The United Kingdom has also instituted the British Calibration Service which is charged with the task of assuring the quality and competence of the laboratories and personnel of the laboratories in the hierarchy of measurement standards. 2.3. RADIONLJCLIDES. 2.3.1.
Elements. isomers
RADIOACTIVITY
nuclidas.
radionuclides
(radioisotopes),
isotopes,
isotones,
isobars
and
The different elements were initially recognized by their more distinctive external characteristics, such as state, colour and density (e.g. mercury, copper, silver, gold and lead); and then, with the passing of time, they became characterized by their physical and chemical properties. The elements are subdivided into nuclides. And a nuclide is defined as anv species of atom having specified numbers of protons, 2 (atomic number), and neutrons, N, in its nucleus. The positive nuclear charge, Ze, which, under normal conditions, is compensated by the charge of the electron cloud around the nucleus, -Ze, determines the kind of element (Table 2-l); and the outermost electrons in the cloud, its chemical properties. The sum of the numbers of neutrons and protons gives the mass number, A, of the nuclide. This is expressed in the symbol for a nuclide A (= Z + N), that is designated in the form *X, as, for example, 6oCo and 85mKr (where "m" indicates a metastable state). Sometimes the value of Z may also be included as in $0 or 853;Kr. The atomic mass number, A, of a nuclide is approximately equal to its atomic "weight" relative to 1% = 12.000000. Unstable nuclides, radionuclides, decay stochastically (i.e. randomly) to stable or unstable progeny of lower atomic mass, the difference in mass being radiated in different kinds of energetic radiation according to the Einstein mass-energy relation E = mc2. Radioactive substances are found in nature, but most are now produced by nuclear reactions, Nearly all naturally-occurring radionuclides (except for some unstable nuclides at low
Radioactivity measurements: principles and practice
724
"OK) belong to the four families of radioactive heavy nuclides (a2.3.7). Z-values, e.g. Most artificial radionuclides are produced by neutron irradiation of stable nuclides in reactors, and many by charged-particle bombardment in high-energy accelerators. Sometimes the term radioisotope (implying "radioactive isotopes of') is used instead of the correct term "radionuclide". The different nuclides with the same atomic number, Z, are the isotopes of one well-defined element. Nuclides with the same neutron number, N, are named isotones, and those with the same mass number, A (= N + Z), isobars. If, in radioactive decay, the transition is to an excited state of the daughter nucleus that, in turn, decays to a lowerGround States of Free Neutral Atoms Table Z-l. ELECTRON CONFIGURATIONS OF THE ELEMENTS ----pNumbers of electrons in the different subshells (after Kaye and Laby, 1973). The capltals of the first line refer to the principal quantum numbers, n= 1,2,3...7. The subshells are designated by laxer-case letters, s,p,d,...h,corresponding to the azimuthal quantum numbers P = 0,1,2,...5. Element
K 1s
1. 2. 3. 4. 2: 7. 8. 9. 10.
H
1
He
2
Li Be B c N 0 F Xe
11. Na 12. Mg 13. Al 14. Si 15. P 16. S 17. Cl 18. Ar ---------19. K 20. Ca 21. SC 22. Ti 23. V 24. Cr 25. Mn 26. Fe 27. Co 28. Ni 29. Cu 30. Zn 31. Ga 32. Ge 33. As 34. Se 35. Br 36. Kr 37. 38. 39. 40. 41. 42. 43. 44. 45. 46.
47. 48. 49. 50. 51. 52. 53. 54.
Rb Sr Y Zr Nb MO Tc Ru Rh Pd
Ag Cd In
Sn Sb Te I Xe
L 2s
M 2P
1 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 __-_------ -. 2 2 2 2 2 2 2 2
--_
3p
3d
;
1
2 2 2 2 2
2 3 4 5 6
6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 ----
2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2
6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6
2 3 5 5 6 7 8 10 10 10 10 10 10 10 10
6 6 6 6 6 6 6
2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2
6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6
10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10
----
2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 _-. 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2
3s
N
: 6 6 6 6 6 6 6 6 6
4s
4p
0 4d
4f
5s
5p
5d
_____----5f 5g
1
n
:
1
2 2 2 3 2 4 2 5 2 6 ____________________-__---------_-------_________ 1 2 6 2 6 2 1 2 6 2 2 2 2 6 4 1 2 6 5 1 2 6 5 2 2 6 7 2 6 1 6 8 1 2 10 2 6 2 6 10 1 2 6 10 2 10 2 1 2 6 10 2 2 2 6 2 6 10 2 3 10 2 4 2 6 2 6 10 2 6 10 2 2 continued next page
Radioactivity
meaeurements:
principles
and practice
725
Table 2-l (cont'd) _____________________------------------_______________--_-__-_________________-------___-________ Element
K
L
M
N 4s
4p
4d
4f
5s
5p 6 6 6 6 6 6 6 6 6 6 6 6 : 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6
2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2
8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8
18 18 18 18 18 18 18 18 18 18 18 18 18 18 18 18 18 18 18 18 18 18 18 18 18 18 18 18 18 18 18 18
2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2
6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6
10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10
2 3 4 5 6 7 7 9 10 11 12 13 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14
2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2
Fr Ra AC Th Pa U Kp Pu
2 2 2 2 2 2 2 2
8 8 8 8 8 8 8 8
18 18 18 18 18 18 18 18
2 2 2 2 2 2 2 2
6 6 6 6 6 6 6 6
1014 10 10 10 10 10 10 10
14 14 14 14 14 14 14
2 2 2 2 2 2 2 2
95. Am 96. Cm 97. Bk 98. Cf 99. Es 100. Fm 101. Md 102. No 103. Lr 104.(Rf) 105. (Ha)
2 2 2 2 2 2 2 2 2 2 2
8 8 8 8 8 8 8 8 8 8 8
18 18 18 18 18 18 18 18 18 18 18
2 2 2 2 2 2 2 2 2 2 2
6 6 6 6 6 6 6 6 6 6 6
10 10 10 10 10 10 10 10 10 10 10
14 14 14 14 14 14 14 14 14 14 14
2 2 2 2 2 2 2 2 2 2 2
55. cs 56. Ba 57. La 58. Ce 59. Pr 60. Nd 61. Pm 62. Sm 63. Eu 64. Gd 65. Tb 66. Dy 67. Ho 68. Er 69. Tm 70. Yb 71. Lu 72. Hf 73. Ta 74. Iv’ 75. Re 76. OS 77. Ir 78. Pt 79. Au 80. Hg 81. Tl 82. Pb 83. Bi 84. PO 85. At 86. Rn ------____ 87. 88. 89. 90. 91. 92. 93. 94.
5d
Q
P
0 5f
6s 6p 6d 6f 6g -------------------_--__-___-_______-
%
1 2 3 4 5 6 7 9 10 10 10 10 10 10 10 10
1 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 1 1 2 2 2 2 2 2 2
1 2 3 4 5 6
6 6 6 6 6 6 6 6
10 10 10 10 10 10 10 10
2 3 4 6
2 2 2 2 2 2 2 2
6 6 6 6 6 6 6 6
6 6 6 6 6 6 6 6 6 6 6
10 10 10 10 10 10 10 10 10 10 10
7 7 9 10 11 12 13 14 14 14 14
2 2 2 2 2 2 2 2 2 2 2
6 6 6 6 6 6 6 6 6 6 6
1
1
--.
1 2 1 1 1
1
1 2 3
energy state of the same nucleus with, usually, a short but easily-measured half the latter transition is known as isomeric, and the decaying daughter is called
6h
7s
1 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 life, then an isomer.
Such isomers are denoted by a letter "m" (for metastable) placed after the mass number of the isomeric nuclide. As an example, '\:Cs decays to isomeric 1375:Ba that, in turn,decays with a half life of 2.55 min to stable '\LBa. The assignment of radioactive isomerism is somewhat subjective as decays from all excited states follow the radioactive-decay law, but mostly with half lives that are too short to be easily measured. Thus the 1.3325.MeV excited state of giNi, in the decay of "207Co, has a half life of the order of 1 ps. but the transition is not considered to be isomeric.
726
Radioactivity
Table
measurements:
2-2
principles
Periodic
and practice
table of the elements
The elements can be grouped according to their atomic structure (and, consequently, chemical behaviour) in the periodic table of the elements (Table Z-2). Nuclides are often plotted in a Z-N table of the nuclides, with Z as ordinate and N as abscissa. A part of a typical nuclide chart is shown (with explanations) in Fig. 2-l (see, for example, Walker et al., 1977). Groups in the periodic table having similar configurations of their outermost electron shells have similar chemical properties (e.g. F, Cl and Br). Isotopes of any given element have essentially the same chemical properties.
spm and
parity
0
d
decay
modes I
2.3.2. Radioactivitv
Fig. 2-l. and activity
Part of a nuclide
chart
The phenomenon, or property, "radioactivity" is quantified in terms of the number of Some 60 years ago when radium was the most nuclear transitions occurring in unit time. important radioactive substance, it was quantified by mass, usually in terms of milligrams Later a quantity, the "curie", was defined as the amount of radon-222 in of radium. equilibrium with one gram of radium-226. Further experiments showed that such an amount of radon-222 was emitting alpha particles at a rate of somewhat more than 3.6 x 1O'O per when the use of radioactive materials multiplied, the curie was Subsequently, second. redefined as an activity of a substance such that it was decaying at a rate of 3.700 x lOi0 In SI units the quantity activity has been defined again in terms of a derived SI 5-l. unit of "one per second" (s-l) with the special name (and symbol) of becquerel (Bq). Because of the widespread use of radiopharmaceuticals in the practice of nuclear medicine
Radioactivity measurements: principles and practice
and the almost universal quantification of such radiopharmaceuticals in terms of "curies" or "millicuries", the unit "curie" (symbol Ci) has been temporarily retained by CGPM as a unit of activity "outside SI". In summary 1Bq = Is-', and
1Ci = 3.7~10~' Bq
The quantity activity that is used as a measure of the property radioactivity has been defined as follows (NCRP, 1985, Ch. 1.3): "The activity of the amount of a nuclide in a specified energy state at a given time is the expectation value, at that time, of the number of spontaneous nuclear transitions in unit time from that energy state". By this definition zero activity would be equivalent to stability of the nuclide, and the definition also takes into account that radioactivity is a process involving the && nuclide (or atom) and not just tzhenucleus. This is epitomized in the case of the decay of l"Re to la70s which could not occur but for the binding energy of the extranuclear, atomic, electrons (see 72.5.2). The probability of decay of some radionuclides can also be modified slightly by the effect of changes in chemical composition and pressure on the extranuclear electronic configurations (Harbottle and Maddock, 1979). The activity concentrations in some radioactive substances that occur in nature or derive from industrial applications are given in Table 2-3. Because of the large variations of these data in practice, only orders of magnitude are given. 2.3.3. Ouantities derived from the auantitv activity "Activity" pertains, by definition ((2.3.2), to one type of nuclide only. Therefore a number of secondary quantities must be derived from the general definition of activity for The term "activity" must always be used with caution, and practical applications. preferably in the context of the specific nuclide (e.g. "the activity of a "Co source"). A quantity that should first be exactly defined is the "specific activity". In agreement with the general use of the term "specific" and the definition of activity, the "specific activity" should be the activity of 1 g of the nuclide itself, as, for example, the activity of "Co in 1 g of 6oCo. This should probably preferably be named "specific nuclidic activity", because "specific activity" has already been defined (ICRU, 1963), as the activity per gram "of the element whose radioisotope is considered". This might be The units of any specific activity are Bq g-' called the "specific elemental activity". (old unit; Ci g-l). In practice, a most important quantity is the "activity concentration per unit mass or unit volume," which is defined as the activity per gram (or millilitre) of a sample; for gases it is either per unit volume (cm3 at STP -- Standard Temperature and Pressure, i.e. 0°C and 760 torr, or = IO5 Pa, i.e. lo5 Pascal), or par mole. It may sometimes be important to state, in addition to the activity concentration, the degree of homogeneity of the sample. The units of activity concentration are Bq g-l = se1 g-l (old unit; Ci g-') or Bq cmm3 = 5-l cme3 (old unit; Ci cmW3). For mixtures of radionuclides, the quantity "total activity" although never formally It is the sum of all nuclidic activities in a sample. defined, is of great importance. The same holds for a "total activity concentration". Because some of the quantities defined above are not yet officially adopted, it is always important to state exactly what is meant by the "activity" in question. 2.3.4. Decav schemes All radioactive transformations can be described as transitions of higher-energy atomic states into lower-energy states through reorganizations of the atom and its nucleus. The excess energy is emitted -- depending on the neutron-proton ratio in the nucleus -- in the form of different radiations. The radiations from radioactive atoms consist mainly of: o particles (doubly positively charged He++ ions), @' particles (positrons) and /l- particles, and monoenergetic conversion electrons, nuclear electromagnetic radiations (7 rays), and atomic electromagnetic x rays and Auger electrons following electron capture (of a shell electron by the nucleus), or internal conversion. The different radiation properties of radionuclides and the characteristic parameters of their decay are usually described by decay schemes. These are diagrams with the total energy as ordinate and the nuclear charge as abscissa. Transitions between energy states are shown by arrows. Branching transitions, shown by arrows starting from the same energy state, are decay modes with discrete decay probabilities, the ratios of which are called branching ratios.
727
728
Radioactivity
Table
measurements:
2-3 - Typical
MATERIAL
average
principles
radioactivity
ACTIVITY
(drink) water
of some common
materials
CONCENTRATION
Bq/g Surface
and practice
Remarks
Wg
0.0004 0.04
to
10-14 to 10-12
Mainly "'Rn + daughters
seawater
0.01
3x10-13
Mainly
4oK
Human
0.1
3x10-12
Mainly
4oK and 14C
3x10-14 to 10-11
Mainly 4oK (+U+Th...)
body
Detector construction materials
0.001 0.3
Food (plants) animals)
0.1 to
3 to 30xlo-~~
Dry substance
0.1
3x10-12
40K/87Rb/lJ+Th = 10/1/l
0.1
3x10-12
Mainly 220Rn
0.5
1.5x10-11
K/Rb/Th/U = 10/3/1/l
1.5
5x10-1'
K/Rb/Th/U = 10/1.5/1/l
0.15 to 150
5x10-12 5x10-9
Carbonate
and
rocks
Air (in buildings Mean
to
x 0.7)
soil
Granits (igneus
rocks)
Medical
springs
to
222Rn -I
,%i;?
226Ra +
4oK
Phosphate
fertilizer
40
10-9
Mainly
Low-level
waste
< 400
< 10-8
IAEA (1970) definition
1.2x104
3.3x10-7
Specific Activity
Intermediate-level waste
400 to 4x108
10-8 to 10-2
IAEA (1970) definition
4OK (Th = 1.3x109
2.6~10~
7x10-6
Specific Activity (y act.
238" (T,, = 4.5x109
a)
a)
x 0.1)
> 4x108
>
2.2x109
0.06
Specific Activity
bOCCl (T% = 5.26 a)
4.2~10~~
103
Specific Activity
Burnt LWR fuel element (0)
4x1014
104
Fission products + actinides; t=O
Burnt LWR fuel element (150)
4x1012
24Na
3x1017
High-level
waste
239P, (Q-h = 24,000
10-2
a)
Fission products + actinides; 150d cooling 9x106
(Tb = 15 h)
Numerical data from Castren (1985), Sauter (1983), NCRP Jaeger and Hubner (1974), ICRU (1972) and others. Some examples
of typical
decay
schemes
Solidified; Cooling needed
Specific Activity
(1976b),
are shown and explained
NCRP in
(1975), Fig. 2-2
Radioactivity
measurements:
Typical
Fig. 2-2.
principles
decay
schemes
729
and practice
of radionuclides
Corresponding data in tabular form are given in Table 2-4 together with data for some important radionuclides not included in NCRP (1985), in which nuclear data for many of the not listed here can be found. In special collections of decay schemes further data are given and parameters are discussed in more detail (see, for example, Lederer and Shirley, 1978; Kocher, 1981; NCRP, 1985). Table 2-5 gives preferred methods for measuring the activities of the 13 radionuclides listed in Table 2-4, together with many other important radionuclides. 2.3.5. Disinteeration
probability
As radioactivity is a stochastic one cannot predict when a radioactive phenomenon, atom will decay and exactly how many decays will be counted in a given interval of time. But, for a mean value, or expectation value, E(n) of the number of atoms decaying in a given time the probability distribution, P, around E(n), of the number of decays occurring in that time can be calculated, because the radioactive decay process follows, except for extremely low decay rates, the Poisson probability distribution (see 73.4.2; Haight, 1967; 1974; Mann et al., 1980). This law states that the Feller, 1968, 1971; Frigerio, probability, P,, of n transformations occurring in the given interval of time is [E(n)]" emE(") P,
=
(2-l) n!
where E(n) is the only parameter is not too small.
of the distribution
for integral
For larger values of n the Poisson distribution symmetrical normal ("Gaussian") continuous distribution P, = [2aE(n)]-'
ev-x*/2E(n)
1 ,
can
be
n, and provided
well
that E(n)
approximated
by
the
(2-2)
where x = [n-E(n)] and 1x1 << E(n) (see Fig. 2-3). This distribution function can be much more easily calculated. The difference in the values of n calculated from these two distributions is less than 1% at a mean of 10, about 0.1% at a mean of 100, and so on (see Fig. 2-4).
730
Radioactivity
measurements:
-2
principles
-1
and practice
l2
l1
0
x/u Fig. 2-3
Normal ("Gaussian") distribution of the probability density for a mean p = E(n) = 1 and a standard deviation D = 1
Poisson and normal decay-probability laws may be used to derive The many characteristic orooerties of radioactive decav. The most imoortant is. that the estimated standard deviation of a measured number of events (e.g. counts) is equal to the square root of the number of these events (NCRP, 1985).
t
0 30
I.
40
50
60
,
70
Oo,o
o,q” 80
90
100
110
I20
IO
nx Poisson
The Poisson distribution Fig. 2-4. distribution (vertical bars) for mean values of 50 and 100: Normal distribution (circles) for mean value of 100
The Poisson distribution for count rates is equivalent intervals of time between counts, and each can be derived form of a Poisson time-interval distribution is P (L>d)= exp(-rt)
I
to a similar distribution for from the other. The simplest
(2-3)
the probability that a time interval larger than d will occur for a mean where PC,,,, is Some properties of radioactive decay can better be understood, if count rate of r = l/d. the time distribution is used instead of the event distribution (Miiller, 1973). However, the Poisson distribution holds exactly only for ideal conditions, as, for in the measured interval of time is example, that the number of decays of a radionuclide negligible compared with the number of atoms of the radionuclide present, that there is complete independence of all events from each other, and that the background approximates a Poisson distribution. These conditions are not always fulfilled in practice, especially at low count rates and for dead-time distortions of the Poisson distribution at high count rates. These distortions are best understood, if the time-interval distribution (Eq. 2-3) With a finite dead time, T , of a counting equipment, is considered. the interval distribution can only be finite for times t DT (the truncated Poisson distribution). This leads to a narrowing of the Poisson distribution of the numbers of events (shifted exponential). There are several other effects which distort the observed distribution that must be carefully considered, such as the possibility of perturbations being introduced by scalers.
Radioactivity
Table 31( B-
DmxY
2-4
1 m.i
aw
22NA
II+
DIKXY
Radiation
I,l#IN,=
mtmsity
‘8.600 5.685
10 4
t2.602
Y
A”O.C_K I
mex
aw
545.9 215.50
1 xsak
B’S
*IBIN,=
Intensity
radionuclides
9.20
89.89 CEl#
0.101
5
0.412
Energy
,k*“l _________
AUg*r-I
x-ray K-ray X-ray x-ray
204TL
K.diation
TYPa TYP* ---------
rnt.n.ity
,k.“, _______--
0.0006 0.0004 0.103 0.0198 0.0066
94.43
7
0.344
5.53
I
0.0489
99.96
10
IC
PICAY
Ic.di.tion
t2.,2
,x1 _________
Y 21
-----___-
0.0025
3
1.20
Auger-l Auger-K
Intmslty CX) _________
0.6 5.19
X-ray X-ray K-r*y
I K(I> KO, Kg
x-ray
139 60.7
0.64 5.88765 5.89875 6.49
3 3
I KO, K(1, K#
B-
DSCAY
1ntsnsity
Alg-rad,
(X1 _________
#.Ci-h, ________
7.6
1.23
9
0.0002
10 68.8950 70.8190 80.3
9 12 18 9
0.0002
20 20
0.75 0.420 0.711 0.314
t3.7s
Y 2,
Kn.rgy Ck.“) __----___
4
0.42 8.2 16.3 3.79
21 14 7 12 25
B-
DllCAY
(5.2714
Y
5,
IIIIIN,=
cx, ____--___
0.0011 0.0005
0.101
nlt.n.ity
ACg-r.d/
,I, _____---_
___-
pCi-hl -___
0.506
0.101
ACg-rad, rCi-h) ________
ansrgy , *a”,
0.0018 0.0067 -0 0.0010
0.0020 0.0005
&i-h) ________
11.2 13 23.2 10 6.35 25 2.34 10 0.176 8
0.0013 O.OlS4 0.0071 0.0028 0.0004
0.300 31.7 68.0
0.0328 3.55 7.71
20 9 4
6
0.101 Atg-rad, Ji-h) --______
0.101
Alg-rad,
Intensity (X1 ___ ______
(XII
Intmw.ity
0.0006
III(m)=
12.2 13 0.2011 6OCO
o.oo,o
big-r.d/ &i-hl
3,@!IN>=
Kll.l-JY tkm”, __--_____
VP
---_____-
=0 0.0014
7 12 5
TC”IN,= 55PK
0.398
3
0.061)
TYPt, _________
ml.rgy
5 21 5 3 19
3.68 1.34 85.1
Radiation
Radiation
Atg-r‘sd, )&i-h, ____- ___
1.0 1.99
0.0002
11
=
1nt.nsity IX1 _________ 7.3 0.77 7.78 1.42 0.472
beg-rad, #&i-h’ ________
lx, _________
omitted
selected
731
0.0121
11
5 21
of
and practice
0.10%
100
0.82
principles
ACg-Tdl rCi-hl ___-____
cx, _________
KlIargy Cb”, _________
TYPO _________
Decay data
1,
,k.“, ____-____
TYPO ___-_____
,9’
Y
mmrgy
Il.diati.2”
s-
(12.35
measurements:
=
0.07X)
0.0034 0.0003
732
Radioactivity
measurements:
principles
and practice
_________ _______ __ ce-r-2
0.9 0.4 4.9 cl.21 1.5 0.24
5 4 7
0.7 1.70 4.2 5.0
20 3 5
2.09 1.50 0.22
8 20 3
7.417
1
_________ ________ 12.9
4
P.OO2cl
Radioactivity measurements: principles and practice
Table 2-5.
733
Preferred methods for activity measurements of selected radionuclides
Radionuclide'
Half life2
Radiations3
Methods4 for standardization
3H :? 18; 22Na 24Na ;;A1 33; 35s 36Cl 37Ar 40K 42K 45Ca 46% 51Cr 54Mn 55Fe 56M, 56co 5’CO %o
59Fe 59Ni 60~0 63Ni 64cu 65Zn 6'Ga 68~e+68~a 74As '5% 79Kr 82Br 85Kr i3Sr Y a9Sr ;;sr+90y 91; 94Nb 95Nb 95Zr+95mNb 99Mo+99mTc ;;;%&+'""Rh llOrnAg ;;;sIl+113rnI, I ;;;Sb 129; 13OI 131I 131cs 131nlX, 132T,+132I 133B, 133X, 1%
;;;%;;13'mB, 139C, 140Ba+140La 14OL, 14lC, 144Ce+144Pr
12.35 a 53.28 d 5730 a 109.7 min 2.602 a 14.96 h 7.2 E5 a 14.29 d 25.34 d 87.44 d 3.01 E5 a 35.0 d 1.28 E9 a 12.36 h 163 d 83.79 d 27.70 d 312.1 d 2.72 a 2.577 h 77.9 d 271.7 d 70.82 d 44.51 d 7.5 E4 a 5.271 a 96 a 12.70 h 243.9 d 3.261 d 270.8 d 17.78 d 119.8 d 35.04 h 35.34 h 10.72 a 64.85 d 106.6 d 50.5 d 28.5 a 64.0 h 58.5 d 2.03 E4 a 35.0 d 64.0 d 65.92 h 367 d 462.6 d 249.8d 115.1 d 13.22 h 60.20 d 59.6 d 1.57 E7 a 12.36 h 8.021 d 9.69 d 11.9 d 76.3 h 10.5 a 5.243 d 2.065 a 30.0 a 2.553 min 137.6 d 12.76 d 40.28 h 32.50 d 285.0 d
fl EC p p+ EC
18.6 7 156.5 EC B+ 7
;+7EC 7 /3 1710 fl 249 /3 166.7 j3 709 (EC) EC B EC 7 UJ+) ; 7257 B 7 EC 7 EC 7 a""7 EC B+ 7 EC 7 EC B+ 7 Br 5"7 B 65.9 B EC 8+ EC B+ 7 EC 7 EC B+ 7 B 7 EC 8+ EC 7 EC 7 8+ ;: EC 7 EC 7 B+ B 1463 B (7) ,9 2283 B (7) ;: ;: Pr EC 87 EC EC Br EC
7 7 7 7
;: Br EC ;7 EC 7 ,":: 87 7 EC 7 Br ;: B7
I s I c E E c P P I P I L C P c c c S E E E E E S E M P E El s s El I1 E I E E L P P P E E E E El E E s El E w c E E P 11 P E I E T s E E E E E
0.3 0.3 0.3 0.5 0.3 0.1 0.3 0.3 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.1 0.3 0.3 1 0.1 0.3 0.3 0.3 0.3 1 0.1 0.5 0.5 0.5 1 1
0.3 0.5 0.3 0.3 0.5 0.3 0.3 0.3 0.1 0.3 0.3 0.5 0.5 0.3 0.5 0.3 0.5 0.5 0.3 0.5 0.5 0.5 0.3 0.5 0.3 0.5 0.3 0.5 0.5 0.3 0.5 0.5
M MPT s CW SW s TM TM PTM TM SP SPE TM SW SW SW PM SPE S UP SW ESW PM S ITP SW S SW PW PW CPU SW SW s WC WC PTM WLM WLM WML C SW S CPL CPL US SWL w S WS PCS SPL SWL LS TS S SW SW s EW PTW w W W WP WPT TWL
routine work
Ll s Ll Sl s s s Ll Ll L Ll I2 s s Ll s s s s s s Wl s s s s L Sl s Sl s s s s Sl s s s Ll L L Ll s s s Wl s Pl w Wl W2 w Wl Pl w Wl Wl s2 Wl w s w s s s w s Wl Pl
0.5
0.5 0.5 0.5
2
1 2 0.5 0.5 0.5 2 0.5 0.5 0.5 0.5 2 0.3 3 0.5 2 2 2 2 2 0.5 0.5 0.5 0.5 0.3 0.5 0.5 2 0.5
0.5
0.5
0.5 1 0.5 0.5 0.5 0.5 0.5 0.5
(S) w P(S) w w WL w us P(S) P(S) PSW (S) PLW WPL P(S) WL w w UP WPL w SP UP WL UP WL (S) w w w PW PW UP UP w IW w w WSP SUP SUP SUP WL WL WL SPL PLW us SLW S s s PS LS SL LS SP w SL SPL SL WL w WL SL WL SLW SLW
Radioactivity measurements: principles and practice
Table 2-5 cont'd 14'P, 152EU 154ElJ :;;EU Yb l'OT, '*lHf gTa w 1921, 195AU 198AU 199ALl 2OlTl 202Tl 203Hg 204Tl 207Bi 210Bi D 2lOP0 222Rn D 226R, D 227Ac D ;;;Th D U D 233P, (D) 233U (D) 234U (D) 235U (D) 236Pu D 238U D ;;;Pu (D) U D 23gNp (D) 23gPu (D) 240Pu (D) 241Pu D 24111, (D) 242Pu (D) 243Am D 243Cm (D) 244Cm (D) 24gCf (D) 252Cf (D)
2.623 a 13.4 a 8.55 a 4.72 a 32.03 d 128.6 d 42.4 d 114.4 d 75.1 d 73.83 d 183 d 2.696 d 3.139 d 72.91 h 12.2 d 46.60 d 3.77 a 32.2 a 5.013 d 138.4 d 3.824 d 1600 a 21.77 a 1.4 El0 a 72 a 27.0 d 1.59 E5 a 2.45 E5 a 7.04 Ea a 2.85 a 4.47 E9 a 87.74 a 23.5 min 2.355 d 2.41 E4 a 6564 a 14.4 a 432.2 a 3.76 E5 a 7380 a 28.5 a 18.11 a 351 a 2.64 a
p 224.7 B EC 7 W+) ;; EC -Y B -r (EC) B 7 ; 7432.6 B EC Y EC 7 ;
‘7
EC
7
EC
7
B
7
B
(EC)
EC
7
P a a
(7)
;
;
a
7
;
5
a
7
a
7
0
7
(1
7
a
7
;
;
B
7
a
7
;
a 0
(a)
2i.82 7 -7
: a Q
; (EC) 7
a
7
7 n
P w c Cl w P c c P w c c c c c c P w P s s s s s c s s P s P s P P s s P2 s s s c s c s
0.5 0.3 0.3 0.3 0.5 0.3 0.3 0.5 0.3 0.5 0.3 0.5 0.5 0.3 0.5 0.5 0.3 0.5 0.3 0.5 1 0.5 0.3 0.5 0.1 0.1 0.5 0.3 0.5 0.1 0.5 0.5 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.3
TM L LW LE c TCL SL PWL TLM CP LW SL WL WL WL WL LTM c TL PL PLC PLC LPC LPS LP LP LPS LP LS LP CL CL LP LP TM CLP LP CLP SLP LP SLP LP
Ll s w Wl w s Wl Ll s w s Wl s s s Pl w Ll s I Sl s s s Sl s s s s s s Sl s s s L3 s s s s s s s
0.5 0.5 0.5 1
0.5 0.5 0.5 1 0.5 1 0.5 0.5
P(S) PWL SL LS s PWL SPL PL WPL SL WL L WL WL WL LW SL WP LP PLW
1 1 1 0.5 0.3 0.5 0.5 1 0.3 1 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.5
LP LP WLP LP LP LP LP LP LP PL LP LP LP P LPW LP LP LP LP LP LP
735
Radioactivity measurements: principles and practice
2.3.6. Radioactive-decay
laws
Radioactive decay is exponential in time. This follows simply from the proportionality of the activity (decay rate) to the number of atoms, N, of the radionuclide present; that is A = dN/dt
= -XN ,
(p-4)
where X is the decay constant. Integration of Eq. 2-4 leads to N, = N,exp(-Xt)
,
(Z-5)
where N, (and -AN,) are the numbers of atoms (and activity) of a given radionuclide with the decay constant X in the given sample at the time t = 0, and N, (and -AN,) at the time iY. The decay constant X is, for practical reasons, usually replaced by the half life T%, the time in which an amount of a radionuclide (or its activity) is reduced by a factor of in which the number N, decays to N,/2. Analytically, NJ2 = two, i.e. the time T N,exp(-XT%), therefore'l'% = ln2/X, and, finally, N, = N,exp(t ln2/2'%) = N,exp(-0.69315t/T$
(z-6)
The observed half lives of radionuclides range over more than 40 orders of magnitude, from just measurable parts of a femtosecond (about lo-l6 s) up to about 10zo years. The radionuclides mostly in use have half lives of hours, days, years and up to thousands of It is interesting to remember that after 10 half lives the number of radionuclide years. atoms is reduced by a factor of 2lo = 1024, i.e. about one thousandfold In health physics and nuclear medicine the biological half life, Tb, is of great importance. It is the time required for a biological system to excrete half the amount of any nuclide introduced into it. In health physics or nuclear medicine this is clearly relevant to any injected or ingested radionuclide in the human body and the resulting dose to various organs in that body. If the decay is not negligible and T,,, is the resulting, effective, half life of residence of the nuclide, and Tti is that of the injected or ingested nuclide, then
l/T,,,
= l/Tb + l/Th
,
or, in terms of probabilities, Lff =&+X 2.3.7 Radioactive f&lies
.
(decay chains. series1
The products of radioactive decays are often also radioactive daughter products. high atomic number Z most, and for Z > 83 (Bi), all nuclides are radioactive.
At
Because mass-number changes are only possible by a decay, all heavy nuclides can be grouped into four families (decay chains) with the atomic-mass numbers A = 4n, A=4n+l. A = 4n + 2 and A = 4n + 3 (Table 2-6). Three of these families are found in nature (natural radioactivity), commencing with their very long-lived parents '=Th, “% and 23%l. Many of the members are of importance in the nuclear-fuel cycles. It is often very important, to take the radioactivity of the daughter products into consideration. In some cases, they may cause strange effects due to their physical properties. For example, gaseous or volatile daughter products could contaminate counters or samples. And they contribute, of course, to the total activity of a sample in which they are being generated (see also (2.7.7).
Radioactivity measurements: principles and practice
736
Table 2-6 - The four decay chain of heavy elements (main branches only, Z 5 100)
A = 4n+l Neptunium series (artificial)
A = 4n Thorium series 252 100Fm 25.4 h
CI
257 100Fm 101 d
248 9*Cf 334 d
a
244 96011 18.1 a
A=4n+2 Uranium-Radium series
A=4n+3 Actinium series
o
254 100Fm 3.24 h
a
255 100Fm 20.1 h
a
253 g8Cf 17.8 d
fi(u
250 g8cf 13.1 a
a
251 98Cf 898 a
a
a
253 ggEs 20.5 d
a
246 g6Cm 4730 a
a
247 g6Cm 1.6xlO'a
a
240 94Pu 6564 a
a
249 Bk 320 d 97
P(a
242 94Pu 3.76x105a LI
243 g4Pu 4.96 h
p
236 92U
a
249 g8Cf 351 a
a
238 g2u
243 g5Am 7380 a
o
232 9OTh 1.41~10~~a a
245 g6Cm 8500 a
cz
2;;Th 24.1 d
j?
';;Np 2.36 d
228 88Ra 5.76 a
P
241 g4Pu 14.4 a
P(a
234 glPa 6.70 h
/J
239 g4Pu 24.1x103a a
228 89A~ 6.13 h
B
241 g5Am 432 a
228 90Th 1.91 a
LX
237 g3Np 2.14x106a LL
230 gOTh 7.54x104a a
231 gOTh 25.5 h
224 88Ra 3.66 d
a
233 glPa 27.0 d
p
226 Ra 1600 a 88
a
231 91Pa 3.28x104a a
220 Rn55.6~ 86
a
233 g2u 1.59x105a
a
222 86Rn 3.82 d
a
227 8gA~ 21.8 a
216 84Po 0.145 s
a
229 gOTh 7340 a
a
218 84Po 3.05 min
CI
227 gOTh 18.7 d
a
212 Pb 10.6 h a2
P
225 88Ra 14.8 d
p
214 Pb 26.8 min 82
p
223 88Ra 11.4 d
c1
212 . 83B~ 60.6 min
a,,L
225 8gAc 10.0 d
a
214 83B~ 19.9 minp(a)
219 86Rn 3.96 s
(I
208 81Tl 3.05 min
@
221 87Fr 4.9 min
a
214 84Po 164 ~LS
215 84Po 1.78 ms
c1
212 84Po 0.298 !_Ls a
217 85At 32.3 ms
a
210 82Pb 22.2 a
/3(o)
211 82Pb 36.1 min
p
208 Pb stable 82
213 83B~ 45.6 min p(a
2iiBi 5.01 d
P(a)
211 83B~ 2.14min a(P)
2.34xlO'a
a
234 g2U
4.47x109a a
2.45x105a a
13 84Po 4.2 ps
(I
210 84P0138d
09 Pb3.25h 82
0
206 Pb stable 82
cx
a
P(a:
235 g2u 7.04x10*a
07 81Tl 4.77 min
a
p(o:
P(a)
p
07 82Pb stable
09 83B~ stable Data taken from NCRP (1985), Westmeier and Merklin (1985) and Nuclear Data Sheets Mean tropical year, 1 a = 365.2422 days.
Radioactivity
measurements:
principles
and practice
737
2.4. RADIATIONS 2.4.1.
Introduction
All radionuclides release energy in the form of radiation. Some are primordial, and others are produced by different processes in nature (e.g. cosmic radiation) and technology The naturally-occurring radionuclides are the members of the three (e.g. by accelerators). natural decay series (q2.3.7) the precursors of which, along with 4oK and "Rb, have half lives comparable with the age of the solar system. Most radionuclides in common use are produced artificially by irradiation of selected nuclides by certain kinds of particles, generally by thermal neutrons in reactors or by protons, deuterons, or ionized helium atoms in accelerators. The discussions here are largely electrons substances ~seean~2~~,~arti~~~tr~~~, discussed,
and others
are mentioned
restricted to those radiations, such as a particles, e~~;~:;~,anetic radiations emitted by radioac.tive and fission products are only brlefly only in passing.
All these radiations differ, not only in mass and charge, but especially in their absorption and attenuation in matter, scattering, and, consequently, in their energy deposition and range. Their general properties are described in this chapter while the details of their interactions with matter, which is important for their detection, are discussed in 74.3. Here the terms "radiation", are used interchangeably. 2.4.2, Aloha
"ray" and
"particle"
all have
almost
the same meaning
and
Particles
Alpha particles are the heaviest particles emitted by radionuclides, except for (i) fission products which are only rarely emitted by radioactive species, and (ii) a recently-discovered and puzzling mode of decay, sometimes called "exotic decay". The spontaneous emission of protons and neutrons has been known to occur, for some time. But, more recently, the emission of heavier fragments, predicted by some theoreticans, has been observed, the best known cases being particles of 14C emitted by certain radium isotopes, with a probability of 10m9 or less (see Rose and Jones, 1984). Still heavier fragments, up to magnesium, have since been found with still lower branching ratios. This new decay mode may be interpreted on the basis of a super-asymmetric fission model. But alpha particles are still the heaviest form of spontaneous radiation to lie within the scope of this report. Alpha particles are doubly-charged positive ions, and thus are bare nuclei. Alpha Their mass is 4.001506 u (u = particles from nuclear transitions are always monoenergetic. the atomic-mass unit, relative to lzC = 12), which is equivalent to an energy of 3,727.409 MeV; their kinetic energies, when emitted from radioactive sources, are mostly around 5 MeV (with energies ranging between 2 and 11 MeV). Alpha-particle energies for calibration purposes are discussed in ~4.11.2.5. The kinetic energies of o particles are approximately equal to the mass-equivalentenergy difference between parent and daughter atoms minus the mass-equivalent-energy of the He atom, and minus the recoil energy of the residual nucleus (about 2%). Monoenergetic groups of alpha particles of slightly different energy are often emitted from the same nuclide, indicating branching decays to different excited states of the daughter (or from different excited states of the parent). The energies of alpha particles and the half life of the emitting nucleus are strongly interconnected, the latter being shorter for higher energies (Geiger-Nuttall rule). The half life can be calculated using a simple barrier-penetration theory. Because of their relatively large mass and charge, a particles suffer strong energy absorption and low scattering during their passage through matter (74.2.2). Therefore, they have short ranges and nearly straight paths in matter. Fig. 2-5 shows the ranges of (I particles of different energies in different materials (Northcliffe and Schilling, 1970). Five-MeV alpha particles, the most common alpha-particle energy, have a range of about 3.5 cm in air at STP which is equivalent to about 4 mg/cm' or 0.03 mm (35 pm) of tissue. (The protective dead-cell skin layer is about 70 pm,) Alpha particles are emitted by most nuclides used as nuclear fuels. Therefore their accurate measurement is of great practical importance. For this and many other standardization purposes 241Am (Fig. 2-6) is an ideal reference nuclide. Its half life (432 a) and consequently its specific activity are very convenient for accurate measurements and its decay scheme allows these to be carried out by different methods, especially by 4s~7 coincidence and by low-geometry defined-solid-angle counting. Furthermore, stable and very thin z41Am sources can be rather easily prepared, e.g. by electrolysis, < "Beta terms used
particles" (@‘) and "electrons" (e-), also sometimes called "negatrons", are for identically the same particles that carry the negative elementary charge.
738
Radioactivity measurements: principles and practice
l/IlIIlIl 0.1
Fig. 2-5.
Fig. 2-6.
0.2
I 0.5
1
2
5
10
2-3
50
100
Mean range of protons and alpha particles in different materials (numerical data taken from Barkas and Berger, 1964; Williamson et al., 1966; Bichael, 1967; and Northcliffe and Schillings, 1970).
Typical alpha-particle energy spectra (241Am) taken with a high-resolution surface-barrier and a low-resolution thin plastic detector.
The first term is used if the particle originates in a nucleus, and the second for particles emitted from atomic shells. Electrons, stemming from decay interactions with atomic shells, namely internal conversion and the Auger effect, are monoenergetic, while beta particles always show an energy distribution from zero to a maximum, Em, that is typical for a given pure beta emitter (Fig. 2-7). Positrons (8') are positively-charged beta particles with continuous-energy spectra; monoenergetic positive electrons are never emitted from the nucleus in a radioactive transition.
Radioactivity measurements: principles and practice
-6
94.6 % E.. 511.6 keV 5.4 % E,; 1173 keV
-5
739
conversion electrons
-4
dN(E)/(dE
‘dt)
1
n
-2
54 -1
E CkeV)
\i
-rJ10
Fig. 2-7.
20
30
40
100
300
500
’
600
620
630
640
High-resolution spectrum of electron radiation from the 137Cs decay.
Beta particles are emitted with different energies, the remainder of the beta-decay energy being removed by neutrinos that have zero charge and very small, if not zero, mass. The neutrino is emitted in fl+decay, and the antineutrino in p decay. The shapes of the resulting beta-ray spectra (e.g. Fig. 2-8) can be rather accurately described by modern theory (Behrens and JBnecke, 1969). They depend on the degree of forbiddenness of the decay (super-allowed, allowed, first-order, second-order, third-order or fourth-order forbidden), which is determined by the difference of the nuclear spins and angular momenta of the involved parent and daughter nuclei. With a shape factor related to the degree of forbiddenness, S(E,E,), such spectra can be plotted versus particle energy E as straight lines terminating in the endpoint of the spectrum (Kurie plots), if the equation for the emission probability N(E) is written in the form: [N(E)/(f(z,E)E(E'-l)~ S(.E,.&,,) II’
=
K(E,-E) ,
(2-8)
where f(Z,E) is the Fermi factor from theory and K is a constant. Integration of the decay probability N(E) (Eq. 2-8) with respect to energy leads to the "comparative half life", ft a constant, where f(Z,E,,,)is the Fermi integral function and t = Tb is the half life of the B-decaying nucleus. The value of ft characterizes the forbiddenness of the decay. The measured log ft values vary between about 3 and about 20.
3
Fig. 2-8.
6
9
12
15
Beta-particle spectra of tritium: theoretical differential spectrum n(E) and integral spectrum N(E) derived from it (and reduced by a factor of 10).
The charge of all electrons is + e = 1.60218 x 10-l' C, the elementary charge, and their rest mass 5.48580 x 10e3 u is equivalent to 0.51100 MeV (u = atomic-mass unit). Beta-particle endpoint energies range from zero to about 2 MeV, e.g. the maximum B-decay energy of tritium is 18.6 keV, and that of "Y 2.28 MeV. Positrons are unstable and annihilate with electrons, partially even before coming to rest (annihilation in flight). The subsequent annihilation radiation consists of two photons having an energy of 511 keV each, emitted in opposite directions. This is much more penetrating than the original positrons. Otherwise positrons are similar to beta particles, but show different spectra at low energies. Monoenergetic electrons are produced through the internal and external conversion of 7 rays and in the Auger effect after electron capture or other vacancy formation in atomic shells ((2.4.5). Because of their relatively low mass and single charge, electrons are much more easily scattered and less readily absorbed in matter than a particles. Consequently their paths in matter are not linear and are much shorter in range (maximum distance from origin), and the range straggling is considerable (up to 10%). The ranges of monoenergetic electrons, which can be defined in different ways are shown in Fig. 2-9 for different absorbing
Radioactivity
740
measurements:
principles
and practice
materials as a function of energy. Because of the relative independence of electron absorption on atomic number the average range may be used for any material when the thickness is expressed in terms of superficial density. For non-monoenergetic beta particles the range can be best extrapolated using the nearly exponential transmission function of number of particles versws thickness of the absorber. The extrapolated ranges of monoenergetic electrons and of beta particle of the same maximum energy are equal within the rather large experimental uncertainties.
XT'
10-l Fig. 2-9.
12
XT'
51020
Maximum range, practical (extrapolated) range and path lengths of mono-energetic electrons (and beta radiations) in narrow-beam geometry (Kanter and Sternglass, 1962; Pages et al., 1972).
Some practical examples of the maximum ranges of ,9 particles from 3H (E,,,,, = 18 keV), 14c (E,,,,, = 155 kev), Is11 (E,,, = 0.81 MeV) and 3zP (EgmsX = 1.71 MeV), are, approximately 0.6 mg/cm', 30 m&m', 240 mg/cm' and 800 mg/cm', respectively; and these are approximately equal to the ranges of monoenergetic electrons having energies equal to E,,,,,. 2.4.4.
Electromagnetic
radiations
The radiations most often met in radioactivity are -y rays, x rays (Helmer et al., which all belong to the immense spectrum of the massless and 1978), and bremsstrahlung, of electromagnetic (Fig. 2-10). The energies electromagnetic radiations chargeless or of their quantum-theoretical counterparts (particles) can be expressed by radiation, If h is Planck's constant then the energy E is their wavelength, X, or frequency, u. given by
E=hu,
v-9)
hc E=-
or
where c is the speed in particle physics,
1n terms of the unit, electron volt, that of light. the relation between wavelength and energy is that
Thus, for example, when x is expressed in Angstram units. The corresponding wavelength of 12.398 A or 1'2.398 x lo-" m. (Hz).
&
lfJ8 10’ 106 105 104 103 102 8
I
lo' I,
1
cm lo-‘2 lo-” lo-‘0 10-9 1l.-s 10-7 10-610-510-d
x rays
Tra_nsition radia(ion
Y rays Fig. 2-10.
10-l 1o-2 I1
10-a 10-2
I
I
l-keV photon radiation has a frequency is 2.42 x 1O1' 5-l
10-a I
10-J
I
1o-4 10-5 I
1
I
1 Synchrotron radiation
The types of electromagnetic
Gamma rays originate in nuclei as a result extend from a few to several million electron typical y-ray spectrum is shown in Fig. 2-11. izations and, accordingly, their energies are shells, which is about energy in atomic The deexcitation of an excited monoenergetic.
a
is commonly used E = 12398/X,
I
10
1o-5 I
lo2
I
I
10-T I
lo3
I
Radio waves
--_
Television
radiations.
of nuclear deexcitations, and their energies volts if emitted by radioactive sources. A The x rays are due to atomic-shell reorgan-smaller than the highest electron-binding 100 keV. Gamma and x rays are always nuclear or atomic-shell state can also take
Radioactivity measurements: principles and practice
741
place by emission of atomic electrons instead of by 7 or x rays by the process of internal Radiative and non-radiative deexcitation processes are conversion or the Auger effect. always competitive (72.4.5).
0 02 04 06 08 10 12 14 16 18 20 22 24 26 Fig. 2-11.
60 Typical gamma-ray spectra of Co taken with a NaI(T1) or a Ge detector (with the source close to the shielded detector).
The probability of gamma-ray emission depends strongly on spins, angular momenta and The gamma-ray-emission processes are therefore parities of the involved nuclear states. classified according to these parameters, as is shown in Table 2-7 fable 2-7
Selection rules for gamma-ray transitions
1
Multipole order
Symbol
AI1)
i2)
An3)
Possible small admixture
Electric dipole
El
0,l
1
Yes
M 2;4)
Magnetic dipole
Ml
0,l
1
TlO
E 2;4)
Electric quadrupole
E2
2
2
IlO
M 3:5)
Magnetic quadrupole
M2
2
2
Yes
E 3;5)
Electric octupole
E3
3
3
Yes
M 4;5)
Electric 2'-pole
El
1
1
no for even P yes for odd I
M(P+1);5)
Magnetic 2'-pole
M1
P
P
yes for even 1 no for odd 1
(a+1);5)
-
1
1) Vector difference of the initial (Ii) and final I(f) angular momentum of nucleus; Ii = If = 0 absolutely forbidden 2) Angular momentum of predominant radiation 3) Parity change in nucleus 4) Absent if Ii = If = l/2 for AI = 0 and if Ii or If = 0 5) Absent if Ii or If = 0 The third electromagnetic radiation, bremsstrahlung, is quite common in radioactivity but is mostly only of very low intensity. It is produced whenever electrons, or other charged particles, are decelerated or accelerated, and can originate in the nucleus (internal bremsstrahlung) or, but with higher intensity, outside the emitting nucleus (external
Radioactivity
742
measurements:
principles
and practice
Unlike 7 and x rays, bremsstrahlung shows a continuous energy spectrum bremsstrshlung). extending to the maximum electron energy and its intensity is orders of magnitude smaller than that of the original process (e.g. p-ray emission). But it can dominate when other for example the radiation outside %r - "Y or i4'Pm heat radiations are suppressed; sources, or outside ampoules containing solutions of pure ,9 emitters, is often exclusively bremsstrahlung. The deexcitation of an excited level can not only take place there is always competition between internal-conversion electron (see 172.4.5 and 2.4.3). emission Other electromagnetic radiations can be encountered in annihilation radiation (y2.4.3) and Eerenkov radiation (74.7). The millions detector)
attenuation of electromagnetic radiation geometry" (collimation in a "narrow-beam follows the exponential law N = N,e-llx
by -r-ray emission, as emission and y-ray
radionuclide
metrology
are
in the range of electron volts to before the absorber and before the
,
(2-10)
where N, and N are the numbers of photons before and after attenuation, and p may be given or better linear attenuation coefficient" "narrow-beam linear in cm-' as the "total attenuation coefficient", or in c&/g as "mass-attenuation coefficient" replacing JJ by p/p, In the first case the thickness x of the absorber where p is the density of the absorber. the "surface, or superficial, in SI units must be given in cm, in the second in g/c&, Fig. 2-12 shows examples of mass attenuation density" (i.e. mass per unit surface). The attenuation law (Eq. 2-10) can be also written in terms of a half-value coefficients. thickness X~ (reduction of the photon flux by one half): N = N e-O.@3Wx, 0 Also
(2-11)
see 75.2.2.3.
Fig.
2-12.
Gamma radiation (narrow beam) mass-attenuation coefficients for different materials and energies (numerical data taken from Grodstein, 1957; McMaster et al., 1969; Hubbell, 1977).
In general one has broad beams comprising The narrow-beam case is rather unrealistic. In this case all the secondary radiations from the absorption and scattering processes. the exponential attenuation law must be supplemented by a build-up factor B, which yields (2-12)
N = N,Be-'x The calculations of build-up factors are difficult, high values, of up to 1000 in extreme situations.
but very
important,
because
B can reach
Of the other known electromagnetic radiations, only cerenkov radiation (T4.7) may be 1975; Kleinknecht, 1984). Eerenkov important in radioactivity measurements (Randolph, ultraviolet region of light, is always with a spectrum in the visible and radiation, emitted when a charged particle traverses a medium, of refractive index n, with a velocity In media with high n (e.g. Perspex v greater than the speed of light in the medium (c/n). radiation is already generated by for which n = 1.51, or water with n = 1.34) &renkov 230 keV for Perspex electrons of rather low energy (Egmln = v/c = l/n), of approximately
Radioactivity
and 260 keV for water. the Eerenkov radiation activity of p emitters
measurements:
principles
and practice
743
Although the intensity of the radiation is very low, measurement of may, in some cases, be the most suitable method for measuring the (Kleinknecht,l984).
Bremsstrahlung can also be used advantageously in radionuclide example the assay of tritium in bulk (Curtis, 1972) or the measurement solutions if high-energy beta emitters in ampoules (A. Spernol et al., Annihilation radiation is less frequently used in radionuclide properties are utilized for many useful applications.
metrology, as, for of the activities of HN, p. 169, 1973).
metrology,
but
its special
Other electromagnetic radiations, such as transition radiation (emitted if high-energy particles traverse the boundary zone between two media) or synchrotron radiation (a kind of very low-energy bremsstrahlung in magnetic fields; Watson and Perlman, 1978) play no role in radioactivity measurements. 2.4.5. Atomic-shell
radiations
followinp. nuclear
orocesses
As the atom is normally in its energetically most favorable state, a minimum-energy equilibrium between the positive nucleus and the negative electronic cloud around it, every transformation also affects the atomic-shell structure, and causes atomic nuclear radiations. The usual classical atomic model provides an explanation for the atomic-shell radiations. It assumes that the electrons surround the nucleus in well-defined stable shells, The electronic binding energies depend on the atomic named K, L, M, etc. (Fig. Z-13). number, 2, and vary between fractions of an electron volt and a maximum of about 100 keV nuclides (Table 2-8) Therefore, in general, the radiations from atomic for very heavy shells are of low energy and are often negligible compared with the energies of the nuclear radiations. But in some cases, especially for electron capture (EC) by the nucleus. atomic radiations may be the only observable effects of the nuclear transformations.
M V
M
IV III II
I
L
Ill II
K Fig. 2-13.
/
i
2
512 312
3
2
3 3 3
1 1 0
3/2 j/2 v2
2 2 2
1 1
3/2 v2
0
l/2
1
0
l/2
Innermost atomic shells (K, L, M) and main possible x radiations; n and 1 are the principal and azimuthal quantum numbers, respectively, and j = J?++ is the inner quantum number.
Radioactivity
744
Table
measurements:
2-8 - Some atomic binding
:1ement
K
Ll....L3
principles
energies,
and practice
in keV,
Nl....N7
Ml....M5
in the different
01...,05
1H
0.016
10Ne
0.870
0.049 0.022
to
2oC=
4.038
0.438 0.346
to
0.044 0.025
to
3oZn
9.659
1.201 to 1.022
0.140 0.010
to
4oZr
18.00
2.532 2.223
to
0.430 0.179
to
0.051 0.028
to
508n
29.20
4.465 3.929
to
8.885 0.485
to
0.137 0.024
to
bONd
43.57
7.126 6.208
to
1.575 to 0.980
0.319 0.002
to
0.038 0.022
to
7o=J
61.33
10.49 to 8.94
2.398 to 1.528
0.480 0.001
to
0.052 0.024
to
80Hg
83.10
14.84 to 12.28
3.562 2.295
to
0.802 0.100
to
0.127 0.008
to
9OTh
109.65
20.47 to 16.30
5.182 3.332
to
1.330 to 0.333
0.290 0.085
to
1ooFm
143.1
7.205 4.498
to
1.937
27.70 20.90
to
* Extrapolated
values
shells
Pl....P3
0.041 0.017
to
*
for fermium
If a shell electron is captured by a nucleus, a vacancy is left in the shell, which is shell with the quickly (within approximately 10-'3s) filled by electrons from an outer emission of energy in the form of a succession of Auger electrons (Burhop and Assad, 1972) The number, kind and energies of these radiations depend on the and x rays (Dyson, 1973). capture probabilities P,, P,, P,, ___ (P,/P,/P,/... are approximately l.O/O.l/O.Ol/...), and the fluorescence yields for the different shells K, L, etc. (Bambynek et respectively, fractio:1 emitted The sum of the fluorescence yield, w1 (the al., 1972; see Fig. 2-14). yield, ai, is equal to one (w, + ai = 1). for an ith-shell vacancy), and the Auger-electron The filling of a vacancy by the Auger effect yields two further vacancies in outer shells conserves the (inclusive of all secondary processes), while x-ray emission (fluorescence) Both electron capture and positron emission reduce the nuclear charge number of vacancies. these two decay modes are competitive transitions, provided they are Therefore, by one. Fig. 2-15 shows some typical EC(K)/fl' ratios (Band et al., 1976, energetically possible. 1978) as predicted by theory.
0 Fig. Z-14.
10
20
30
40
50
60
70
80
90
Fluorescence yields, w , in the different atomic shells (numerical data mainly from Bambynek et al., 1972).
Radioactivity measurements: principles and practice
Fig. 2-15.
745
2 34 OS 1 0.2 0.02 0.05 01 Examples of theoretical estimations of K-electron-capture to positron-emission ratios, EC(K)/fl+, for allowed and firstforbidden non-unique transitions (numerical data taken from Zweifel, 1957,and Zyryanova and Suslov, 1968).
Very similar atomic-shell effects, to those following electron capture, occur if an atomic-electron-shell vacancy is formed by internal conversion (IC) instead of emission In this case the whole energy of the electromagnetic of a nuclear 7 ray (72.4.4). radiation is transferred to a shell electron, and in addition to the emitted monoenergetic conversion electron, the whole cascade of shell processes takes place, as in the case of electron capture. The probability of internal conversion, P,, relative to the probability of -y ray emission, P,, is given by the internal-conversion coefficient, a, which is equal The total internal-conversion coefficient is the sum of the conversion coefficto PJP,. ients in the different shells, namely ot = oK + uL + oM + . . . . . where czK= PK,/P,, etc. The numerical values of the total internal-conversion coefficients range between the measurable limits 10m5 to lo5 (Carlson, 1975). All atomic-shell or nuclear processes in which electrons are involved, are accompanied by very-low-intensity internal bremsstrahlung, and cause external bremsstrahlung (q2.4.4). 2.4.6. Neutrons. fission Droducts and other radiations Many of the very heavy nuclides also decay by spontaneous fission, in competition with the "normal" decay modes. This fission process is quite similar to the induced fission in "fissile" (induced by thermal or fast neutrons) or in "fissionable" (induced by fast such as 235U, '%, 23sPu, or WJ, respectively. neutrons only) materials, When undergoing fission, nuclei generally emit two fission products per fission (of The mass distribution of nearly equal energy and mass) and several neutrons and y rays. the fission particles (Vandenbosch and Huizenga, 1973) and their yields (Blachot and Fiche, as are also the 1977) are well known for the most important fissile nuclides, fission-product absorption properties. Spontaneously fissioning radionuclides are often used as convenient sources of neutrons or fission products. Such a nuclide of special interest is "'Cf with its useful Other frequently used "radioactive" neutron sources are based on half life of 2.65 a. (e.g. Ra+Be, Pu+Be). For (a,n) or (7,n) reactions in beryllium or other light elements (Schneider, 1973; the emitted neutron spectra are of importance many applications Cierjacks, 1983). Neutrons are not only useful in radionuclide metrology in the form of radioactive and spontaneous-fission neutron sources; but they may also disturb radioactivity measurements Because the absorption of in the vicinity of neutron-producing accelerators or reactors. (elastic and inelastic scattering and neutrons happens only by nuclear reactions transmutations (capture, etc.)), the cross sections of which are much lower than those of So, it is not reactions between charged particles, their mean free paths are very long. that NaI(T1) detectors, installed several hundred metres away from powerful surprising linear accelerators, show annihilation-radiation peaks due to "Na from neutron activation of Na, and short-lived activity due to "'1 from l"I. Sometimes, therefore, the shielding of radioactivity detectors must be reinforced by highly neutron-absorbing low-2 materials. mentioned The radiations and radioactivity measurements
above are the only immediately Many others are applications.
important ones known, but are
for too
Radioactivity
746
measurements:
principles
and practice
short-lived (proton emitters), show too little interaction with matter energies far away from the energy range useful for radioactivity leptons, mesons, trachons, transition radiation, etc.). Nevertheless, necessary to make measurements on them too (e.g. meson therapy).
(neutrinos), or have measurements (heavy it may sometimes be
2.5. ENERGY 2.5.1. Kinetic.
total
and rest enereies
of oarticles
The term energy is normally used in atomic physics for the kinetic energy (E,.) of particles. For non-relativistic massive particles (moving with a velocity v that is very small compared with the speed of light, v/c = p << 1) Ek is equal to mOvz = p2/2m,, where momentum. m, is the rest mass (for v = 0) of the particle and p its non-relativistic The kinetic the total energy is simply
energy of relativistic particles can be derived from the expression for E, = mc', and its rest mass energy E, = moc2, where m = m,(l - &+-'". It
Ek = E, - E, = mc' - m,c2 = m,c'[( 1
=
8').
,
m,c'[(l + +9'/2)-l - l] = m,vZ/2
This relation can also be derived or its equivalent
from
the relativistic
r, -
11
for fl << 1
mass
equation
(2-13) m = m,(l
EZ = E,z + p2cz.
equal
- p2)-
shows the relative of kinetic energy. Table
Z-9
velocity
p
=
v/c
of
electrons
and
Q
particles
are
for
Relative velocity of electrons and a particles for selected values of kinetic energy, E
E (keV)
1 10 100 1000 10000 2.5.2. Binding.
,
(2-14)
For particles with zero rest mass (photons, for example) kinetic and total energy and E, = Ek = pc = hv, where h is Planck's constant and u the frequency.
Table 2-9 selected values
4
disintegration
- 1)_2]% /3 = v/c = [l-(E/E, electron (2 particle E,=0.511 MeV E,=3727 MeV
0.0625 0.1950 0.5482 0.9411 0.9988
and reaction
0.0007 0.0023 0.0073 0.0232 0.0731
energies
(0 values1
The energy of a radiation is one of its most important properties, especially for its measurements are an integral and important part of Therefore, energy identification. They are therefore treated in some detail in 94.11. Here only radionuclide metrology. the basic concepts relating to energy are outlined. Some further and more specific energy definitions are necessary for the description of The binding energy (Eb) is released when two or more certain radioactivity phenomena. the small to form one common particle of mass m, and, neglecting particles combine difference in mass resulting from from the rearrangement of the atomic electrons, is given by E, = (2%
+ Nm, - m)c2
"mass defect", the difference The binding energy is therefore the energy equivalent to the IMKle0n masses (at rest) of the initial individual between the sum of the individual It is also equal, of particle and the mass of the resulting final compound particle. supplied to the compound particle in order course, to the amount of energy, which must be to break it into its nucleonic constituents. The reaction energy (Q value) of a nuclear reaction (or transformation) 1(2,3)4 is the net energy set free or absorbed in the reaction Q = (ml + m, - m3 - m,)c'
,
of
the type
(2-15)
incoming, outgoing and m, being the masses of the neutral ground states of the target, Similarly, the disintegration product particles, respectively. (decay, transition) energy also tabulated as Q, values, is the maximum available energy, i.e. radionuclide, of a
Radioactivity
measurements:
principles
and practice
available to be shared by all the radiations emitted in the ground state of a parent atom to that of the daughter. The following two examples will energy calculations:
serve to illustrate
a radioactive
the
principles
747
transition from
of such mass-
(i) *l'Po decays to the ground state of 'OsPb by emission of a 5.304-MeV a particle. The difference between the atomic masses of the parent and daughter atoms is (209.982848 205.974440)~ = 4,008408u, lu being equivalent in energy to 931.5016 MeV (Wapstra and Audi, (a particle plus two 1985). Then subtracting 4,002603u, the mass of one 4He atom electrons), and multiplying by the ratio of MeV/u gives Q, = 5.407 MeV. The difference of 0.103 MeV from the experimentally observed 5.304 MeV should represent the recoil energy of the residual ZOsPb atom (see y2.4.2). (ii) 6oCo with an atomic mass of 59.933820 u in the ground state decays by @- emission to one of several energy states of s0Ni that has a ground-state atomic mass of 59.930789 u. The sum of the maximum energy of any /? branch plus the T-ray energy emitted, in the decay of the excited level of s0Ni to which the p decay occurs, is 2.8234 MeV, which is equivalent to the mass difference. Here the recoil energy is negligible. 2.5.3. Units and svmbols. conversion factors The special name of the SI unit of energy is the joule (J), expressed units by J = Nm (N: newton, the special name for the SI unit of force), and units J = m'kg s?. It may be noted that the the pascal, the special name for of pressure (used elsewhere in this report), is equal to one newton per square
in other SI in basic SI the SI unit metre.
In atomic physics the conventional unit of energy, also temporarily retained with SI, is the electron volt, the energy acquired by an electron when it traverses a potential difference of one volt in vacuum. One electron volt, 1 eV, is equal to 1.60219.10-19 J. Atomic masses (equivalent to energies, according to Einstein's law, E = mc') are often also expressed in multiples of the electron rest mass, m, = 511.003 keV, or of the atomic mass unit u (l/12 of the mass of a % atom); 1 u = 1.66054 x 1O-27 kg, approximately or, as stated above, 931.502 MeV. The conversion factors between the most important units are collected in Table Z-10.
microscopic and macroscopic energy
2.6. DOSIMETRY 2.6.1. Definitions and concerts Dosimetry is the body of knowledge concerned with the measurement of ionizing radiations for the purpose of quantifying some radiation effects. Dosimetry is usually concerned with the assessment of absorbed dose or related quantities (exposure, kerma) arising from the interaction of radiation with matter. Radiation dosimetry response functions are usually expressed in terms of dose-vs-effect relationships, that are intended to give a means of assessing the upper and lower measureable limits of such dosimetric effects. Dosimetry is therefore a prerequisite for all radiation applications, especially for radiation therapy and for radiation protection. The principles and applications of dosimetry have been discussed in many publications (see, for example, Attix et al., 1968; Jaeger and Hiibner, 1974; Kase and Nelson, 1978; McLaughlin, 1982; Greening, 1985; Kase ec al., 1985, 1987; Attix, 1986; IAEA, 19&e). In the final analysis, the quantification of radiation effects demands an understanding of the interactions of charged corpuscular radiation with matter, because sufficiently energetic photons interact with structured matter only through their corpuscular surrogates, such as photoelectrons, Auger and Compton-recoil electrons, and electron-positron pairs; and neutrons mainly through recoils. The concepts, quantities and units of dosimetry have been defined by the International
748
Radioactivity
Commission be grouped 2.6.1.1.
on Radiation as follows:
Ouantities
Units
and Measurements
characterizinp
Particle
principles
(ICRU,
the radiation
energy
Energy
imparted
(by particles)
(of particles)
Energy
flux
Fluence Energy
(particle) fluence
Fluence
rate
and practice
1980).
The
relevant
quantities
may
field
number
Radiant
Flux
measurements:
(particle)
N
1
R
J
e
J
i
s-1
d
w
*
mm2
0
J me2
i
*-2 s-1
W mm2 Energy fluence rate $ The definitions of flux and fluence are not necessarily or exactly the same as they are, or were, in other branches of physics; the former, in the past, has been associated with area or volume and confused with flux density, and the latter differs in that it pertains to particles incident upon the cross-sectional area of a sphere. (See ICRU, 1980, for definitions.) 2.6.1.2.
Ouantities
Cross
used
in characterizine
section
Mass attenuation coefficient (photons)
the interaction
of radiation
Svmbol
Special Unit Used with SI
o
b (1 "barn" = 10-28 mz
mzkg-'
Mass energy-transfer coefficient (photons)
mz kg-'
Mass energy-absorption coefficient (photons)
m2 kg-'
Linear stopping power (charged particles)
with matter
*
J m-l
eV mm1
Total mass stopping power (charged particles)
J III' kg-'
eV l m z kg-'
Collision mas.s stopping power (charged particles)
J mz kg-'
eV+m' kg-l
Radiative mass stopping power (charged particles)
J mz kg-'
eV*m' kg-1
Linear energy transfer (LET), upper energy h. (L, = SC011 + S,,d)
J m-l
Radiation chemical yield
mol J-'
Mean energy expended ion pair formed
per
J
aVf&
(100
l
e”;-’
aV* = 1.60219.10-'g J
J.H. Hubbell (in McLaughlin, 1982, p 1269) has supplied useful tabulations of massattenuation and energy-absorption coefficients for photons (energies 0.001 through 20 MeV in their interactions with many elements and compounds. ICRU Report 37 (ICRU, 1984b)als.o tabulates stopping powers for electrons and positrons in many elements and compounds for a large number of energies in the range from 0.01 through 1.00 GeV.
Radioactivity
2.6.1.3. Energy
Dosimetric
Symbol:
z.
principles
749
and practice
auantities
(to
imparted
measurements:
unit volume)
SI unit: J. c
R,, - R,,t + 1 Q,,>
=
(excluding rest energies) of all those charged and where R,, is the sum of the energies uncharged ionizing particles that enter the volume, Rout is the sum of energies (excluding rest energies) of all those charged and uncharged ionizing particles that leave the volume, and C Q., is the sum of all changes (decreases, positive sign; increases, negative sign) of the rest-mass energy of nuclei and elementary particles in any nuclear transformations that occur in the volume. Absorbed Symbol:
dose SI unit:
D
J kg-' D
where
dP is the
mean
Absorbed-dose
rate
Symbol:
SI unit:
b
Kerma
(kinetic
Symbol:
K
=
SI derived
imparted
J kg-' se1
SI unit:
released
by ionizing
names:
Gy; rad
SI derived
radiation
units with
to
special
matter
names:
units with
special
names:
of mass
dm.
Gy s-l; rad s-'
Gy; rad
= d&,/h,
where dEt, is the sum of the initial kinetic energies of all the charged liberated by uncharged ionizing particles in a material of mass dm. Kerma
(= 1 cGy)
in unit mass of absorber) SI derived
J kg-l K
special
dT/dm,
energy
energy
units with
ionizing
particles
rate
Symbol:
ic
SI unit:
J kg-' 5-l
X
SI unit:
C kg-l
SI derived
units with
special
names:
Gy 5-l; rad S-I
Exposure Symbol:
X
=
where IdQl is the "absolute air when all the electrons in air.
SI derived
unit with
special
name:
R
IdQl/W value" of the total charge of the ions of one sign produced in completely stopped liberated by photons in air of mass dm are
bremsstrahlung emitted by the electrons is The ionization arising from the absorption of not to be included in IdQl. Except for this difference, significant only at high energies, the exposure is the ionization equivalent of the air kerma. X = qp_,e/pW where ~,,/p is Exposure, X, and the photon energy fluence, q, are related by the mass energy-absorption coefficient in air, e is the elementary charge and W is the mean relation is only valid if W is assumed energy expended in air per ion pair formed. This and if p_,/p is a mean value weighted by the spectral energy to be energy-independent, fluence. Exposure Symbol:
rate i
Air kerma-rate Symbol:
I’,
SI unit:
C kg-l 5-l
SI unit with
special
name:
R s-l
m2 J kg-'
SI unit with
special
name:
m'Gy; Bq-ls-'
constant SI unit:
l-6 =
&/A.
of a radionuclide emitting photons of energy greater than where i, is the air-kerma rate 6, at a distance 1 from a point source of this nuclide having an activity A. It is assumed that the attenuation in the source and along the path length 1 is negligible. This is an dosimetry to radioactivity. important quantity, that links This quantity replaces (ICRU, constant or the specific gamma-ray 1980), but is not identical to, the exposure-rate constant, previously recommended by ICRU (1962, 1971).
Radioactivity
750
measurements:
principles
and practice
Km-ma factor Symbol:
k,
SI unit:
J mz kg-l
SI units with
special
names:
Gy m2; rad mz
k, = KU1
where K is the kerma for a given kind of particle (usually neutrons), and @ is the particle fluence; it is also related to the mass-energy-transfer coefficient, for monoP’t,/P I energetic neutrons of energy E (see R.S. Caswell et al., in McLaughlin, 1982, p. 1227). A dosimetric quantity that is of great interest to most users of ionizing radiation is the absorbed dose (at a point in a specified medium). However, it has long been established practice to measure, using ionization chambers, another, more readily accessible quantity, namely the exposure, and to derive from it, by application of certain conversion and correction factors, the absorbed dose to the medium at the point of interest. Detailed protocols for this conversion are available (ICRU, 1969, 1970, 1973, 1984b; IAEA, 1986b). Closely related to exposure, but based on energy transfer rather than charge production, is air kerma. Its unit, the gray, is the same as that for absorbed dose. Air kerma, apart from a usually small correction that takes account of energy loss by bremstrahlung, equals the energy equivalent of exposure. While exposure is conceptually limited to photon radiation, kerma is defined for all types of uncharged radiations. Absorbed dose may be derived from air kerma in the same way as it is derived from exposure (IAEA, 1987). 2.6.1.4.
Ouantities
used
in radiation
protection
Svmbol
Dose equivalent
H = DQ
J kg-l
Quality
Q
1 (for photons)
factor
Effective
dose equivalent
Dose-equivalent Absorbed-dose
index
Absorbed-dose-index Dose-equivalent
rate
index
Dose-equivalent-index Shallow
rate
dose-equivalent
Deep dose-equivalent
index
index
SV
rem
(=
1 c.J kg-')
Sv
H, = xI,H, *
rate
SI Derived Units with Soecial Names
SI Unit
H
J kg-' s-l
Sv s-l
DI
J kg-'
GY
DI
.J kg-l s-l
HI
J kg-'
HI
J kg-' s-l
Gy 5-l SV Sv s-l
rem 5-l rad
(= 1 cJ kg-l)
rad 5-l rem rem 5-l
H,,,
HI,,
* gT ir the mean dose*qui"Ble"t in an organ.or tissue.T, and WT 15 B weighting factor
Two new concepts, ambient dose equivalent and directional dose equivalent have been introduced (ICRU, 1985) to link the external radiation field to the effective dose equivalent and to the dose equivalent in the skin. For purposes of individual monitoring the two concepts individual dose equivalent, penetrating and individual dose equivalent, superficial were introduced (ICRU, 1985). For the definition of these and other important quantities used in radiation protection the reader is referred to ICRU Report 39 (ICRU, 1985). Also see IAEA (19863).
it is not sufficient to know just For biological and radiation-protection applications, the quantity of the radiation energy that has been absorbed, but also how the biological effect on the tissue irradiated varies with both the nature and energy (and energy range) of the radiation. Thus the biological effect will be different for electrons, protons and alpha particles and will also vary with the energy (and hence LET) of each. For this reason, the quantity absorbed dose is multiplied by the quality factor Q to give the dose equivalent listed above. In other words, the quality factor Q is used to weight the absorbed dose to give the biological effectiveness of the charged particles producing the absorbed dose, and is equal to 1 for photons, and for a charged particle is a function of the stopping power in water, Lo, for that particle (for electrons and positrons, see ICRP, 1977). While values of the quality factor Q are generally used for the purposes of routine radiation protection, its predecessor, the relative biological effectiveness (RBE), is still widely used in radiobiology. RBE is defined as the quantity of 250.keV x rays needed to produce a given
Radioactivity measurements: principles and practice
biological effect divided same effect.
751
the quantity of the radiation of interest that produces the
The quantities absorbed-dose index D,, and dose-equivalent index H,, also listed above, have been introduced in order to estimate maximum absorbed doses or dose equivalents to all, or parts, of a human body after exposure to ionizing radiation. For further information concerning these dosimetric concepts and quantities, reference should be made to ICRP (1977, 1979) and to ICRU (1980, 1985), or to any of the other references given in 72.6.1. 2.6.2
Methods of absorbed-dose measurement
In many absorbing media the radiation energy imparted is ultimately degraded to heat Assuming that no heat defect and will cause a temperature rise that can be measured. occurs (gain or loss due to exothermic or endothermic radiation-induced reactions), or that its amount is known with sufficient accuracy, and that the specific heat of the absorbing medium is known, such a calorimetric method may be used as a dosimeter. Absorbed-dose calorimeters have been built by standardizing laboratories and are being used as dose standards (Domen, 1969; Domen and Lamperti, 1974; Domen, 1987). However, they are not recommended for day-to-day laboratory use, except for measuring high doses when electron accelerators are used for radiation processing (Morris, 1988; Miller and Kova&, 1986). For practical use a dosimeter should meet a number of requirements, such as suitability for the type of radiation to be measured, suitable range of dose and dose rate, matching the dosimeter to the medium of interest, size of the detector, ability to integrate dose or to measure dose rate, stability, accuracy and precision, and simplicity. Ionization chambers are most widely used for dose measurements in radiotherapy and radiation protection. They offer high accuracy, cover a wide dose range, and may be used Ionization chambers are fragile and need sophisticated for different types of radiation. They may serve as reference instruments, as well as field electronic readout devices. instruments (Attix et al., 1968; Burlin, 1970; Jaeger and Hiibner, 1974; Greening, 1981; IAEA, 1981; Kase et al, 1985; Boag, 1987). (Also see Ta4.4.1 and 5.4.6.) There are many chemical systems (mostly aqueous solutions) in which absorption of radiation energy leads to the formation of initially-absent compounds, ions or radicals, related to absorbed dose. quantitative measurement of which can be The best known and most widely used aqueous chemical dosimeter is the Fricke dosimeter, composed of a solution It is very nearly water-equivalent, of FeSO, in diluted H,SO, (Fricke and Hart, 1966). relatively easy to handle and has high accuracy. A spectrophotometer is required for its The radiation chemical yield (G-value) of readout (Helm and Berry, 1970; Attix, 1986). optically-absorbing species (ferric ion, Fe"), is related to the molar linear-absorption coefficient (c,) for that species at a given optical wavelength (X = 304 nm). The product of the two is well established for electrons and for x and 1 radiation (G.r, = 352 x lo-' m2 kg-' Gy-I; see ICRU, 1984b). This dosimeter requires the use of ultrapure water and reagents as well as ultra-clean glass containers. A disadvantage in its use in radiology and radiation protection lies in its limited range of response, namely from lOI to 4 x 10' GY. Thermoluminescence dosimetry (TLD) has become one of the most widely used dosimetry systems in recent years. It involves the use of a solid-state dosimeter, the sensitive material being LiF or some other thermoluminescent substance (74.6.2). The energy stored by the radiation-induced filling of electron and hole traps in these crystalline materials is released as luminescence when the dosimeters are subjected to heating at a controlled rate. The intensity of this luminescence is plotted as a function of time to give a "glow curve", its amplitude at a given temperature, or integrated over a given temperature range (thermoluminescence intensity), being a reproducible function of absorbed dose. Its main advantage is that the dosimeter can be made very small, providing a means for "point" dosimetry. Another advantage is the relatively wide range of absorbed-dose response of different thermoluminescent materials, from nanograys to kilograys. The dosimeters can also be used over and over again by the use of repetitive cycles of annealing at elevated temperatures. A disadvantage is the difference in their response from that of water or tissue over broad spectral distributions: for example, the photoelectric effect for lowenergy x rays in TL materials has a distinctly different spectral distribution from that of hydrogenous materials. There is also a marked difference in electron stopping powers in the two types of material; the stopping power in hydrogen being about double that in other For readout the TL probe must be heated in an elements and non-hydrogenous materials. oven, and the light emitted measured by a phototube. Automated TLD systems are largely replacing film systems in national radiation-protection services (Helm and Berry, 1970; IAEA, 1981; Oberhofer and Scharmann, 1981; McLaughlin, 1982; McKinley, 1983; Horowitz, 1984; Kase et al., 1985; Attix, 1986). A promising dosimeter material that simulates many biological tissues, and one that can be utilizes in a form small enough for in viva dosimetry in radiotherapy (with a dose range from and above 1 Gy) is the amino acid, alanine (Regulla and Deffner, 1982). When pellets of alanine are irradiated, stable free radicals are produced, the concentrations of
752
Radioactivity
measurements:
principles
and practice
which can be measured, in terms of populations of unpaired electrons, by means of electronspin-resonance (ESR) spectrometry. The amplitude of the resulting ESR signal is proportional to the absorbed dose. The response of this dosimeter can be calibrated by comparison with crystalline samples having known numbers of unpaired electron spins per unit mass (Regulla and Deffner, 1982). 2.6.3
Doses
from distributed
internal
radioactive
sources
It is often necessary to calculate the dose to different tissues of the body from an administered radiopharmaceutical that becomes distributed around the body with varying amounts concentrated in different organs. For this purpose it is usual to evaluate the dose to the rest of the body due to the activity residing in each of the most active organs in turn, such, as for example, that arising from the thyroid in the case of 1311, If A, is the activity of the radiopharmaceutical, administered at time t = 0, then the activity residing in the source organ of interest, A,(t) at time t, will be equal to ~cune fraction f(t) of the administered activity, i.e. A,(t) = A,f(t), and the time integral of the administered activity, in the source organ, is given by m
/
A,(t) dt = A, 0
J
fm(t) dt = A,rr
,
(2-16)
0
the time integral of the fraction f(t) being the residence time T,. In effect, Aor, is the total number of disintegrations that will occur in the source organ during the time that any significant amount of the radiopharmaceutical remains in it. This is called the cumulative activity. Group OR Reference Man (ICRP, As pointed out in Appendix I of the Report of the Task such as alpha particles and beta rays will be 1975), shallow-penetrating radiation, But in the source organ or within relatively short distances from it. absorbed within the organ, much of the body may be case of photons emitted by a radionuclide in the source Following the schema developed by Loevinger and Berman (1968), the task group irradiated. (ICRP, 1975) denoted that fraction of the decay energy produced in the source organ, S, This is called the absorbed that is absorbed in any given target organ T, as $(T + S). fraction. The fraction of energy absorbed per unit mass of the target organ, the specwhich is equal to Q(T + S)/m,, where mr ific absorbed fraction is denoted by Q(T + S), is the mass of the target organ. In the last column of decay data shown in Table 2-4, as an example for a few radiois given for the ith type nuclides, the mean energy, Ai in gram-rads per microcurie-hour, of radiation emitted by each radionuclide. Similar data are given for 279 radionuclides in belong to the older system of The units of Aiv g-rad/&i-h, Appendix A.3 of NCRP (1985). In the SI system A1 = PiE,, where units that is, however, still widely used in medicine. Pi is the probability of emission per nuclear transition of an i-type radiation of mean energy Ei, with units J Bq-' 5-l. As one Bq.s is one nuclear transition, A1 is the mean energy per ith transition in joules. For any given radionuclide the mean energy emitted per nuclear transition, A, is the sum of all A,'s, that is (2-17)
A=CA,. i The product of the cumulative specific absorbed fraction gives designated target organ, i.e.
activity, the mean
A,?,, the mean energy per decay, energy absorbed per unit mass,
A, and the D, of the
D(T + S) = A, TT.C A, +,(T + S)
I
In order to enable the calculation of D for explicit target organs due to photons emitted from specified source organs the Task Group on Reference Man has published extensive tables of the specific absorbed fraction for the target organ for photons (with energies ranging between 0.01 and 4.00 MeV), and for 16 source organs (plus total body) and 20 target organs (including total body, skeleton and skin) (ICRP, 1975; Appendix I, Table Most of the data were obtained using Monte Carlo calculations and an anthropomorphic 1.2). This publication also tabulated values of phantom described by Snyder et al. (1979). for 20 target organs and 10 source organs, absorbed fractions, as its title implies, including whole body, for a number of specified monoenergetic photon emitters such as laF. The 1985). 2.6.4.
above
concepts
Further
have
also
been
discussed
by
R.
Loevinger
in NCRP
Report
58
(NCRP,
reading
In addition to the references given in 72.6.1, Volumes I and II of The Dosimetry of Ionizing Radiation, edited by Kase, Bjarngard and Attix (1985, 1987) contain eleven reviews of the theory and practice of the measurement of both external and internal radiation. These reviews are thorough in their treatment of several important dosimetry topics, including radiation protection, environmental radiation, external photons and ,9 rays, external
753
Radioactivity measurements: principles and practice
beams of heavy particles, microdosimetry calorimetry, and ionization chambers.
(also with applications
in biological
systems),
charged-particle, Twenty-four papers dealing with many aspects of ionizing-photon, and neutron dosimetry have been published in a special issue of the International Journal of Applied Radiation and Isotopes entitled Trends in Radiation Dosimetry, edited by W. L. McLaughlin (1982). Subjects include dosimetry in biology, medicine and in the environment, systems, tables of stopping powers (energy range 0.01 radiation protection, dosimetry energy-absorption coefficients (energy range through 1,000 MeV), of mass-attenuation and 0.001 through 20 MeV), and of neutron kerma factors of elements and compounds for neutrons (energy range 8 eV through 29 MeV). Recent ICRU reports, from 1980 through 1986, have focused on radiation dosimetry quantities and units (1980), the dosimetry of pulsed radiation (1982), microdosimetry (1983), the dosimetry of electron beams (energies 1 to 50 MeV) (1984a), stopping powers for electrons and positrons (0.01 to 1,000 MeV) (1984b), dose equivalents (1985), and the quality factor (1986). 2.7. SOME USEFUL CONSTANTS AND MATHEMATICAL RELATIONS 2.7.1. Introduction All figures given in aq2.7.2 and 2.7.3 are certain, in the sense that the uncertainty More exact data with discussion of the of the last figures is negligibly small. uncertainties can be found in the literature (see, for example, Petley, 1985; Wapstra and Audi, 1985; Cohen and Taylor, 1987). 2.7.2. Constants useful in the calculation of atomic-decay processes
In 2 = 0.6931472
log e = 0.434294
e = 2.718282
7r= 3.141593
1 d = 8.6400.104 s [Half lives, of radionuclides, that are longer than 365 days are usually given in For convenience however, especially in tables of years, but the unit year is not SI. nuclear data, the unit of one mean tropical year taken as 365.2422 days, is used. In the published literature it is desirable that the quantity year should be specifically defined The most commonly used symbols are "y" or "a" (for and the symbol denoting it described. an&s or annum), but "Y" also appears frequently in computer printouts.] The mole (symbol mol) defined as the amount of substance of a system that contains as many elementary entities as there are atoms (unbound and at rest in their ground state) in 0.012 kg of carbon-12. The Avogadro constant, NA, = 6.0221 x 10z3 mole' of 1%)
(equals the number of atoms in 0.012 kg
The unified atomic mass unit, u, = l/12 of the mass of one atom of "C state = (O.O12/N,)/12 = 1.66054 x lo-*' kg.
in the ground
u/c* I 931.50 MeV (see Wapstra and Audi, 1985). The Faraday Planck's
constant,
constant,
Elementary
charge,
NAe, = 9.64853
x 10' C mol.'.
h, = 6.62607 x 10m3" J s. e, = 1.60218
Speed of light
in vacuum.
Fine-structure
constant,
x 10-r' C.
c, = 2.99792458
x lo* m s-l.
a, = poce2/2h = 7.29735 x 1O-3
(l/a = 137.036)
(dimensionless),
Permeability of vacuum, pO, = 4?rx lo-' N A-'. 2.7.3. Mass-enerw
relations
Energy and mass are related to each other, in any consistent system of units, by the Einstein equation, E = mc'. In SI units, for a mass of 1 kg, 1 cz = 8.9875518 x 10's J. But the electron volt, 1 eV, is also a unit of energy used with SI (72.5.3), and is the kinetic energy acquired by an electron in passing through a potential difference of 1 volt in a vacuum. In SI, one electronvolt of energy is 1.60218 x lo-'s J; the electron charge being 1.60218 x 10‘I9 C and one volt being 1 J/C (BIPM, 1985; NBS, 1986). The conversion factor from kilograms to units of electron volt is
754
Radioactivity measurements: principles and practice
5.6095 x 10z9 MeV/kg. m, = electron rest mass = 0.91094 x 10m3c kg = 5.48580 x lo+ u. m,,c2- 0.51100 MeV. mr = proton rest mass = 1.67262 x 10-z' kg = 1.007276 U. mscz = 930.27 MeV. m,,= neutron rest mass = 1.67493 x 1O-27 kg = 1.008665 u m,,c'= 939.57 MeV. m, = alpha-particle rest mass = 6.64478 x 10-r' kg = 4.001506 u. m&s - 3727.41 MeV. 2.7.4. Decay and erouth of radioactivity The law governing the decay of radioactivity, discussed in 72.3.6, applies also to induced radioactivity. This term is used when an appropriate material is irradiated by activating particles (neutrons, protons, etc.) which transform atoms of the target substance (subscript 1) into atoms of the radioactive product (subscript 2). The competitive processes of production and decay of the radioactive atoms are described at any given time, per gram of the target material, by dn,/dt = -X,ri,+ a12~hl , (2-18) where n2 is the number of product atoms per gram of target material, is the X, = In 2/T decay constant of the product nuclide, 4 the average fluence rate (flux density!I of the activating particles, n1 = N,/A, the number of atoms per gram of target material, N, the Avogadro constant, A, the molar mass, and g12 is the cross section for the reaction considered. Integration over the activation time ti and introduction of the waiting time t, (time between the end of irradiation and the onset of counting) yields, for t, = 0 and IQ(O) = 0, the activity, A,, at the time ti + t, as Ac = +t,+t,)
= o,,4n,
(1 - e
-In 2.t,/TQ) e-ln 2.t,/r&$
2.7.5. Snecific activitv of nure nuclides and of nu&&c
(2-19)
mixtures
For a pure radionuclide of atomic mass A, decay constant X, half life TG and number of atoms per gram n (= NA/A; NA = the Avogadro constant), the specific (nuclidic) activity A s' is
A*
=
An
NA In 2 ___
=
(2-20)
ATk
in s),
= 4.1742 x 10z3 (AT%)-'
(A, in Bq g-' = s-lg-', if Tb
= 1.3228 x 10's (AT&l
(A, in Bq g-', if T% in years; "a"),
lo5 (AT%,-1
(A, in Ci g-l, if Tti in years; "a").
= 3.575
X
For a mixture of n nuclides with mass numbers AI.......%, half lives III,.......% (in g), the formula for A,, in Bq g-', is
T,.......T,
(in a) and masses
A,
=
[1.3228 x 10's i m,/(TiAi)] /t m, i
(2-21)
2.7.6. Mass and atom nercentages of nuclide mixtures Sometimes the nuclidic composition of a mixture is only known by atom percent (a,) and not by mass percent (pi). The mass percent can easily be calculated from the atom percent and vice versa by means of the following two equations
and
100
gi
=
ai
= 100 [&/(A,
I
(2-22)
“cgjAJ)l
(2-23)
[a,A,/ "c aj Aj] j=l
j=l
Radioactivity measurements: principles and practice
755
2.7.7. Activity of dauehter oroducts in radioactive families Let N: (parent), and N,O, ...NO., ...N.O be the numbers of atoms each of the family at time t are X,N,, members present at the time t = 0. Then their respective activities, . &N,. .A&, and one has (Bateman, 1910)
=
Y
(2-24)
;s., n=l a-%t
k-l k N,O lI Xi 1 i=n i=n
(2-25) k lI (X,-X,) m=n wi If we now consider the important case where, at t = 0, only the freshly separated parent is present, and which may be expressed by Ni = 0 for n > 1. We obtain S,
where
=
Nk
=
S,
=
k k-l Nyll Xi 1 i=l i=l
e-&t (2-26) k n (X,-X,) m=l tii
The activity of the daughter thus becomes
4
=
X,N, Al% N,
-
(e
_ e-x t
-x,t
2),
(2-27)
AZ - Al and that of the "granddaughter",
4
= X,N, =
e-&t
NT X,X,
e-&t +
+
[
(&-A,) l&-Q
C&-X,) (X,-Q
e-w 1 .
(2-28)
(X,-X,) (&-&) If the half life of a daughter product is much shorter than that of the parent, their activities, when measured several half lives of the daughter later, become equal, and This is known as secular equilibrium (from both decay with the half life of the parent. Latin saeculum, an age), and is best exemplified by the growth of zzzRn into freshly separated 226Ra. In the case of a radioactive parent decaying to a shorter-lived radioactive daughter, and with the time t after separation being long enough that exp(-X,t) can be neglected compared with exp(-X,t), their activities are related by the following simple approximation of equation (2-27): 4
:.
4
=
X,N,
=
NYX,e -X1t[&,/(X,
= 4
L&/(-h
- &)I
- A,)1 ,
(2-29)
at time t. In other words, for large values of t the activity of the daughter merges with This state of equilibrium is known as transient and merges with the that of the parent. secular as the ratio X,/X, becomes so large that the activities A, and A, are essentially equal. But if X, is not significantly greater than X,, as in the case of '&OLa (T& = 40.3 hours) and lroBa (Tb = 12.7 days), then the daughter grows and then decays with an activity greater than that of the parent by the significant ratio X,/(X, - X,). In the case of a short-lived parent and longer-lived daughter, the former decays to "zero" while the daughter grows to a maximum and then decays with its own half life. But in both cases
156
Radioactivity measurements: principles and practice
the decay curve of the parent crosses the growth-and-decay maximum of the latter curve.
curve of the daughter at the
Examples of both of these types of parent-daughter activity freshly separated 14OBa decaying to 140La, and for a sample hours) decaying to lz31 (Tk = 6.6 hours), are given in Mann ec 2-7). The latter example would typify the accelerator production for medical purposes.
decay-growth curves, for of lz3Xe (T+ = 2.08 al. (1980, Figs 2-6 and of lz3Xe to provide lz31
Another important example is that of the isotopes of uranium, where there is a daughter alpha-particle activity ingrowth per annum of about 0.05% for 233U, 0.001% for 234U, and 0.056% for 235U.
3.
GENERAL
PROBLEMS
IN RADIONUCLIDE
METROLOGY
3.1. INTRODUCTION Radioactivity measurements can be rather complex and can also be very different for But several problems and procedures are common to different modes of radioactive decay. Some of them are discussed in this chapter in connection with most types of measurement. and handling of radioactive sources (73.3), radiation protection (13.2), the preparation and the evaluation of radioactivity measurements (73.4). 3.2. RADIATION 3.2.1. Basic 3.2.1.1.
PROTECTION
facts
General
dosimetry has produced a. profuse and sometimes The subject of "cause-and-effect" mysterious literature, in which the number of terms has proliferated and the values of certain adjusting factors have, from time to time, changed. In 72.6 measurable dosimetric quantities have been defined. But in this chapter we will be dealing with the somewhat At the lowest levels qualitative assessment of effects arising from exposure to radiation. this assessment is largely a matter of probability: If a single unit of of radiation, electromagnetic radiation interacts with a single biological cell, will a chromosome be And is affected, and, if it is, will a possibly resulting mutant be beneficial or not? there a threshold or not? At higher radiation levels, data from, and calculations based such as those given in nuclear accidents no" enable estimates, on, several unfortunate Table 3-1, to be made for the onset of the effects for different levels of radiation dose equivalent. Table 3-l Somatic effects due to different levels of radiation Dose equivalent received (Sv) Radiation Effect 0 to 0.25
0.25
to 0.5
no detectable improbable
clinical
effects:
late effects
very
slight transient blood changes (reduction in the lymphocyte number, etc.): late effects improbable
0.5 to 1.0
marked changes in blood picture with delayed recovery; temporary nausea and fatigue; late effects not improbable, but no serious shortening of life expectancy
1.0 to 2.0
nausea and fatigue with possible vomiting within 24 hours; marked changes in blood picture; following latent period of 1 to 2 weeks,pallor, epilation, general weakness with very probable recovery; few deaths possible in 2 to 6 weeks; shortening of life expectancy due to late effects by about one percent
2.0 to 3.0
nausea, vomiting and possible diarrhea within few hours; strong changes in blood picture: following latent period of about 1 week,epilation, loss of appetite, pallor, sore throat, general weakening and fever; in general,recovery within 3 months, but some probability of death within 2 to 6 weeks; about a few percent shortening of life expectancy due to delayed effects (cancer)
3.0 to 6.0
nausea, vomiting and diarrhea in 1 to 2 hours; strong changes in blood picture, after latent period of up to one week,epilation, fever, general weakness, severe inflammations of mouth and throat, emaciation, hemorrhage, purpura, petechia; at about 4.5 Sv 50% death probability, at 6 Sv nearly certain death within 2 to 6 weeks due to failure of blood-forming organs; serious delayed effects of survivors
6.0 to 12
above
12
above ~100
as above; epilation weeks due walls as above; damage to
nausea etc. within one hour; redness of skin; etc. within a few days; death within 2 to 3 to loss of body fluids from damage to intestinal peeling central
as above;
immediate
of skin; death within nervous system coma;
757
death within
a few days due to
hours
750
Radioactivity
measurements:
principles
and practice
In this report the discussion of this subject will be limited to a brief explanation, for the benefit of dosimetric neophytes, of some of terms used in the field of radiation dosimetry dealing with cause and effect, and to currently recommended upper limits of expthat are contemporaneous with their proposed use of radioactive osure. For recommendations materials, readers should consult the frequent reports issued by the International Commission on Radiological Protection (ICRP) and the International Commission on Radiation Units and Measurements (ICRU); and also those issued by their own national radiation-protection in the Federal Republic of organizations such as, for example, the Bundesgesundsheitsamt the National Radiation Protection Board in the United Kingdom or the National Germany, Council on Radiation Protection and Measurements (NCRP) in the United States. For the neophyte it may also be helpful to explain three terms that appear frequently in the literature of radiation dosimetry, but that do not always find their way into the "Committed" is essentially the glossaries. They are committed, effective and equivalent. In radiation as used in the term "cumulative activity" in 72.6.3. same as "cumulative" protection it refers to the effects due to an ingested or inhaled radionuclide during the The term "effective" refers to the time of residence of that nuclide in the body (82.3.6). normalizing the effects of a radiation dose absorbed by one tissue to the process of These ICRP risk to the whole person, using a weighting factor appropriate to that tissue. "Equivalent" is used in weighting factors (ICRP, 1977,1981) are quoted in 73.2.2.2 below. the same sense as it was many years ago to define the unit "rem" (radiation-equivalent man) whereby the absorbed dose was multiplied by a "quality factor" (and sometimes an additional "adjusting" factor that has varied between 1 and 5) in order to allow for the variation in biological effectiveness of u, /3 and photon radiations, and to reduce the absorbed dose to A useful discussion of these terms is given by J.R. a common base (see NCRP, 1987a). Johnson in Kase et al. (1985, Chapter 6). Persons handling radioactive materials should be aware of the principles of radiation protection and observe the related regulatory precautions, because excessive exposure to radiation can be harmful. The aim of all such protective measures (IAEA, 1973a,b; Jaeger and Hiibner, 1974; NCRP, 1978a; IAEA, 1979a; Martin and Harbison, 1980; PTB, 1980; Stewart, is to limit any radiation exposure to as low as reasonably possible, 1981; Sauter, 1983) or to "acceptable" levels. These are aimed at excluding any detrimental effects (ya3.2.1.2 natural radiation and 3.2.1.3), but must also be chosen in relation to the irreducible background (73.2.1.4) in order to permit the beneficial uses of radiation. The damage caused by the irradiation of human tissue derives from atomic and molecular which lead, eventually, to interactions, such as ionization, excitation and dissociation, cellular damage. The resulting biological effects of exposure of man to radiation are well known (from experiments, accidents, medical treatment, Hiroshima and Nagasaki (Hiroshima 1981). They are subdivided into somatic effects (Gk. soma, body) which are and Nagasaki, manifest in the exposed individual itself (and are immediate or late) and into genetic Hazardous radiation can also to descendants. effects, which, in general, are transmitted The effects of low-level from ingested sources. derive external sources, or internally radiation are not yet completely understood (NAS, 1980; NCRP, 1981). 3.2.1.2.
Somatic
The
somatic
biological effects
effects
due
of radiation
to different
exoosure
levels
of
radiation
received
are
summarized
in
Table 3-1, and in references such as those given in 73.2.1.1. It must be emphasized that all statements and figures in this table are hypothetical averages, from which rather large deviations occur in individual cases. The late effects of radiation exposure are difficult to distinguish from natural illnesses and often vary considerably from individual to individual. Therefore an estimate of 1 to 2 lethal cases 10 to 30 years after whole-body irradiation per 10' person-sievert average dose-equivalent can only be regarded as valid to an order of magnitude (ICRP, 1977; and Nagasaki, 1981; NCRP, 1987a). IAEA, 1978a; Hiroshima [l rem = 0.01 sievert (Sv); dosimetric definitions are given in 72.6.1 3.2.1.3.
Genetic
effects
of radiation
exDo.sure
The genetic damage to a population caused by radiation is, for the same reasons, also difficult to quantify. A rough global estimate can therefore only be given, namely that the natural background radiation is responsible for a few percent (
The natural
radiation
background
and "beneficial"
radiation
The whole biosphere is continuously exposed to natural background radiation (Eisenbud, 1973; NCRP, 1976b, 1987c; KovaCs, 1984). This comprises three main components of nearly equal risk to man, namely (i) cosmic radiation coming from the universe. (ii) terrestrial radiation from radioactive materials in the earth's surface, and (iii) "internal" radiation from the radionuclides contained in the human body (see Tables 3-2a and 3-2b, the former based on worldwide estimates and the latter on U.S.). The total natural radiation
Radioactivity
measurements:
principles
and practice
background leads to an effective dose equivalent for the individual man of about 1 to 2 mSv per year at sea level. This value is a rough world mean based on the (100 to 200 mrem) 1977; Jacobi, 1982; Sauter,1983). It data from many sources (NCRP, 1971, 1975; UNSCEAR, by less than 30 percent, but can reach up to ten times the "normal" varies, in general, value in proximity, for example, to monazite sands (without observable biological effects). The cosmic-radiation component increases rapidly with altitude above sea level, e.g. by a factor of from 3 to 4 at 2 km, and of from 25 to 40 at 8 km. The internal component can vary considerably and reach rather high values (Table 3-2a) if the inhalation of decay products of the natural radioactive series from the construction materials in badly ventilated houses is taken into consideration (Jacobi, 1982). Since the beginning of nuclear-bomb testing, radiation due to fall-out has to be added to the "natural" radiation It is expected to contribute in the northern hemisphere a whole-body mean background. dose-equivalent commitment of 750 ~SV , accumulated over the period through the year 2,000 (NCRP, 1987a; Table 6.3). But this quantity varies considerably from one organ to another and can reach 650 @J for the endosteal bone from 'OSr alone (NCRP, lot. cit.). About one third of the "natural" background is due to radon and arises from the recent propensity of many of the world to live in brick, and air-tight, houses (Jacobi, 1982; Cast&n, 1985). Recently the general public has become increasingly concerned with the risk from radon, even though it dates to some degree from primordial times as part of the environment that fashioned what we are. The increased risk arises in well-sealed houses into which radon (mainly its isotope "'Rn) can penetrate through brick or concrete, from the surrounding soil through pores and cracks in the walls, or from the domestic water supply. The draughtier the building the less the risk, at least from radon, although other risks may arise. On the other hand, simple expedients such as withdrawing air from the basement, or from channels under the lowest floor of the house can lower any accumulation of radon in the living quarters. With regard to the water supply, one of the authors has, for decades, preserved the genetic purity of the yeast that brewed his beer, by the very simple expedient of first boiling the water to drive off the radon. Table 3-2 (a and b) - Average effective dose equivalent to adult man per year due to the different sources of radiation (a) Worldwide (NCRP, 1975; Jacobi, 1982; Sauter, 1983). and (b) in the United States (after Fig. 8-l of NCRP, 1987).
(a)
Radiation
mrem (1 mrem = 0.01 mSv)
source
Total natural
radiation
100 to 200
Cosmic
30
Terrestrial
40
Total internal (inhalation
5 100 included)
40K ^^ U series (2zz Rn + daughters) Th series (220Rn + daughters) Others (14C etc.) Fall-out Medical
applications
Industrial
applications
Coal and nuclear
= = = =
20 65 15 1
=
1
= 100 5
1
energy
(b)
FIHI
39/H-D
The percentage contribution of various radiation murces to the total average effective dose equivalent in the U.S. pop&Cm.
759
Radioactivity
760
measurements:
principles
and practice
The sources and risks of radon have been well described in a recent report published by the U.S. Department of Energy entitled Radon (DOE, 1987). Radon, by virtue of its short half life and multiplicity of short-lived daughters cannot be assayed directly, as by, for example, internal gas counting. It is usually measured in terms of solution standard of "'Ra from which known quantities of radon can be withdrawn after complete de-emanation the radon reaches 97% of equilibrium (see, e.g., Mann et al., 1980). The principal ways to measure radon concentrations is to compare them with the "radon standard" (i.e. the "sRa solution) by means of a pulse ionization chamber or scintillation counting using an enclosure into which the radon sample can be introduced; the walls of the enclosure are coated with ZnS(Ag) except for a transparent window through which a phototube can record the scintillations generated by the a particles from the short-lived 222Rn progeny. Both these devices must be calibrated; they are described, along with other measuring methods, in a recent comprehensive review by Co116 and Hutchinson (1988). While the methods are relative, the inherent uncertainties are well within the limits needed for radiation protection. The principal exposure of man from medical applications of radiation is due to x-ray diagnosis and cancer therapy, and the use of a variety of other ionizing radiations, such as gamma rays, electrons, ?r mesons, neutrons, protons and heavier charged particles. small contributions to radiation exposure arise from the radioactive Further substances that are emitted from the combustion of coal and from nuclear electric-power and from radioactive industrial products such as fire alarms and fertilizers, production, Table 3-2a refers to two recant estimates of radiation exposure and occupational exposure. table 3-2b includes them under "consumer products" and of man from all these sources: "other" (NCRP,1987d ); for all aspects of nuclear-power production see NCRP (1987e). 3.2.1.5.
Non-radiation
hazards
from radioactive
materials
It is often overlooked that radioactive substances may be chemical the case for uranium and plutonium; the chemical toxicity especially, rather higher than its radiotoxicity (Medical Research Council, 1975).
poisons. This is, of the latter is
Radiation can also be indirectly hazardous. For example, intense irradiation of some plastics could lead to the formation of toxic (e.g. halogenated) gases, which could introduce an occupational hazard unless precautions are taken. 3.2.2. Legal 3.2.2.1.
radiation-urotection
Princiules
regulations
and concerts
The serious hazards associated with the use of ionizing radiation has given rise to The basic regulations set limits for legal protection regulations in different countries. the absorbed-dose equivalent received by the different groups of the population, which is radiation-protection quantity. For practical purposes, secondary limits, the basic reference levels, etc., can be derived from the basic data, using models. And, finally, specific regulations are necessary for special situations involved, e.g. licensing of radiation installations and working conditions, transportation and storage of radiation use of specific sources in industry, agriculture and industry, sources, the occupational considerations include authorized control and handling personnel and etc. Other procedures, insurance, and emergency measures in case of accidents. Most countries have approved such legal regulations. All are based on the pertinent ICRP and IAEA recommendations and are sometimes supplemented by national laws (for the USA These basic ICRP and IAEA recommendations have been see, for example, Stewart, 1981). This has caused some continually developed and often changed during the last decades. the present situation is discussed here. This is, confusion and therefore only characterized by the dose-limitation concept (ICRP, 1977, 1979/1980; IAEA, essentially, 1982c). 3.2.2.2.
The system
of dose
limitation
and urimarv
limits
The aim of the dose-limitation concept is to minimize the absorbed-dose equivalent received by the different groups of the population, while still allowing the "beneficial" This implies the prevention of non-stochastic effects uses of radiation (IAEA, 1982d). (as defined in ICRP, 1977X) and the limitation of the occurrence of stochastic effects* to This is achieved by adhering to three criteria: (i) no practice an acceptable level. involving exposure to radiation (after comparison with available alternative methods, with regard to dose) shall be permitted by the competent authorities unless it produces a net benefit, assessed on a "risk-benefit" analysis for the individual, or a "cost-benefit" society; (ii) any radiation work must be performed in such a manner that analysis for exposures are As Low &s Reasonably Achievable, ALARA (ICRP, 1973); and (iii) as the limits (in terms of the radiation-protection quantities of interest) essential element, must be defined and not exceeded. The primary (effective) dose-equivalent limits (the weighted-mean whole-body dose-equivalent limits) are the most important ones, and are the basis for the derivation ICRP recommends different limits (ICRP, 1979/1980; IAEA, 1982c) of all others. for
Radioactivity
measurements:
principles
761
and practice
stochastic and non-stochastic effects and distinguishes between uniform and non-uniform intake of radioactive exposure to external radiation and that due to substances. Furthermore, the limits must be different for the different groups of the population, such as radiation workers, critical groups with more than natural-background exposure and the general public including everybody. For occupational workers exposed to external and uniform radiation, the annual dose-equivalent limit with respect to non-stochastic effects is 0.5 Sv (50 rem), except for the eye lens, for which it is 0.15 Sv (15 rem). This limit applies only to individual tissues or organs, which do not show stochastic effects such as carcinogenesis. For stochastic effects the dose-equivalent limit for uniform and non-uniform external irradiation of the whole body, HWb,L, is 50 mSv (5 rem) for any year. To obtain the effective dose equiv-
where wr is equal to 0.25 for gonads, 0.15 for breast, 0.12 each for red bone marrow and lung, 0.03 each for thyroid and bone surface, and 0.30 for the remaining organs, total 1.00 (also see 72.6.1.4). The committed (i.e. cumulative) dose equivalent to tissue T, H,,,,, is the dose to tissue T resulting from the total intake of radioactive materials during the year considered, with summation of the dose over the next 50 years as a function of the residual activity resident in that tissue. This represents a lifetime effective-dose equivalent. NCRP (1985) recommends observance of the limits 1 "THs, T 5 Hwb T ’ for stochastic
=
0.05 sv
,
(3-l)
effects,
and for non-stochastic
H 50 T 5 0.5 sv
(3-2)
effects.
In order to allow for deviations from uniformity in total-body irradiations, all ICRP limits are intended, the effective dose equivalent has been defined as
for which
HE = 1 "THT T
The committed effective dose equivalent for a given time t, Ht,T, defined by the ICRP (ICRP, 1977; NCRP, 1985, 1987a), refers to an effective dose equivalent from one dose to tissue T and accumulated over the subsequent time t. Thus, the lifetime dose equivalent, H 50.T, is used to describe the effective dose equivalent from all ingestions of a given radioactive material during the year considered, and accumulated over the 50 years following ingestion. The committed effective whole-body dose equivalent,
should not exceed 0.05 Sv, and that for a limited volume of one organ should not exceed 0.5 Sv. The ICRU has named these limits "stochastic" and "non-stochastic", respectively (ICRU, 1980). The National Council on Radiation Protection and Measurements (NCRP, 1985a; Appendix A) now defines two quantities, H,,, and H,,,, for single and continuous intakes. NCRP (1987a; Appendix A) also has a useful glossary of radiation-protection terms and quantities. Where workers receive radiation from external sources and from intake of radioactive materials together (e.g. in uranium mines), the effective dose equivalent from the external exposure and the 50.years committed dose equivalent from total intake during the year in question must be added and kept below the limit of H, for stochastic effects and 0.5 Sv (50 rem) for non-stochastic effects. that all limits are standard It must be emphasized. mean values, independent of any consideration such as age or sex. For members of critical groups of the population, e.g. those living near to a nuclear-power plant, the annual limits have been set ten times smaller than those for workers, i.e. 5 mSv (500 mrem) for stochastic effects and 50 mSv (5 rem) for non-stochastic effects of individual tissues or organs. For the annual mean effective-dose equivalent of
762
Radioactivity
measurements:
principles
and practice
the total population a limit of 0.5 mSv (50 mrem) is recommended by ICRP (ICRP, 1979/1980) while IAEA recommends a limit of 1 mSv (100 mrem) (IAEA, 1982d). This limit is not critical, it is not regarded as a genetic limit, which would be higher, but as a limit to all exposures from justified practices. Exposure arising from medical treatment and "normal" radiation background are not included in the limits, but the first should also be reasonably minimized and the second must be taken into account if it is enhanced (e.g. by high-altitude flights). These basic primary limits call for a precise and more detailed statement, as for for women of example, exposure exceeding the limits (e.g. life-saving emergency measures), reproductive capacity or pregnant women, child workers in condition A (e.g. special medical care), etc. They can be found in the literature (ICRP, 1979/1980; IAEA, 1982d). 3.2.2.3.
Secondary.
derived
and authorized
limits,
reference
levels
The primary limits cannot always be directly used in practice. In these cases secondary and derived limits are applied which must always be lower or equal to the corresponding primary limits. Secondary limits can be expressed for external exposure in terms of dose-equivalent indices (H,, H,, and if,,; where I is the annual intake in becquerels), and, for intake of radioactive material, by ALI's (&uual Limit on Intake) (ICRP, 1977, 1979/1980; IAEA, 1982d). limits are for radiation In accordance with the primary limits, these secondary workers and external exposure H, = 50 mSv (ICRP, 1979/1980) or better H,, = 0.5 Sv (50 rem) for non-stochastic effects and H,, < 50 mSv (5 rem) for stochastic effects. For intakes the ALI's are the highest value of the annual intake I (in Bq) of a specified nuclide which satisfies both the inequalities: 1 w,I (H 5.,T per unit T for stochastic
effects.
intake)
5
0.05 sv,
(3-3)
and I (H,,,, per unit
intake)
5
0.5 sv,
(3-4)
for non-stochastic effects. (H,,T per unit intake) is here the 50 years committed dose equivalent in tissue T from the intake of unit activity of the radionuclide considered by the specified route, and wT are the weighting factors for the effective-dose equivalent. Consequently, for external exposure and intake of several radionuclides by ingestion (ING) and inhalation (INH), the following relation must always be respected (with H,, in Sv):
The secondary limits for critical groups of the population and for the general public are one tenth and one hundredth of the limits for workers, respectively, but if these limits do not correspond to the primary limits, they must be reduced accordingly. With additional model parameters, e.g. the volume of air breathed by workers (0.02 m3 min-I), further limits can be derived from the ALI's, namely the Derived limits of Air Concentration for a radionuclide during any year (DAC'S). DAC (Submersion) values are limits for operations in a cloud of a radioactive gas, and can be derived from ALI's and additional data. The recommended limits for the dose-equivalent indices are the same as for the dose equivalent (73.2.2.2), or lower. The recommended ALI's vary (ICRP, 1979/1980; NCRP, 1985) from 3.10' Bq (80 mCi) for 3H to l/20 of that for % (except CO and CO,), 1 to 3.10' for 3zP, 1 to 2.106 for 1311, 4 to 6.106 for 13'Cs and 8.106 to 5.104 for ingestion and 5.104 to 2.10' for inhalation of The corresponding DACs vary from 8.105 Bq 226Ra, 25iCf and most of the U and Pu isotopes. mm3 (20 PCi mm3) for 3H to l/20 of it for 14C (except CO and CO,), lo4 to 6.103 Bq mm3 for 32P, 7.10' Bq mm3 for 1311, 2.103 Bq mm3 for 137Cs, and 2.10-l to 8.10.' Bq me3 for most of the alpha-particle-emitting heavy nuclides. The ALI's for ingestion and inhalation of a radionuclide are, in general, not very different, except for alpha-particle emitters for which the difference is 2 to 3 orders of magnitude. For the calculation of the inhalation limits, the radionuclides are classified in three groups (D, W, Y), those with biological half lives of less than 10 days (D), 10 to 100 days (W) and above 1.00 days (Y), There are no generally accepted standards yet on surface contamination, although detailed regulations have been established by several national laws. A distinction must be made here between the limits of contamination of the skin or clothes of persons (national limits about 4 to 0.4 Bq cme2) and the tolerable limits of surface contamination of laboratory equipment (national limits about 400 to 0.4 Bq cm-*. There is also no international agreement yet on the limits of contamination of food, which turned out to be The present national, mostly provisional, a serious problem after the Chernobyl accident.
763
Radioactivity measurements: principles and practice
limits vary between a few hundred and a few thousand of bequerels per kilogram. Further limits used in radiation protection are the authorized limits, which are authorized by a competent authority or management for a certain purpose (operational Finally the They should be lower than primary, secondary or derived limits. levels). They are recommended by an authority frequently used reference levels must be mentioned. or management and indicate which level has to be applied for a given purpose. e.g. recording of dose equivalents received, investigation of the reasons for a larger value (greater than l/20 of the dose-equivalent limit), intervention, etc. 3.2.2.4. Further lea.1 reeulations Besides these most important regulations for limits of exposure, several other regulations are needed at different levels, international, national, and the working place itself. Considerable agreement exists worldwide on the application of IAEA recommendations The IAEA for the transport and packaging of radioactive sources (IAEA, 1979a, 1982b). rules are very detailed and contain many special restrictions (e.g. for fissile materials) The radiation dose-equivalent rate at the and exemptions (e.g. for low activities). surface of the packages is limited to 5 pSv/h (0.5 mrem/h; Cat. I, white label), 0.5 nSv/h 2 mSv/h (200 mrem/h; Cat. III, yellow label). A (50 mrem/h: Cat. II, yellow label) and typical label is sho& in Fig. 3-l. 1.5 cm
--
A
10cm
1_. I
I
5R
10
I
--I
t
Left: IAEA recommended symbol for the presence of ionizing radiation Fig. 3-l. Label for shipping containers of radioactive Right: (black on yellow ground. materials (text and symbol in black on yellow ground, with red bars indicating the category; yellow ground under the symbol for categories 2 and 3).
of any purchase of Several necessary national regulations pertain to licensing radioactive materials and any radiation work (except for very low activities), registration and notification of all radiation operations and exposure, maintenance of inventories of radioactive materials, financial insurance against radiation accidents, as.surance of the competence and the controls of the working environment of radiation installations, waste treatment, medical and social measures. But on These regulations must be observed in all laboratories and other facilities. the laboratory level still further regulations apply, such as a clear definition of the responsibilities, the installation of a widely responsible radiation-protection officer (RPO), clear and optimized organization of the work, recording of work performed and of doses received, the maintenance of health-physics records (that should be kept for 30 years after cessation of work), safe storage of radioactive materials (also safe from theft), emergency measures. 3.2.3. Safe handline of radioactive sources 3.2.3.1. General The success of all radiation-protection regulations and recommendations depends on Therefore, a well-organized and the manner in which the actual laboratory work is done. detailed operational radiation-safety philosophy and program is important for every laboratories the laboratory (e.g. NCRP, 1978b). For metrological radioactivity requirements are still more severe, because, in this case, not only the exposure and the
Radioactivity
764
measurements:
principles
and practice
possibility of accidents must be minimized, but also every disturbance of the measurements Some of the most important problems must be avoided, especially any cross-contamination. connected with the operation of radioactivity laboratories are discussed in detail in the following paragraphs. Radioactive sources may be sealed or unsealed, and solid, liquid or gaseous; they may weigh from fractions of micrograms to kilograms (fuel elements), may emit quite different activities from parts of picocuries to many megacuries. radiations, and may have Consequently, radioactivity work is, in general, very complex and involves very different But there are several general principles. Thus, for every experimental procedures. operation detailed procedures should be established and trial, "blank", experiments performed. Further, the minimum activity needed and the minimum operating time should be and maximum distance between source and operator, and as much shielding as chosen, The use of tweezers, pincers, tongs and gloves is almost always reasonably possible used. of advantage. The optimization of an operation is often very difficult and calls for much which may Lead to accidents. For example, a experience, and should avoid over-protection, short but safe operation with high exposure may give rise to a Lower acquired dose than a longer operation with much less exposure, which may also have larger accident probability. 3.2.3.2.
Laboratories
and working
areas
While even rather active sealed radioactive sources may be used with precaution in suitable locations (e.g. for industrial radiography), unsealed radioactive material of not IAEA proposes to distinguish, very low activity must be handled in special laboratories. three classes of radioactivity laboratory, A, B and C (Table 3-3), in general, between depending on the activity and radiotoxicity of the sources handled. For special purposes, outside this classification. For example, for special laboratories may be designated, metrology laboratories the permitted source activities could be more severely limited, or strong criticality precautions must be for laboratories working with fissile materials taken. Table
3-3 - Classification
of radioactivity
laboratories
Activity Radiotoxicity of nuclide (IAEA, 1973b))
Minimum significant quantity $ib)
Well Chem.
limitsc)
C equipped Laboratory
a)
for Laboratory B Radionuclide Laboratory
very highd)
0.1
< 10 &i
10 PCi-10
high
1
100 &i-LOO
moderatee) low
10 100
<
1mCi
< 10 mCi
1 &i-l 10 mCi-10
of type A Hot Laboratory
mCi mCi Ci Ci
> 10 mCi >lOO mCi >
1 Ci
> 10 Ci
FOOTNOTES
=) Special criteria for fissile materials; b) This quantity may be free from licensing; c) These limits should be multiplied by the following factors; 100 for simple storage, 10 for very simple wet operations, 1 for normal chemical operations, 0.1 for complex wet operations, 0.01 for dry and dusty operations; (1 &i = 37,000 Bq); d) most alpha-particle emitters; e) most radionuclides. to a high degree on its design and Safety in a radioactivity laboratory depends important principles of the design of radioactivity equipment. One of the most laboratories is a reasonable zoning, with a clear classification of the different working areas, according to the level and type of activity handled, and an optimum location of the different zones according to activity levels. The IAEA recommends (IAEA, 1973a) that a They could be named: inactive (i.e. distinction be made between classes of working areas. cold chemistry, detector systems; class 4), environmental (clean, "white administration, counting rooms with possibly room," for samples with low or no activity, and well-shielded activities; class '2.)and hot (high radon-free air supply; class 3), warm (intermediate controlled air flow; class 1). Garment-changing and control rooms may be activities, required between the zones. Access to the environmental laboratory should be through an air lock where laboratory coats and clean footware can be donned. The changing room between zones 3 and 2 should also allow for some foot-wear change and hand and foot monitoring. The entrance zone to any class 1 laboratory should be provided with a safety
Radioactivity measurements: principles and practice
shower and radiation-monitoring equipment. Areas where quite different activities are handled should not be directly accessible to each other. Essential facilities include a source preparation room, a draught-free, temperature- and humidity-controlled weighing room, and counting rooms with low-level detectors, and ventilated source-storage space All zones should be quite Useful facilities are mechanical and electronics workshops. clearly labelled, not only with the radiation warning sign, when necessary (Fig. 3-l), but also with information about the type of work performed therein. Special attention must be paid to all problems connected with the HVAC system (Heating, yentilation, and Air Conditioning), the water supply. the waste- treatment area, and the air and environmental monitoring. Finally, it is a part of radiation protection that radioactivity laboratories be constructed as safely as possible also against natural catastrophes, such as fire, earthquakes and floods. 3.2.3.3. Tvuical radioactivitv work. safe handline. storaEe and waste disuosal The handling of radioactive materials usually begins with the arrival of a shipment, followed by contamination monitoring and the unpacking of the parcel. It is important to prepare carefully for such shipments, to become acquainted with the standard packages (Fig. The unpacked samples must 3-2), and to make provision for adequate handling equipment. always be checked for damage and contamination, and may need undergo further checks. The next step is storage of the unpacked sample (usually a radioactive solution in an This storage area must be sufficiently ampoule or bottle) in a central storage facility. shielded and ventilated if samples in vented vessels are to be stored, in order to avoid damage due to overpressure caused by radiolysis (decomposition of water into hydrogen and oxygen under irradiation). This pertains especially to radioactive solutions emitting alpha particles with activities above about 1 mCi/mL (40 MBq/mL) and beta-particle store all breakable It is also wise to activities above about 100 mCi/mL (4GBq/mL). containers with radioactive solutions in additional vessels large enough to hold the contents of the bottle in case of breakage. In addition to a central storage facility, These auxiliary local storage facilities should be available in all experimental rooms. could be small, but must be well shielded (to minimize influence on counting background) and would be preferably placed in a fume hood in a corner of the room. It is obligatory and vary useful to keep exact records of the stored radioactive samples. This includes all data on the type of source, its container, the position in the storage area, times of removal and return, and any handling of it together with the names of those responsible for
Fig. 3-2. Examples of typical returnable (a) and non-returnable (b) packages for the transport of radioactive materials (different scales).
765
Radioactivity
766
In its "se and custody. radiation-protection officer
measurements:
many cases such or health-physics
principles
records group.
are
and practice
lodged
with
the
staff
of
the
When moving radioactive samples from storage areas to the experimental rooms, it is a few standard containers very advantageous to have, for such within-laboratory transfers, available, and care should be taken not to cause background problems, in the transfer, for other radiation detectors. They will not be The experiments performed with the sample can vary considerably. described here; but one procedure is always necessary, the opening of containment vessels. in order to avoid contamination. Every care must be given to this critical manipulation, a possible overpressure in an ampoule or bottle could cause serious and In particular, The most important experiments in a metrology laboratory are, harmful contamination. in 73.3. It is important besides counting, dilution and source preparation, as described to record all such operations in a logbook or on appropriate forms for standard procedures. especially for a metrology measurements, A very important aspect of radioactivity e.g. by "se of the same pipette for is the avoidance of cross-contamination, laboratory, Therefore disposable instruments should be used wherever possible. different solutions. it, concentrate and confine it as If contamination occurs, it is important to understand much as possible, and to remove it as soon as possible (ICRP, 1978; NCRP, 1980). A crucial problem with radioactivity work is waste disposal (IAEA, 1979a,1983a, 1984; As the activity of wastes can vary over many orders of magnitude, they must Moore, 1981). be carefully contained and suitable arrangements made for their collection from the place The classification of wastes recommended by the IAEA (Gera, 1974) can of their production. a distinction must be made between solid Especially, be used for their segregation. and gaseous waste, and between Liquid (inorganic or organic) (compact or powder), and long-lived intermediate-level and high-level activity, between short-lived low-Level, activity, between combustible and noncombustible waste, and between waste with or without 1n a laboratory, in general, not all categories of waste will be fissile material. there in amounts and which are not shortcollected, but only those which are produced In any individual case the most important criterion for the separation of the lived. The final waste- conditioning and disposal wastes is the method of their later processing. Radioactivity laboratories have, is mostly carried out by regional or national agencies. This pertains also to to collaborate closely with these institutions. consequently, for which local possible release of effluents to drains, sewers or to the atmosphere, regulations must be observed. 3.2.3.4.
Some special
practical
Due to the complexity intricate problems.
nroblems
of radioactive
decay modes,
radiation
protection
may pose
rather
The obviously most important nonclassical problem is the avoidance of a nuclear This is criticality situation, i.e. a spontaneous nuclear chain reaction (Stewart, 1981). done by keeping the mass of any fissile material considerably below the minimum mass necessary for a critical excursion, the critical mass, The critical masses of the common fissile materials are: 6.7 kg for a%~ 20.1 kg for 235U and 4.9 kg for a3'Pu, if the materials are pure metals, have the form of a sphere and are fully reflective (e.g. surrounded by sufficient water to reflect all neutrons). The neutron reflection by water reduces the critical masts by a factor greater than one and up to nearly ten. Therefore, every possibility that a subcritical system could be flooded must be eliminated, The critical mass is still smaller by a factor of about 10 if the fissile material is in solution. when, in the future, greater amounts of heavier fissile nuclides will be available, still smaller critical mase.es will have to be taken into account, e.g. about 10 in solution and fully reflective, g of *%n Sometimes radioactivity measurements can be considerably disturbed by secondary radiations, such as the external electromagnetic bremsstrahlung (q2.4.4) from beta-ray emitters. While beta radiation indicated in the decay scheme is absorbed by thin Layers of material, bremsstrahlung may penetrate these absorbers easily and pose a shielding problem; a typical example is provided by 3zP that gives rise to bremsstrahlung of maximum energies equal to 1.71 MeV. Another penetrating secondary radiation is annihilation radiation, two photons of 511 keV emitted in opposite directions, following positron-electron annihilation (772.4.3 and 2.4.4). Among the most important of the secondary radiations are the x rays and Auger electrons following electron capture (EC) by the nucleus or internal-conversion (IC) electrons (72.4.5). Thus the x rays can often create shielding problems when working with electron-capturing nuclides. Many different secondary radiations are emitted in and following nuclear fission, also several strongly- penetrating gamma rays. Secondary radiations can also be produced by nuclear reactions of the primary particles (activation). This pertains especially to neutrons which produce, for example, positron-emitting 13N around all fast-neutron sources, such as linacs and other accelerators). But (a. n + 1) reactions can also disturb experiments with radioactive alpha-particle sources.
ed
Another potentially hazardous below or above a shield and
type of interfering secondary radiation is that scatterproducing a high radiation level at the place of the
Radioactivity measurements: principles and practice
767
operator in front of the shield (e.g. the "skyshine" effect; Borak, 1975). Scattered radiations can also seriously interfere with measurements of radioactive sources. An absolutely unwanted occurrence in a radioactivity laboratory is an accident. Even if all possible precautions are taken, accidents do happen, mostly due to human error. Any deviation from the foreseen course of an experiment must be considered to be an Many accidents, especially the accident, but the accidents are of different gravity. "usual" ones like fume-hood fires, could be avoided, if sufficient attention were always to be given to the prescribed routines. Most important is the rapid recognition and identification of an accident, which allows one immediately to summon trained personnel and to take, as quickly as possible, previously planned and well prepared countermeasures. When urgent first measures have been taken, the accident should be thoroughly analyzed, and reported in detail so that further preventive measures can be planned and carried out. The detailed initial and later measures, which depend on the individual circumstances, are described in the literature (ICRP, 1978; NCRP, 1980, 1987f; IAEA, 1982d).
It happens that radioactivity laboratories have also to handle neutron sources, especially sources of spontaneously fissioning radionuclides such as zszCf or "radioactive" neutron sources, such as Ra-Be, Pu-Be or Sb-Be sources (Cierjacks, 1983). In this case, special precautions should be taken and, if necessary. special monitors used. 3.2.4. Instruments and materials 3.2.4.1. Radiation monitorine instrumentation Radiation monitoring is an unavoidable daily necessity when handling radioactive materials. The necessary instrumentation used for monitoring varies from simple pocket dose meters (Fig. 3-3) to elaborate systems with many functions controlled by a central computer (NCRP, 1978a; IAEA, 1980). Because different radiation-monitoring instruments can be used for different purposes, if their responses are suitable, it is more important to classify them according to their characteristic measuring properties, namely: The principal radiation measured, namely alpha, beta, x and gamma radiations, (1) neutrons, fission products and combinations of these different radiations; (ii) quantity measured: absorbed dose rate (in rad/s, Gy s-l, or .J kg“ s-l), exposure rate (in R/h, i.e. 7.17.10-s A kg-l, C kg-' s-l, or A kg-l) or accumulated (cumulative) exposure (in R, i.e. 2.58.10m4 C kg-', or C kg-l), or count rate or counts corresponding to dose rate and dose; (iii) detector characteristics: type (see chapter 4), size, efficiency with respect to the main radiation and unwanted radiations, selectivity for desired radiation; (iv) response to the energy spectrum of the measured radiation, especially the energy threshold, below which the instrument is ineffective (often as high as 50 keV), and the energy resolution, if possible; (v)
directional response;
range (vi) (background);
of
measurement
(e.g.
0.1
mR/h,...
to
1000
R/h)
and
detection
limit
(vii) read-out system and speed of indication, i.e. immediate (scale reading) or after treatment (film); and such as compactness, weight, long life, (viii) construction and utilization details : fail-safe provision, portable or fixed location, internal test source, energy supply (mains and, or, battery). An essential The best choice of a suitable detector is often rather difficult. For condition is an exact definition of the purposes that the instrument has to serve. many purposes equipment with exchangeable detector heads are often the best solution. Therefore, but also for general convenience and efficiency, a certain standardization of the monitoring equipment and, especially, of all connectors is most advantageous. equipment, Because of the importance of proper functioning of the monitoring Calibration calibration and regular maintenance and testing should be a normal routine. can be performed in an appropriate radiation field by comparison with an instrument with known response, or by using a calibrated radioactive source and calculating the radiation The calibration of the monitor should also be field to which the monitor is exposed. preserved by checking it regularly against a sealed long-lived radioactive source emitting similar radiations to those for which the monitor was calibrated, and always under the same conditions. The duplication of monitors is reasonable in case of hazardous operations.
768
Radioactivity
3.2.4.2.
Suecial
monitoring
measurements:
principles
and practice
instrumentation
Most radiation-protection surveys are performed using monitoring equipment designed for this purpose. But these may not be suitable in all circumstances, because special instrument properties may be needed in some cases, such as for example, to monitor neutrons (which can only be detected through secondary nuclear reactions) or fission products (with extremely short ranges in matter). Radionuclides which emit radiations of extremely low energy can only be measured with special monitoring instruments, e.g. gaseous tritium using internal gas counters (Budnitz, 197413; NCRP, 197ba), windowless proportional counters or ionization chambers, or "*I with special thin-window or windowless detectors (IAEA, 1978b). A very special radionuclide is "'Rn, which is measured, in general, by means of its several daughter products, and needs, specialized equipment therefore, (Budnitz, 1974a). Many special monitoring instruments are constructed for one application only, e.g. whole-body counting, hand-and-foot monitoring, large-area-contamination monitoring, Filter systems are specially developed for the measurement of low contamination of air (IAEA, 1978a). Special instruments are also needed for the measurement of extreme count rates; low-level systems for highest sensitivity (NCRP, 197ba) and high-level instruments for monitoring of accidents (IAEA, 1982a). 3.2.4.3.
Other
radiation-urotection
eauiDment
Radioactivity laboratories often need special equipment which is not always used in a normal, well-equipped chemistry laboratory. This equipment can vary considerably, depending on the kind of experiment that is planned and the activity level involved. Only the most important special equipment needed in a radioactivity laboratory can be briefly discussed in this report. For work at low activity levels, ordinary laboratory coats are normally used and clean shoes and head coverings may be desirable, but light-weight surgeon-type gloves should always be worn and adequate monitoring instruments should be available. At higher activity levels, changes of clothing may be required for work in "warm-" and "hot-" laboratory areas. For work at the highest levels of activity, respirators, face masks with air SUPPlY? or completely ventilated suits may become necessary. The emergency equipment, such as showers, and first-aid chemistry laboratories should also be available in radioactivity by decontamination materials and equipment (NCRP, 1980). shielding is always required Proper shielding for gamma radiation (Sauermann,
in
radioactivity
kits found in "inactive" laboratories, supplemented
laboratories,
especially
A transparent a sufficient
A simple a
lead-loaded-glass
a radioactivity
a
good
a set a set
, the open sources (such as Am and Fe) should best be metallic layers electrodeposited on standard source supports, the gamma-ray sources should be easy to handle.
Radioactivity measurements: principles and practice
769
Fig. 3-3 Examples of typical monitoring instruments: a) Film badge, about 4 cm x 3 cm; b) quartz-fibre electrometer, typical ranges 100 mR, 200 mR and 1 R; c) finger-ring TLD dose meter; d) personal pocket dosimeter, with indication of exposure and accumulated dose and an audible alarm; e) portable survey meter with exchangeable detectors, typical range 1 to 10 mR/h. 3.2.4.4. Minimum radiation-urotection
equipment for a small radioactivitv laboratory
The radiation-protection equipment needed in a radioactivity laboratory depends entirely on the size of the laboratory and its specific work. But every laboratory requires a minimum of general-purpose equipment, which will be briefly discussed in the following four paragraphs. An important requirement for laboratories of any size, but especially for small ones is, as far as possible, the standardization of the radioprotection equipment and, in particular, of their electrical connectors and cables. The minimum personnel-monitoring equipment could be a thermoluminiscence dosimeter for which processing is often commercially available) and a (or a film badge, The pocket direct-reading pocket monitor for everybody working with radioactivity. monitors could be penlike quartz-fibre electrometers, similar pocket ionization chambers or, better, "beepers" or "chirpers" that are pocket instruments, equipped with a small Geiger-Miiller counter, which give an audible alarm signal at a certain, adjustable radiation intensity. Modern instruments combine a warning "beeper" to indicate exposure rate and a cumulative direct-reading dosimeter. Such an instrument is the "Canary II",
with a piezoelectric beeper and silicon p-i-n
diode detector, that is now available in a package about the same size as a medical pager. It has an exposure-rate range of 10 @R/h to 10 R/h and beeps for every 10 rR accumulated. Survey monitors are also indispensable. They should be as versatile as possible (with exchangeable detector probes), and should be especially suited to the task at hand, having, for example, the necessary range intervals, and showing a suitable response to the radiations to be detected (also see li3.2.4.1). For work with sealed radioactive sources some further items of equipment may be needed, such as more shielding, including a lead shield with a lead-glass window and tongs The for remote handling, additional shielding material and a set of standard sources. handling of open sources may require additional equipment, such as surface monitors (preferably with a large area, and a, +9, and 7 discrimination), an air monitor, personnel protection material, and provision for decontamination. It is always desirable to have available, even in a small laboratory, instrumentation for the identification of radioactive substances, by spectral-energy analysis of the For this, a versatile lOOO-channel analysing system with a different radiations emitted. set of suitable detectors should suffice. This latter set could consist of a high-resolution, average-size alpha-particle detector (surface-barrier or drifted Si), a Si(Li) or thin Ge detector for beta- and x-ray detection, a medium-size Ge gamma-ray detector (Ge(Li) or HPGe), and a 3" x 3" NaI(T1) crystal.
Radioactivity measurements: principles and practice
770
3.3
RADIOACTIVITY SOURCE PREPARATION
3.3.1. Sources for radioactivity measurements 3.3.1.1. General: The need for calibrated radioactive sources The radioactive samples met in practice can be of very different origin, They may stem from field-sampling (73.3.2.1) environmental for controls, from geological prospecting, from irradiation of suitable materials in reactors or accelerators (Servian, 1975), from research work (e.g. TLC plates (Thin Layer Chromatography; Chapman and Ayrey, 1981)), or from commercial suppliers (73.3.1.3). All artificial radioactivity is produced by some kind of irradiation, so that many procedures have been worked out for the preparation of targets for irradiation and for their successive processing (Harley, 1972; Kobisk and Adair, 1982). These procedures cannot be described here, where discussions are limited to the sources for preparation of radionuclide metrology. the But target-preparation procedures related to the source-preparation techniques must always be taken into consideration when metrological sources are prepared. Radioactive samples and sources are used for many different purposes. Consequently, they can vary widely; their activities from much less than 1 pCi (0.04 Bq) (e.g. samples for % dating) to many MCi (tens of PBq; for e.g. food processing or medical radiation; and their mass from much less than 1 picogram (e.g. sources prepared in an isotope (mass) separator) to many kilograms (e.g. fuel elements). They may be sealed, or unsealed, solid, liquid or gaseous; their shapes may be completely different (from irradiated foils such as cobalt to such chemical systems as radionuclide generators). Only those sources prepared for normal radionuclide metrology are discussed in the following sections in detail. In general, the original radioactive samples received by a laboratory, such as many environmental samples, are not in a form that can be measured accurately. Their activities are often too high or too low, and their configuration may be unsuitable for the counting method selected. Therefore, a quantitative preparation of sources for measurement must frequently be carried out using the original samples. This "source preparation" can be very complex, sometimes beginning with the purification of the primary material, followed by chemical treatment (e.g. combustion of organic matter (Gorsuch, 1970) or separation (Trautmann and Hermann,l976), dilution or enrichment (e.g. by electrolysis) and quantitative deposition on a suitable support for counting or, for example, mixing with a liquid scintillator. Some problems, unknown in the chemistry of stable elements, complicate the situation, e.g. the need to add sufficient carrier element or compound to prevent losses Therefore, the final accuracy of a whole radioactivityfrom solution by adsorption. measuring procedure can depend, to a high degree, on the quality of the source preparation which must always be carried out with the greatest care. Here, only the most important techniques of source preparation for metrological purposes can be discussed in detail, namely the quantitative preparation of thin-solid, homogeneous-liquid, and gaseous sources from well- characterized aqueous solutions or solid materials (773.3.3 and 3.3.4). Some interesting special source-preparation techniques are discussed only briefly (a3.3.5). 3.3.1.2.
TYDe
and calibration of radioactivitv sources
Laboratory sources including all types of research sources may vary considerably in their properties, but all may ultimately be needed for accurate radioactivity measurements. Typical laboratory sources are: calibrated radioactive solutions, solid reference sources, liquid reference sources (quenched and unquenched) for liquid-scintillation counting, calibrated sources of mixed radionuclides used to simulate another ("mock" sources), sources for special applications (e.g. for energy measurements, measurement of surface contamination, calibration of radionuclide ("dose") calibrators, and so on). Some of these sources are shown in Fig. 3-4. As calibrated laboratory sources serve mostly for accurate measurements, their relevant properties must be well defined, but the most important property of a source is, of course, its emitted radiation. Current calibrated alpha-particle sources are chiefly s41Am,andthen, less frequently, 'i"Po (but chemically unstable and contaminating), ssgPu (with a few accompanying radiations) and Z44Cm. Alpha-particle radiation is almost always accompanied by electrons and x rays of low to high intensity and low-energy gamma rays. Widely used beta-particle sources (pure beta-particle radiation or beta rays with accompanying gamma rays) are 'H, l"C, "P, 35S, %l, 'sSr + "Y, 147Pm, ""Tl and sl"Bi. s2Na and %o are most often used as positron sources and i3'Cs and sloBi as single-energy As x-ray sources pure electron-capture nuclides (e.g. 55Fe) or photoelectron sources. stable nuclides excited by alpha particles or by other radiations can be used. Many radionuclides serve as gamma-ray sources in the energy range of a few keV to 2.7 MeV, especially the following, listed in the order of increasing energy, '"'Am, ""Cd, 57Co, sOsHg, %r, 137C~, 54Mn, s"Co, sZNa, s8Y (see NCRP 1985). Higher energies can be reached by (a,n+y) sources, e.g. 6.13 MeV with (238Pu>13C). Neutron sources are prepared from spontaneously fissioning from mixtures which s%f or produce (o,n) processes (e.g.r4iAm/Be, 'ssRa/Be, *i'Po/Be) or (7,n) processes (e.g. lz4Sb/Be). Californium-252 can, of course, also be used as a versatile fission-product source.
Radioactivity measurements: principles and practice
Fig. 3-4.
771
Examples of commercially available calibrated radioactivity sources; (a) standard solutions in vials, ampoules or bottles: (b) calibrated (for activity), open sources on foils; (c) calibrated (for emission rate), open sources on thick supports; (d) sealed reference sources; (e) sealed sources for industrial applications; (f) set of calibrated sources; (g) large-surface reference sources; (h) gaseous sources.(Also see IAEA, 1986c)
Other characteristics of laboratory sources which should be known with an appropriate accuracy are: all geometrical dimensions of the source and the source support or capsule, mass, chemical composition (including carrier concentration, which is important for dilutions), isotopic composition (i.e. the relative numbers of atoms of the different isotopes of the element concerned), source activity (or emission rate for gamma-ray sources), uncertainty of the stated source activity, radionuclidic and radiochemical The first points are self-explanatimpurities and stability (including hygroscopicity). ory, and the last two are discussed in the next sections ((73.3.2.3 and 3.3.2.4). But, in each individual case, some of the listed characteristics will have to be known with high, and others with less, accuracy. The high quality of international radionuclide metrology is to a large extent due to In such interintercomparisons organized by BIPM (and also, earlier, by ICRU and IAEA). comparisons of source-activity or activity-concentration measurements, but also on many This is only reasonably other occasions, sources must be circulated amongst laboratories. possible, if the properties of the sources, especially their geometrical dimensions, used Although this aim may never be achieved in different laboratories, are the same. Some promising results have been completely, it should be sought with perseverance. obtained, as most commercial suppliers offer solid sources with the same diameters (25, 30, 38, 50 and 75 mm) and, in international comparisons, standard ampoules (NCRP, 1985; 74.4.7) are a matter of course for the international reference system, SIR (Rytz, 1983). 3.3.1.3. Suuuliers of calibrated radioactivitv sources Many labelled radioactive chemicals and calibrated radioactivity sources are Their addresses can be found in the trade available from commercial and other suppliers. It is impressive and also very directories published by many of the scientific societies. instructive to read the brochures and catalogues of the big commercial and other suppliers (see Table 3-4). Calibrated sources of high quality are available in many countries from The Fachinformationszentrum of Karlsruhe has also published their national laboratories. an "International Directory of Certified Radioactivity Sources" (Grosse and Bambynek, 1983) prepared by IAEA and CBNM, which lists many more suppliers and their products. 3.3.2. Main urocedures and uroblems with radioactivitv sources 3.3.2.1. Samoling and sample treatment
Radioactivity
772
measurements:
principles
and practice
An essential part of radioactivity measurements begins with the field collection of terrestrial, aquatic or atmospheric samples of different type, which are to be processed for measurement and analvsed. This samoline is often the crucial step of the whole measurement (IAEA, 1970, 1$78a; NCRP, 1976;). ”The chief objective of the sampling is to Table
3-4.
suppliers
Some
of
AACC
calibrated IPEN
radioactivity ,ns,um,ode
sources
Perquwar
EnergCncar
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SAO PAULO.
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Products
I,OC”pe Producls Labora1ones 18oU Nonh Ke,smne
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ENGLAND
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Corporamn
Amerrhm 2636 South Arlmgmn
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Radtarmn
Beljmg PEOPLES
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Radioactivity
measurements:
principles
and practice
773
ensure that the collected sample, or samples, be representative of the wider distribution of material to be analyzed, and the sampling should follow a well-devised and tested program. When filters are Another essential problem is the effectiveness of the sampling. used, their effectiveness can simply be tested by using several equal filters in series. But, in general, the problem is more complicated, especially if low activities are present, which can lead to losses by adsorption to the walls of the reagent vessels during ignition and dissolution. Therefore, the addition of an appropriate carrier at every critical point of the procedure is of great importance. Furthermore, the collected samples must be stable between the time of collection and that of the preparation of the final sources for counting. cleaned, combusted, Most of the original samples must be processed, extracted, dissolved, precipitated, or otherwise treated chemically or physically, in order to be measurable ((NAS-NRC, 1965-1987; Harley, 1972; Spinks and Woods, 1976; Friedlander et al., 1981; IAEA, 1981). The end product of these procedures should be stable, homogeneous, sufficiently-active and easily-measurable sources. As losses are inevitable in such as few steps as possible should, however, be used. manipulations, Only minimal treatment may be needed if the samples can be measured using high-resolution gamma-ray spectrometry. 3.3.2.2.
Dilution
and dispensing
A procedure which is quite often needed during source preparations is quantitative dilution of an original "master" solution (by aliquoting and aliquanting) to solutions with lower radioactivity concentrations (Van der Eijk and Vaninbroukx, 1972; Campion, 1975; NCRP, 1985). The parent "master" solutions, prepared from field samples or irradiated materials or simply purchased are, in general, aqueous solutions of HCl or HNO,, about 0.1 mol/L of acid and 100 pg of inactive salt per dm3 of solution. The latter is a minimum carrier concentration to avoid wall adsorption, but it still allows one to prepare sources with small self-absorption. The activities of master solutions are in general rather high, in order to allow for the preparation of sources which are sufficiently active for all counting methods. For example, the measurement of photon emitters in glass ampoules in a reentrant ionization chamber or with NaI(T1) detectors is best made with solutions of from
Diluent,with
proper
t
catnercontent. acidity,
etc....
7 c._-.
_
\ “Master”solution
6111
6112
(A)
8113
Third
Fourth
dilution
dilution
level
(D)
D12nl
level
(E)
E12nll
Fig. 3-5. General scheme for the dilution of a liquid sample. The ampoules Bill, Blkm, C1211, C12np,... could be saved, if filled quantitatively, further measurements.
A2, for
Radioactivity
774
measurements:
principles
and practice
0.4 to 4MBq g-= (10 to 100 &i/g); considerably higher activities still are needed for making good measurements with Ge detectors. For most methods these master solutions must be diluted, e.g. by a factor of about ten, for the preparation of sourcea for 4a measurements. dilution procedure should always be The performed according to a well-devised scheme (Fig. 3-5) with at least two, but preferably three or more, samples at every dilution level. Other samples, at a suitable dilution, can be sealed, and then used to check the half life or dilution factor (i.e. the volume or mass ratio between the final and the original solutions). Volumetric dilution using calibrated pipettes, burettes and flasks is the simplest and fastest dilution technique. However, for small samples, as are mostly used in radioactivity work, it is often not accurate enough, so that weighing techniques must be In this case, applied. an empty dilution flask is first weighed, with or without stopper (mass A), then the diluent is poured into it from a dispensing vessel and the dilution flask reweighed (mass B). Finally the required amount of the master solution is added, preferably by using a "pycnometer" for smaller (Campion, 1975; NCRP, 1985) or a pipette for larger quantities, and the total mas.s of the flask is again measured (mass C). The dilution factor is then DF = (C-A)/(C-B) If pycnometers are used for the dispensing of the master solution their mass before (D) and after (E) dispensing give the dilution factor (C-A)/(D-E). Splashing should be avoided by all means. For very accurate measurements the weighings could be repeated every 10 or 20 seconds in order to account for evaporation (extrapolation method). The contents of the dilution flask should be thoroughly mixed (by shaking or stirring) and, therefore, the flasks should never be filled to more than half of their capacity. A well-equipped chemistry laboratory is the basic condition for precise source-preparation work. It should include a separate balance room with at least two balances. The balance room should be as draught-free as possible (perforated false ceiling), and air conditioned with a temperature constant to within 0.5OC (top warmer), and a relative humidity around 50 to 60 percent, constant to within about 5%. All equipment should be in thermal equilibrium when in use and, therefore, be placed in the balance room at least two hours before use, and the operators should enter the room 15 to 30 minutes The balances should be mounted on vibration-free tables in direct prior to weighing. contact with the ground and without contact to the building. One balance, mainly used for drop weighing (73.3.3.), should cover the range of about 1 mg to 1 g with a precision of better than 10 hg. (Drop masses are about 20 mg.) Such microbalances are now often automatic electro-balances. The second balance must serve many purposes, especially for the preparation of dilutions and dispensing. It should therefore cover an approximate range from 0.1 g to 200 g with a precision of better than 0.1 mg. Regular cleaning and testing of the balances and of their "weights" are mandatory for continuous high-quality work (J.S. Merritt, HN., 1973, p. 325). A set of well-maintained standard "weights," down to the milligram range, can be of great help for the testing and could be used for the substitution method. Some types of balances need recalibration of their optical scale, .some need static-charge elimination (best accomplished with an alpha-particle source of at least 1 MBq). The buoyancy correction (about + 0.1% for brass or stainless steel "weights") must always be applied. And it cannot be stressed enough, that all equipment used must be extremely clean (Campion, 1975). 3.3.2.3.
Purity
of radioactive
An important general samples being measured.
other
samules
problem
Radiochemical impurity refers than those which are desired.
Radionuclidic impurity refers daughters) which is certified.
in
radioactivity
to chemical
measurements
compounds
to radionuclides
is
the
of a radionuclide
that are present,
other
purity
of
the
(and daughters),
than
that
(and
Chemical impurity refers to chemical compounds other than that in which the certified radionuclide is stated to be present; they may be radiochemical impurities or even stable The term isotopic impurity can be used instead of radionuclidic chemical impurities. impurity, that by definition includes isotopic impurity, when the impurity nuclides happen also to consist only of isotopes of the certified radionuclide. As the above terms are not always used in the same manner (e.g. daughter may or may not be included), the intent should always be clearly stated.
activities
should always be accompanied by a statement of all measurable A metrological source impurities and by any relevant high-resolution energy and possible future radioactive It is also important that purity checks be continued from time to time during the spectra. whole working life of a radioactive reference source, because long-lived impurities in shorter-lived sources. For instance, old lJ"Cs sources usually increase in proportion, become, within several years, l"Cs sources and lg7Hg sources, within a few weeks, '03Hg
Radioactivity measurements: principles and practice
775
Further, it should not be forgotten that the purities of most radioactive samples sources. deteriorate continuously because of the radioactive decay itself ("primary internal radiation effect") and due to radiation damage in the surroundings of the active material, (Bayly and 'Evans, especially in labelled compounds ("primary external radiation effect") 1968; Evans, 1976). 3.3.2.4. Stability of radioactive samples with radioactivity samples is Another general, sometimes underestimated, problem In principle, radioactive compounds and solutions are never their long-term stability. stable, as the number of their radioactive atoms decreases and that of the impurities This cannot be avoided but caused by radiation effects increases in the course of time. may be taken partially into account; however, other ageing effects could be prevented. The adsorption of activity on the container walls and impurity centers such as dust particles (and resulting possible chemical changes) can be avoided, or reduced, by adding suitable amounts of carrier to the solutions (0.02 to 10 pg per gram of solution, in general). Also the action of microorganisms can be avoided by addition of suitable reagents, and careful The following effects which cannot be avoided cleaning and sterilization of containers. radiolysis should be considered, minimized as far as possible, or a correctionmade: (hydrolysis, water decomposition by radiation), hydration of solid sources, self-decomposition due to radiation (e.g. of labelled compounds), production of radioactive gases such as Rn isotopes, contamination by recoil atoms or agglomerates from alpha-particle sources, Finally, the continuous exposure to ingrowth of daughters with all secondary effects. radiation and the intense irradiation of sources and source supports may cause mechanical instabilities, which also must be checked thoroughly in order to avoid contamination. For all these reasons, the "useful working life" of a calibrated radioactive sample or source may be of limited duration, and is often specified in terms of the half life of the radionuclide considered. 3.3.2.5. Oualitv and safetv control Contamination by radioactive sources presents a hazard to man and the possibility of Therefore, every prototype commercial error in other calibrated radioactivity sources. source should undergo severe safety tests during development, and all its progeny should be routinely tested during preparation. Leakage tests of sealed sources are particularly important, because such sources are used rather freely. Standard procedures for such tests have been proposed internationally (ISO, 1979). The recommended tests for routine checks during production include wipe tests, bubble tests (at reduced pressure), immersion tests (at different temperatures), and emanation tests. Prototype sources may be tested by impact, heat, pressure, vibration, percussion, etc. And the long-term behaviour of radioactive sources must always be periodically checked. Open sources for laboratory use differ so much from each other, that standard procedures for testing and quality control cannot be indicated. Where possible, the criteria developed for sealed sources may be applied. However, open sources must be handled with special care, owing to the greater contamination danger. Laboratory sources are characterized by their geometrical form, self-absorption, radionuclidic purity and other relevant characteristics. Often, the most important characterization of a laboratory source following that of the activity or activity concentration is that of its uncertainty. Such a statement is even more credible, if the calibration of a source is traceable (72.2.3.) to a national or international laboratory. 3.3.3. Preoaration of thin solid laboratory sources 3.3.3.1. TVDGS of solid source needed for metroloau. Radionuclide-metrology laboratories must prepare and calibrate many different kinds of solid sources, sealed and unsealed, which may vary widely as to size, form and activity. Such sources are most often prepared by dispensing one or more drops of a calibrated solution on to a suitable support. The preparation can be very difficult, as loss of activity by splashing, evaporation or sublimation must be avoided. Several different methods are used for the calibration of radioactive solutions, but most of them require the preparation of sources of as low as possible self-absorption. Such sources are, in general, prepared by quantitative deposition of drops of the solution on to very thin supports (Yaffe, 1962). This technique is most important for metrological laboratories and is discussed in some detail in this chapter. A survey of currently used source-preparation techniques may be found in Table 13 of NCRP (1885). 3.3.3.2. Source swoorts.
backine and cover foils
Many different source supports and mounts are used for thin sources, mostly plates or discs of suitable dimensions and suitable low-Z materials if low-energy-electron scattering is to be minimized. In general, the supports and mounts are to be electrically conducting, in order to avoid electrostatic-charge accumulation which could cause counting errors. For many simple measurements, aluminium, steel or platinum discs of 0.1.mm to l-mm thickness
Radioactivity
776
measurements:
principles
and a diameter appropriate to the counter (20 to measurements rather sophisticated supports may be
50
and practice
mm)
suffice.
For
very
accurate
et al., 1970), or the thinnest possible conducting plastic foils (for 4a measurements in gas-flow counters). Thin supporting foils are, in general, placed on thin aluminium or stainless-steel annuli with inner diameters of 16 to 28 mm and thicknesses between 0.1 to 0.5 mm. Plastic foils of not-too-low thickness (more than about 100 pg/cm2 or 0.001 mm can be bought from many commercial suppliers in the chemical industry; very thin foils, down to about 5 pg/cmZ must be prepared by the user (Maissel and Glang, 1970). A simple method of preparation is the pipetting of a suitably concentrated solution of a polymer plastic (such as cellulose, polyvinylchloride, polyvinyl polystyrene, alcohol, polyvinylchloridepolyvinylacetate copolymer (VYNS), dissolved in cyclohexanone or a similar solvent) on to a rotating glass plate. The latter may be a square of 10 cm x 10 cm and one millimeter thick, and it should rotate at about 500 to 5000 revolutions per minute, depending on the expected foil thickness. The glass plate must be prepared by cleaning with some watersoluble substance (preferably detergents) and then coated with a thin gold layer (by vacuum evaporation or other means) before use. The glass plate with the plastic foil on its gold-coated surface can again be coated with a suitable gold layer (or other conducting material (Lowenthal and Smith, 1964). Then the doubly-coated plastic film is cut into pieces of appropriate size, using, for example, a razor blade, and taken off the glass plate by cautiously dipping into water. The floating foil pieces can be caught on annular supports and and the thickness determined by weighing or measuring in any other suitable The conducting layers should have the bulk resistivity of the material used, which is way. usually gold, and the layers should be at least 10 pg/cm' or, better, 15 to 20 /lg/cmz thick. It is wise to use a plastic with a thin layer of conducting material that is resistant against the source solution, because otherwise the sources could deteriorate too rapidly. Many variations of this method for the preparation of thin foils are used successfully (Pate and Yaffe, 1955). Thin foils for source covering or sandwiching, needed especially for efficiency extrapolation (75.5.2.3),are prepared in the same way, but here the inner diameters of their annular supports must be greater than the outer diameters of the sources to be backed or covered. 3.3.3.3. Quantitative dror, deoosition The crucial step in the preparation of thin solid sources from radioactive solutions is the quantitative deposition of drops onto thin supports. The determination of the drop masses can be performed volumetrically, by using calibrated pipettes or burettes (J.S. Merritt, HN, 1973, p. 325; Y. Le Gallic, HN, 1973, p. 333; NCRP, 1985), or gravimetrically. The accuracy of the first method is only moderate, about 0.5 to 5%, but it suffices for many applications. For accurate measurements the mass of the deposited drop or drops must be obtained by weighing with a precision microbalance (73.3.2.2), which can yield, under favorable conditions, uncertainties as low as 0.01% (Merritt, lot. cit.). Two drop-weighing methods are commonly applied, namely the pycnometer method and the extrapolation method. The first, which is generally recommended as the most accurate, is based on the weighing of the vessel (pycnometer) containing the radioactive solution before and after dispensing the source drop. The mass of the latter is given by the difference of the two weighings. Different pycnometers have been used, but disposable small, low-mass, plastic ampoules with long tips (NCRP, 1985) proved to be the most suitable. In the extrapolation method the mass of the deposited source drop (from a micropipette kept about 5 mm above the foil) is weighed as a function of the time elapsed after deposition of the drop (for about 0.5 to 3 minutes). Extrapolation of the weighings to time zero eliminates to a certain extent the evaporation and yields the value of the mass dispensed. Due to effects (especially cooling of the drop) at the moment of deposition, the extrapolation method gives systematically 0.2 to 0.3 % too low results for the drop mass. But modern electro-balances with continuous indication of the mass could give a better extrapolation. 3.3.3.4.
Methods
for imurovine. source
Quality
as possible Metrological sources must, in general, be as thin and as homogeneous (throughout the well-defined source area). But simple drop deposition from a salt solution does not generally lead to the wanted uniform formation of small crystals in the source This can easily be seen by inspection with a magnifying lens or under a microscope, area. a test which should be performed on every individual high-quality source. Therefore, several different techniques are routinely used to improve the quality of drop sources, of which only the most important ones can be mentioned here. Wetting agents such as insulin or Catanac (Baerg et al., 1964; supplier's addresses are given in NCRP, 1985) can be deposited onto the supporting foil and dried before depositing the drop; seeding agents such as Ludox SM (Pate and Yaffe, 1955; NCRP, 1985) can be added to the deposited drop before drying; drops of solutions of suitable chemicals can be added to the deposited drops in order to induce precipitation and uniform crystallization. The method of precipitation may often be the only possible one for the preparation of stable sources, as for example, in the case of sublimating HgS sources (by precipitating with thioacetamine(TAA)or H,S, or in the case of low salt concentrations (Korenmann, 1966).
Radioactivity
Although testing, as be performed outside the can be done surface, or 3.3.4.
principles
and practice
most unsealed laboratory sources are legally not subject to safety and quality are sealed sources (73.3.2.5), every possible, reasonable testing should also on them. Especially important, in this case, is to check for contamination stated active source area (which can often occur because of splashing). This by defined-solid-angle counting using suitable diaphragms just above the source by auto-radiography.
Preoaration
3.3.4.1.
measurements:
Tvpes
of liauid
of source
and easeous
laboratorv
sources
needed
In addition to many types of solid sources, different liquid and gaseous sources must be prepared quantitatively, or measured in metrology laboratories. The preparation of the most frequently needed ones is discussed in what follows; in particular, "liquid sources" in the form of ampoules for gamma-ray or bremsstrahlung measurement (e.g. 32P), vials for liquid-scintillation counting, and "gaseous" sources, i.e. suitable ampoules filled with radioactive gases. Such source preparations have been discussed in NCRP (1985) in some detail. 3.3.4.2.
Ooeninp
filling.
emotvine. and sealine
of amooules
and vials
The handling of ampoules and vials, especially their filling and emptying, is probably one of the most frequent functions in activity-calibration laboratories. There are two reasons for that: first, most radioactive solutions of high quality are stored in ampoules or vials, and second, most of them can be measured easily, fast and with considerable accuracy in standard ampoules using standard ionization chambers (SIR; see 72.2.3) or similar standard devices with other detectors (NaI(Tl), Ge, etc.). The filling of new, well-cleaned ampoules must be performed gravimetrically, if high accuracy is required. They are first weighed empty and reweighed after filling from a pipette or burette. It is most advantageous to use some mechanical, precision positioning device for the movement of the ampoule towards the pipette or vice versa, in order to avoid splashing, etc., during filling. After reweighing the ampoules should be flame-sealed and the vials closed by a suitable stop or cap as soon as possible. They could be again weighed after sealing for control. Ampoules should be filled to a part of their capacity (about half), in order to keep the liquid well away from the hot top when sealing. The latter is best accomplished using commercial equipment which produces only negligible evaporation. The opening of the ampoules must also be carried out with the greatest care. After an outside wipe test and careful shaking and draining of the solution from the tip, a file mark at the narrowest diameter is drawn and the tip is cracked by contacting the file mark The emptying of the ampoules with a small bead of molten ("red-hot") glass or a hot wire. may be done in a similar way as the filling, using the same mechanical device or a The use of standard ampoules is mandatory for the SIR (72.2.3), but also of pycnometer. great advantage for all other purposes. 3.3.4.3.
Preparation
of sources
for liauid-scintillation
counting
Most radioactivity measurements in life sciences and many in other fields are made by of the light emitted due to liquid-scintillation counting (LSC), i.e. by measurement radiations from radionuclides in a scintillator solution (75.4.3). The basis of all LS solutions is an organic (aromatic) solvent (e.g. toluene, xylene, dioxane) with a primary and a secondary solute (wavesolute (scintillator; a few percent of PPO) . The main problem in length shifter; e.g. a few tzn:hs of a percent of POPOP). LSC is to introduce aqueous radioactive samples into the LS solution in such a way that stable and homogeneous solutions or dispersions (of sufficiently small particles) with a This can be done in different ways: essentially, high counting efficiency are formed. ideal solutions, "real" solutions and emulsions three kinds of LS sources can be prepared: Ideal (molecular) solutions are, of course, obtained, (Coursey and Moghissi, BIPM, 1980). if the solvent is itself labelled with the activity (eg. 3H-toluene), but also noble gases, (of halides, metals (Grignard), lipids, etc.) yield ideal and many organic compounds The mostly needed uniform mixture of the LS solution with an aqueous solutions. agents are radioactive sample is, however, only possible if other added, such as complexing agents, emulsifiers, etc. The resulting ternary "real" solutions solubilizers, neighborhood of relative concentration, and emulsions are only stable in a limited temperature, pH value, salt (carrier) content and chemical behaviour, etc. Therefore, it is often the most important experimental work to find these proper conditions for the a considerable part of all "applied" LSC measurements is individual cases. Nevertheless, - ethanol (up to 15%) - water made using "real" solutions, especially toluene-scintillator naphthalene - water mixtures and scintillator (less than about 1%) systems: dioxane mixtures with alkyl phosphate chelating (complexing) agents (e.g. HDEHP). The greatest part of LS counting in life sciences is probably carried out using (colloidal) emulsions. The counting samples are in this case ternary mixtures of the basic LS solution with a dispersing agent (emulsifier; surfactant or detergent; e.g. 20 to 30% of Triton-X100) and small drops) in the aqueous radioactive sample, the water forming micelles (microscopically The size distribution of these the scintillator which are stabilized by the emulsifier. micelles and how this can be influenced is not yet completely understood. Also the limited stability of the emulsions, which can even break up into several phases, makes their use
777
Radioactivity
778
for
metrological
purposes
measurements:
principles
and practice
difficult
Liquid-scintillation counting offers, in general, several advantages for metrological purposes, especially its versatility (more than 60 of the important radionuclides have already been measured by LSC and its possible high efficiency (4x-geometry). But it has also serious disadvantages because, in addition to the chemical and stability problems encountered in source preparation, the counting efficiency is often but poorly known. Due to quenching, i.e. absorption of the light produced by the radiations from the radioactive sample, which is caused by impurities (especially oxygen), by sample heterogeneity, colour quenching, etc., the counting efficiency of LS samples is never equal to the theoretically possible lOO%, especially for low-energy radiations as those from 3H, etc. Therefore, the determination of the counting efficiency is a most important part of accurate LS measurements, which are essentially comparative (relative) assays. Several methods have been proposed for the experimental determinations of the LSC efficiency; but most of them call for standards. Therefore, metrology laboratories should be able to of standards for LSC: internal standards (75.4. 3 ) prepared from supply a variety calibrated radioactive aqueous solutions for the individual LS measurement conditions, unquenched ("ideal" solution) standards for the determination of optimum measuring conditions and efficiency calibrations, and differently-quenched standards prepared from standard solutions, for the efficiency determination using the channel-ratio method or the external- standard method. All these standards must be prepared quantitatively, as must the sources from the original solutions; but the stability, homogeneity and accuracy of the standards should be the best available today. The preparation of metrological LS sources follows widely the guidelines discussed in the preceding chapters, but some special problems must be mastered. In order to avoid disturbing phosphorescence, the whole procedure of source preparation and subsequent storage (and the storage of the materials used) should, when necessary, take place under red light or in the dark. Also the strong evaporation of organic solutions causes problems, and may necessitate the application of extrapolation techniques (weighing at subsequent time intervals) after deposition, and extrapolation to the time zero). A proposed standard procedure for the preparation of LS sources, especially standards, is to pipette about 0.1 ml of the radioactive solution into a 100.ml bottle or Erlenmeyer flask, weigh it by the pycnometer method (73.3.3.3) or the extrapolation method, add about 50 ml of the scintillator solution and reweigh the filled bottle (if necessary again by the extrapolation technique). It may be important to shake the mixture very thoroughly (10 minutes mechanically) in order to get homogeneous "real" solutions, which can then be filled in the normal way into vials (83.3.2.2). Instead of this method which implies premixing of the scintillator and solubilizer and, finally, the radioactive solution, all the parts can be filled quantitatively into a container and mixed there. But one must make sure that the weighings exclude non-negligible losses of volatile organic solutions. A method of mixing after sealing was used by Garfinkel et al., (1965) in the calibration of the NBS tritiated-toluene radioactivity standards. 3.3.4.4.
Gaseous
sources
Some radioactive substances must, or can advantegeously, be measured as gases, e.g. In this case the compounds, etc. 3H, 14C02, *'Kr, 331'333Xe, Rn, some metallo-organic classical (vacuum) equipment for the handling of gases is needed for the preparation of Such a samples for the generally used measuring method, internal gas counting (75.4.4). vacuum line for radioactivity work involves not only the stainless-steel tubing, currently in use, but also accurate temperature and pressure-measuring devices, combustion ovens (eg. for H,O to H, or CH,), freezing traps, calibrated volumes for quantitative mixings, etc. An important problem is also the suitable admixture of a carrier gas to the active Most gaseous samples, especially in order to prevent wall adsorption, etc. component, But special standards, are filled into ampoules with easily breakable seals (Fig. 3-4). ampoules could be for measurement in ionization chambers, such as are used in SIR. "gaseous sources" are flow standards, needed to monitor gaseous special Very Other effluents from nuclear installations, etc., which are available commercially. gaseous standards needed for applications are environmental standards, but their preparatin and use is quite similar to the preparation of sources for high-accuracy internal gas counting. 3.3.5.
Special
3.3.5.1.
laboratory
General
sources
and special
and soecial
source-ureoaration
techniaues
techniaues
While sources of the types discussed in 73.3.3. and 73.3.4. are used in the vast special sources are sometimes needed for particular majority of radioactivity measurements, Their preparation will be described briefly in 873.3.5.2. 3 and 4. Other applications. electrolytical deposition on special procedures can only be enumerated here, namely: (Verdingh and Lauer, 1967; thick or thin (foil) backings (Talvitie, 1972), electrospraying 1971; G.C. Lowenthal and H.A. Wyllie, HN, p, 353, 1973), molecular plating, Verdingh, deposition from organic solutions, electrophoresis (Verdingh, 1971), use of isotope (mass) separators (Landgrebe, et al., 1970) or lasers (Murnick and Feld, 1979; Hurst and Payne,
Radioactivity measurements: principles and practice
779
1984), vacuum evaporation, sputtering, distillation, transfer by recoil, sedimentation, (Van Audenhove and Joyeux, 1972), surface adsorption, painting, mechanical processing precipitation, ion exchange, chromatography, solvent extraction, differential absorption, etc. And radioactive atoms introduced into molecules of organic surface-active substances, such as stearates, can be used to prepare sources on monomolecular-layer (MML) films of The preparation and use of such MML have recently been calcium and barium stearates. reviewed, with references, by Watanabe et al. (1987) and by Dobrilovic et al., 1986). 3.3.5.2. Snectrometrv sources and other verv thin sourcee For the spectrometry of a or fl particles or of low-energy 7 or x rays, very thin sources are required. Preparation on thin foils improves the energy resolution and reduces the disturbing effect of backscattering. In general, such sources do not need to be For many applications electrodeposition and vacuum evaporation prepared quantitatively. (volatilization from a hot filament) may be the most suitable techniques (Bambynek and Reher, 1967). Only in extreme circumstances, are more refined methods necessary (Reher et al., 1982). Of course, the difficult deposition of radionuclides in an electromagnetic or in general - used only for a laser separator yields the thinnest sources, but these are research work. The quality of thin sources is best described by their contribution to the FWHM (Full Width at Half @ximum) of measured spectral lines. However, it would be quite useless to try to reduce this contribution far below the limit that is set by the resolution of the For the best commercially available detectors, these limits are today detector system. 12 keV for 5.MeV o particles, 4 keV for electrons, 0.15 keV for approximately as follows: 5.9 keV x rays, 0.5 keV for 122-keV 7 rays, and 1.8 keV for 1.33.MeV 7 rays, or better (see Ch. 4). 3.3.5.3. Multi-gamma-ray
sources
Sources emitting 7 or x rays of one or more different energy values and emission probabilities in known ratios are often used for calibrating defined-solid-angle devices. For 7 or x radiations above about 30 keV, and also, to a certain extent, electrons, This can be defined-solid-angle counters must be calibrated for the energy range used. done by means of a set of x- and y-ray standards of single radionuclides with photon energies distributed over a useful range (e.g. rGIAm, "'Cd, 57Co, r3'Ce, "'Hg, 51Cr, rz7Cs, 54Mn, %b, %c, %o, '*Y). But a single measurement with a calibrated mixture source would be more practical. Such mixed sources are available commercially, but the relative emission probabilities change considerably with time and require frequent corrections. Single nuclides having a complex spectrum and a long half life are therefore preferable. Such calibrated sources are e.g. rszEu (0.1 to 1.4 MeV), r3'Ba (30 to 400 keV), '**Ta (58 to 1231 keV), etc. Although the emission probabilities for the different photon energies are well-known, corrections for correlated (coincidence) summing must always be applied, because the radiations are emitted practically simultaneously. Some mixtures of a few T-ray emitters are also recommended for calibration purposes, expecially a 125Sb-'5'Eu-'55Eumulti-T-ray and x-ray standard, which has 18 peaks between 25 and 1600 keV, has a useful life of more than 10 years, and needs only small coincidence-summing corrections. Samples of certain a-particle emitters are also useful as multi-y-ray and x-ray sources for energies between 20 and 500 keV. Accurate photon-emission probabilities can be determined, provided that the decay data are sufficiently well known, because a-particle activities are in general easy to measure. 3.3.5.4. Other special laboratorv sources There are many other types of source that may have to be prepared and occasionally measured by radionuclide-metrology laboratories. Such are the long-lived, rigid (metallic, if possible), low-activity standards for o particles and x rays, as, for example, 235U, natural uranium, and 239Pu. An even more useful group includes sources of moderately long life and intermediate activity, such as %o, rJ7Cs or 9c(Sr + Y). Sources of %o prepared by irradiation of samples of 59Co, the only stable cobalt isotope, in a nuclear reactor provide extremely useful laboratory standards for different purposes and for many years. Simulated or "mock" standards (that are not generally recommended) and radionuclide generators ("milking cows"; sometimes referred to as "isotope generators") effectively extend the periods of availability of short-lived radionuclide sources, while maintaining, usually for medical purposes, the advantage of their rapid decay. Simulated standards are mixtures of longer-lived radionuclides, or sometimes single radionuclides, emitting gamma rays of approximately the same spectral distribution as the one to be simulated. The most important example is that of mock iodine, i.e. the simulation Of r3r1 (T& = 8 d) by a mixture of 133Ba (T = 10 a) and r3'Cs (Tb = 30 a), maybe ti with a cadmium filter to absorb x rays. An isotope generator comprises a column containing
a longer-lived parent nuclide
780
Radioactivity
measurements:
principles
and practice
(e.g. -MO, 66 h) adsorbed on to some resin from which a short-lived daughter (in this exMore than one hundred such systems are known ample, ggmTc, 6 h) can be eluted as needed. (Lebonitz and Richards, 1974; Knapp and Butler, 1984), about ten are available commercially, and some play an important role in nuclear medicine. Special laboratory sourcesmust sometimes be prepared for special applications, such 7 rays (6.13 MeV from 238Pu/13C (a,n), Robert et as, for example, sources of high-energy x-ray sources (Knoll and Rogers, 1982, large-area or largeal., 1977) ) ultra-low-energy and Line-shaped or wire-like sources for the volume sources for contamination measurements, calibration of ,9-ray spectrometers. In order to complete this enumeration of special sources it is appropriate to mention for the labelled compounds (Welch, 1977), neutron sources (Cierjacks, 1983), and sources M&ssbauer effect (Gibb, 1976) for x-ray flourescence-spectroscopy systems (Dzubay, 1977), and for activation-analysis detectors and standards (Schneider, 1973). However, sources included in this group are, in general, prepared only by specialized laboratories. 3.4.
EVALUATION
OF RADIOACTIVITY
3.4.1. Characterization 3.4.1.1.
Results.
MEASUREMENTS
of the results
correction
of a radioactivitv
measurement
factors
Referring to a statement already made in a more general context (see 72.2.1), the result of a radioactivity measurement is to be described by the "best value" for the This "best value" is normally the activity and a realistic estimation of its reliability. No result should be arithmetical mean calculated from all partial results obtained. discarded without a cogent reason. Each individual result may be considered as being more or less affected by various of the disturbing influences for which corrections must be made, e.g. by multiplication Each method calls for a different set of such result by appropriate correction factors. correction factors the values of which vary from one experimental configuration to another. It is useful to write down this fact in a single analytical expression that should be If M denotes the with most pulse-counting methods. used throughout, where applicable, B+ and I+ those of background and interfering radiations, number of counts registered, during the measuring period, T, and R the respectively and both properly corrected, including dead-time losses, pile-up (random correcting factor for finite time resolution, summing) and accidental coincidences, we can write for N(t,), the number of disintegrations occurring during T and referred to the time t,, as
or
N(t,)
=
(MF-B+
N(t,)
=
(MR
-I+)GPQCDAHWESZ, B+- I+) F Z
The factors G, P, _........., following corrections:
Factor
(3-7)
(with their overall
product
equal
to F) represent
the
Effect
G
geometry
P
decay-scheme-dependent
factor
= 4rrsr/n,rf; correction
(e.g. r-ray-emission
source effects
Q
(anisotropy of emission, inhomogeneity, source geometry);
source, C
absorption, attenuation and of the detector;
D
detector
A
electronic
H
higher-order effects, fluorescence radiation;
W
"wrong
radiations",
E
finite ility,
energy discrimination including summing;
S
coincidence
Z
decay
Three
(3-6)
very
response pulse
during
useful
and
scattering
shaping,
between
including
(efficiency)
influence
secondary
scattering
energy-to-voltage
radiations,
(threshold
and absorption
the surfaces
of amplifier
e.g. 7 rays in p-ray
probability);
of the source
conversion;
time constants,
e.g.
in the
annihilation
and delays; or
induced-
and zero-detection
probab-
detectors; or window)
summing; the measurement
applications
and conversion
of an analytical
to the reference
expression,
such
time,
as Eq.
to
3-6,
can be
Radioactivity
measurements:
principles
and practice
the evaluation seen immediately in the definition of efficiencies, If Eq. 3-7 is inverted, ments, and the calculation of uncertainties. MR
781
of relative one obtains:
measure-
- B+ - I+ = N(t,)/F = N(t,)e = M
,
(3-8)
This equation shows quite clearly which is the definition of an overall efficiency, B. conditions, even, that efficiencies are not set a priori, but depend on the experimental For practical purposes it is, therefore, in general necessary possibly, on the decay rate. to separate the count-rate-dependent and the decay-scheme-dependent parts from the overall In any case, efficiency efficiency and to define efficiencies as instrumental constants. definitions should be fully explained. Equation 3-6 also helps one to understand the advantage of relative measurements. If the source to be measured can be compared with a very similar standard, so that c = cSt, all corrections cancel, and it follows that N(t,) = N(t,),,(MR - B+ - I+)/(MR - B+ -I+),t
(X-9)
= N(t,),,(M/M,,) If the source and the standard accordance with Eq. 3-6.
differ
in any
respect,
then
corrections
Finally, it is evident that an analytical equation is needed overall uncertainty from the component uncertainties, using the (Eq. 3-38). 3.4.1.2.
General
orinciules
for reliability
are
necessary
in
for the calculation of an error-propagation law
statements
A result of a measurement is of little use if it is not accompanied by a statement on In calculating the best value (or the mean) of a how reliable it can be considered to be. reliabilities have to be taken into account. number of individual results, their "Reliability" is not a generally accepted term with a clearly defined meaning, and the important question of how it should be expressed by a numerical value is treated in very in the abundant literature (Topping, 1962; ICRU, different and rather controversial ways 1968; Bevington, 1969; Ku, 1969; Dietrich, 1973; Wagner, 1977; Mfiller, 1979a; Romanowski, 1979; Ferro Milone and Giacomo, 1980; Miiller, 1984). were elaborated by a working group A few years ago, simple and clear recommendations of experts from eleven national laboratories and issued by the BIPM (1981a). These recommendations have been found useful and satisfactory in many applications, especially in international comparisons of activity measurements. They are as follows: The uncertainty in the result of a measurement generally consists of 1. several components which may be grouped into two categories according to the way in which their numerical value is estimated: A. Those which are evaluated repeated determinations; and B. those which
are evaluated
by
applying
statistical
methods
to a series
of
by other means
There is not always a simple correspondence between the classification into categories A or B and the previously used classification into "random" and uncertainties. "systematic "systematic" The term uncertainty" can be misleading and should be avoided. Any detailed report of the uncertainty should consist of a complete list of the components, specifying for each the method used to obtain its numerical value. 2. The components in category A are characterized by the estimated sl) and the number of variances, s:, (or the estimated standard deviations degrees of freedom, ui. Where appropriate, the covariances should be given. The components in category B should be characterized by quantities uf, 3. which may be considered as approximations to the corresponding variances, the existence of which is assumed. The quantities u: may be treated like variances and the quantities uJ like standard deviations. The combined uncertainty should be characterized by the numerical value 4. The obtained by applying the usual method for the combination of variances. should be expressed in the form of combined uncertainty and its components "standard deviations". applications, it is necessary to multiply the 5. If, for particular combined uncertainty by a factor to obtain an overall uncertainty, the multiplying factor used must always be stated.
782
Radioactivity measurements: principles and practice
Proposals similar to the above (3 and 4) regarding the estimates of category-B uncertainties (i.e. those not amenable to statistical analysis) were also made by Jaech (1973; see his "systematic-error"variance) and continue to be used (see ANSI, 1987, p. 23) at facilities, established by the then U.S. Atomic Energy Commission, for the processing nuclear materials. It cannot be denied that some arbitrariness always remains in the assignments of uncertainty, and that the conditions for a probabilistic treatment are never completely However, this is not really disturbing as long as the terms used are clearly fulfilled. defined and every reported numerical assignment is fully explained, in such a way that a reanalysis, under different hypotheses, would equally well be possible. In the case of activity measurements, the quantity being measured is itself subject to But even when a constant quantity is measured repeatedly, the results random fluctuations. obtained deviate from each other. The amount of this dispersion, which is normally expressed as a variance or standard deviation, is an inverse quantitative measure of the repeatability of measurements, provided they are taken by the same observer, using the same method and the same instruments, at the same location and under the same conditions of use, within a short period of time. However, when some or all of the above conditions change (in a specified manner) between individual measurements, one speaks of reproducibility (see ISO, 1984). The term accuracy is applied to any estimate of the closeness of the agreement between the result of a measurement and the true but unknown value of the measured quantity. On the other hand, the term precision (expressed as a variance or standard deviation, that include repeatability and reproducibility) is used for expressing the closeness of results among each other. These two terms, if explained in detail, are the most important for the characterization of a measurement. Precision should m be confused with accuracy. It is very clear and must be accepted that an overwhelming number of metrologists in many scientific disciplines have an inkling as to the meaning of the terms "preclusion" and "accuracy" as they relate respectively to "random" and "systematic" uncertainties. The Webster dictionary gives a definition of "systematic" as in "systematic bias". It is also clear that these terms overwhelmingly dominate the scientific Literature, often ambiguously, and will probably continue in use for decades hence (see, for example, INDC, It is therefore important to take cognizance of the present "state of the art" if 1985). one is to continue to enjoy the privilege of reading about the work of our colleagues, past, present and future. In the first place, it is of the utmost importance when giving an estimate of the uncertainty associated with the measurement of a physical quantity that, as has been stated above, the nature of the uncertainty be clearly stated and its method of estimation be fully explained so that it can be "unscrambled" and reassembled in any other way to suit the requirements of the reader and possible user of the datum. The three principal statistics for estimating random uncertainty are: the standard deviation or its square, the variance, of an individual measurement; the standard deviation of the mean (sometimes called "standard error") or its variance; and the confidence level of the mean given for a stated confidence limit, e.g. 68, 95, 99 percent or any other suitable Limits. The terms "error" and "uncertainty" are almost synonymous, but the latter may perhaps be preferable in most contexts: Unknown to the observer his result may actually be the "true" value, and therefore have zero error, but the uncertainty is never zero. So often in reading the scientific literature, a measurement of a quantity is quoted with an appended fU with no indication at all as to which estimate of the three statistics mentioned above has been used, nor with any indication as to whether an estimate of systematic uncertainty has been included. Quite often an average of several measurements will be given togerher with an estimated standard deviation, and one is left to speculate whether it is the actual standard deviation, or that of the mean which is n* times smaller (see Eq. 3-23 below). In assessing the magnitude of possible systematic uncertainty, an estimate by an The former will experienced experimenter may be quite different from that of a novice. know his equipment and its capabilities and may be able to estimate its maximum conceivable limits of systematic bias. As no such estimate is likely to be better than 10 percent, let alone 1 percent, it can be considered to be approximately equivalent to the 90 or 99 Some observers find that they can estimate such percent confidence-Level statistic. systematic uncertainty more readily at the 68.percent level of confidence (73.4.2.1; and Miiller, 1979a), but so be it. It is, however, essential that the level of the estimate and the manner of combining it, linearly or in quadrature, with any estimates of other always -be stated. systematic uncertainties and with the random uncertainties m Some uncertainties may start as "non-random" but gradually take on the nature of randomicity. Such might be the dead time of a detector system which may have been measured only once or twice at the initiation of the system, but many tens of times, after a few weeks.
783
Radioactivity measurements: principles and practice
3.4.1.3. Some basic statistical concewts and definitions * The result of a measurement can be regarded as a random quantity, x, which may be If x takes on only discrete values (e.g. 0,1,2,...) then the discrete or continuous. expectation value, E(x), is defined as E(X) = C xjP(xj)
3
(3-10)
j where P(x,) is the probability of finding x=x3, and the sum is extended over all possible values XJ. Similarly, if x is continuous, one has E(x) = s x f(x)dx
l
In OL
3.4.1.3 a
recent.
and
sxtensivs
3.4.2.3
paper
by
.J.
us*
w. Ma1er
,
(3-11)
1% made (1984a).
where the function f(x) is called the probability frequency whole range of existence of x.
The integral extends over the
The variance, o'(x), is defined as o'(x) = E([x-E(x)]') = E(x')-E*(x)
.
Its positive square root is called the standard deviation.
(3-12) The ordinary moment (of order
r) of a random variable, x, is defined by m,(x) = E(x=)
,
(3-13)
and the central moment (of order r) by r,(x) = E( [x-E(x)]=)
Hence
PI(x) = 0
and
/Am
(3-14)
= E([x-E(x) 1’)
= d(x) = m,(x) -m:(x). It should be noted that this relation is valid quite generally, irrespective of the The only assumption required is that the first two ordinary moments distribution of x. exist (i.e. are finite). independent of each other, whereby this If two random variables are not interdependence may be from very weak to very strong, they are said to be correlated. Formally, an observed correlation of the variables x and y can be described by the definition of their covariance, Cov(x,y), where Cov(x,y) = E([x-E(x)l[y-E(Y))) (3-15)
= E(xy)-E(x)E(y) Two special cases are worthy of note: if x = y, it follows that
Cov(x,y) = G(X),
and if x and y are independent, then
COV(X,Y) = 0.
It is often practical to form
the
Cov(x,y) P(x*Y) = ___ 0(x)0(y)
correlation coefficient, p(x,y), defined by
9
(3-16)
which lies always between the limits -1 and +l. If x1 and xz are two random variables such that x1' = a,x,+b, and x2'= a,x,+b,, where alI b lI a2 and b, are constants, then the following rules will be useful: E(x;+x;) = a,E(x,) + a,E(x,) + b, + b,
,
l
for expectation values:
l
for variances: 02(x;+x;) = a+2(x,) + 2.,%+(x,) + 2a,a, Cov(x,,x,)
(3-17)
,
(3-18)
Radioactivity
784
l
for covariances:
l
for correlation
measurements:
principles
Cov(xi, xi) = 8182 Gov(x,,x,) coefficients:
p(x;,x;)
and practice
(3-19)
>
= p(x,,x,)
For a1 = az = 1 and b, = b, = 0, one obtains
(3-20)
the important
relation
uZ(xl+xz) = 02(x,) + 02(x,) + 2Cov(x,,x,)
(3-21)
According to Eqs. 3-12 and 3-15, the terms on the right-hand side of Eq. 3-21 contain differences of expectation values, i.e. values that could only be known after taking infinite numbers of measurements. Because this is not possible, especially with radioactivity measurements, one has to use approximate values. Such an approximation is the sample mean of n measurements 4 1 x
1-
Further,
I
:xj j=l
n
(3-22)
it can be shown, and it also follows
from the first rule of Table
3-5. that
02(x) d(a)
=
(3-23) n
is n This important result indicates that the variance of the mean value of n measurements It is, however, measurement. only of an individual times smaller than the variance strictly true for large numbers of observations and should used with caution for n less than 5. If we define
the
sample variance 1 s2(x) = n-1 z
it can be shown
by n
jc_1(xJ-z)2
f - EZ
(3-24)
that E(s2) = o'(x)
%'
A generalized each multipled
(3-25)
form of Eq. 3-21 can be obtained by extending it to n random variables, by a constant factor, a,; in other words, xl' + xl is replaced by
z
=
+
alxl
+x2
+...+
a&
(3-26)
=
j=l whence n
d(z)
=
will be used This equation propagation of uncertainties. 3.4.2.
Statistical
3.4.2.1.
Probabilitv
evaluation
1 +?(XJ) j=l
in
+ 2 1 a& j>k
73.4.2.3
for
of radioactivitv
distributions:
the normal
COV(X,,Xk)
deriving
a
(3-27)
general
expression
for
the
measurements distribution
do not reproduce exactly the same values. An Repeated measurements, in general, infinite, or at least very large, number of repetitions would be needed in order to find the distribution function which gives the probability to obtain any particular value of the This function is called the parent distribution (of the parent populvariable considered. ation). Any finite number of measurements is taken as a sample of the parent distribution. This means that the characteristic parameters of the parent distribution (mean, variance and higher moments) can be estimated from finite samples and are, in mo.st cases, sufficiently good approximations.
It is often assumed ("Gaussian") distribution
that the results from repeated (see 82.3.5 and Fig. 2-3).
measurements
follow
a
normal
785
Radioactivity measurements: principles and practice
(x-P)2
1
P(x) =
-h
0(2*)
(3-28)
exp (- -), 202
The Gaussian for the probability frequency, where p and oz are its mean and variance.* It distribution is a two-parametric, continuous and symmetric (about the mean) function. is often used for the statistical evaluation of experimental data because of its relative simplicity, although the experimental data are sometimes not distributed completely normally [but are leptocurtic or platycurtic (Aitken, 1949; Romanowski, 1979)]. The normal distribution has many times been tabulated, mostly as a standardized normal distribution, 1
P(z) = (2*?
exp(-z2/2)
,
(3-29)
* This is, however, only true for IE(x)-XI << E(x) and large numbers of events. where
x-IJ -, 0
z=
(3-30)
or as its integral, the "Gaussian" error integral or error function, ~G(z) =
J" P(E) de a
,
(3-31)
with the lower limit a = 0 or -z or -m (see, for example, Abramowitz and stegun,
1965).
It should be noted that
P(z)dz = I
(3-32)
0 The best (unbiased) estimates of p and o2 of the parent distribution from a sample of n measurements, as indicated in Eqs. 3-22 and 3-24.
are calculated
Using the normal as the parent distribution, it is possible to calculate the probability of finding a result, x, within the interval from (r-o) to (r+o), namely 68.3%. The probability, P,, of x to be found between (p-w) and (r+co) can also be calculated by using the error function, Eq. 3-31. The results for the most frequently used confidence limits, c, [i.e. the probability that a result will lie within the confidence interval between For statistical correctness, for limited sample (/J-cu) to (r+co)l, are shown in Table 3-5. size, c should be replaced by Student's t value (o is the selected confidence level, and P?V u is the number of degrees of freedom), but this is only clearly different from c for low values of n, and far from the mean value (Aitken, 1949; Joiner, 1969).
Table
3-5
Confidence level for normal distribution, P,, as a function of the confidence interval. *co
0.674X
0.5000
1.645
0.9000
2.327
0.9800
1.0
0.6827
1.960
0.9500
2.576
0.9900
1.177**
0.7608
2.0
0.9545
2.807
0.9950
* 0.674
is called
the "probable
**2 x 1.177 = 2.355 = FWM
error”,
(full width
because
4.0
PO.6745
at half maximum,
= 0.5
see 73.3.5.2
786
Radioactivity
measurements:
principles
and practice
At this point it may be well to reemphasize that the standard deviation of an individual observation, x, about the mean value, oand that of the mean, TI, are parameters that apply only for a population, namely a %'ery large, if not infinite, number of observations. The estimators of these parameters for a small, or limited, sample are usually designated as sx, the estimated standard deviation, and sthe estimated standard deviation of the mean. The Student-t factor can be used to esti&te the interval (? ts-) within which the mean may lie at a given level of confidence (e.g. 95 or 99 percent), f'sr as few as two observations n (i.e. u = n - 1). In this case, for n = 2 and u = 1, t is, of course, very large, namely 63.657 at a confidence level of 99 percent. But for as few as six readings it has already dropped to 4.032, and then, as implied above, it rapidly approaches c in value as n increases. Finally it should be mentioned that an estimated standard deviation has also its uncertainty the relative value of which, $for the case of a normal population and due to limited sampling, is equal to 1/[2(n-1)] (see Cramer, 1946; Miiller, 1979a). Table
3-6 gives
the corresponding
Table X,Y: a,b:
variables constants (positive
Function
estimated
Variances
3-6
variances.
of some common
functions
or negative)
Variance
z = ax + by
G(z)
z = axy
sZ(z)/zZ = sZ(x)/xZ + sZ(y)/yZ + 2Cov(x,y)/xy
z =
ax/y
= a%s(x)
sZ(z)/zZ = sZ(x)/xZ + sZ(y)/yZ - 2Cov(x,y)/xy
z = axh
s(z)/2 = bs(x)/x
z = a&x
s(z)/2
z = a ln(bx)
+ b's'(y) + 2 abCov(x,y)
= bs(x)
s(z) = as(x)/x
Uncertainty components which cannot be estimated by applying statistical methods (i.e. the recommendations and discussion of non-random components of category B, to which or, at 73.4.1.2 apply) must be evaluated "by other means", i.e. by auxiliary measurements As is pointed out in the above-referenced recommendguessing". least, by "intelligent it is highly important that the result of a measurement be accompanied by a ations, detailed list of all the uncertainty components indicating their values and the way in It is up to the experimenter to use all his experience and which they have been obtained. imagination in order to track down unsuspected influences that might falsify his This may be attained by extensive variation of important parameters or by using results. All these procedures must be reported in different instruments and independent methods. full detail, if the result should not run the risk of losing its value. Experimenters often neglect covariances even if the measured quantities involved are This can lead to considerable errors in the uncertainties stated, not really independent. as has been illustrated by Mannhart (1981) in a simple example involving the use of three well-characterized gauge blocks by three different experimenters, A, B, and C, to derive, for the same length. We have taken the liberty of between them, two different variances but the help of only two of his with three gauge blocks, borrowing his illustration These two experimenters set out to measure a given length of xs, equal to 25 colleagues. mm, in different ways that yield quite different values for the variances if correlations The lengths of the three gauge blocks chosen for the purpose, are not taken into account. together with their estimated standard deviations and variances, were as follows: Length (mm)
Estimated std. devn. (pm)
Estimated variance (gms)
50
0.05
0.0025
15
0.03
0.0009
10
0.02
0.0004
Radioactivity measurements: principles and practice
787
3.4.2.2. The statistics of radioactive decay: the Poisson distribution All the statistical considerations discussed above apply to measurements of radioactivity, but, in this case, an additional feature must be taken into consideration, namely the statistical character of the radioactive decay itself (see 72.3.5). The quantity usually measured, a count rate, is not an invariable physical constant, but a stochastic quantity, the expectation value of which has to be determined. Even under ideal conditions (no "systematic" or other non-random errors) and after applying appropriate adjustment for radioactive decay, repeated count-rate measurements do not yield the same result, but are The probability distribution function that governs the distributed around a mean value. radioactive decay is the single-parameter, asymmetric, Poisson distribution, based on a decay probability equal to
1 - emXr, namely
P(x)
=
fix e-p X!
,
(3-33)
where x = 0, 1, 2... Its most important property is that its variance and mean are equal (see NCRP, 1985, TB.3.5), i.e. 02(x)
=
E(x)
=
(3-34)
/J
Thus, in the case of radioactivity measurements, a single result may already be regarded as an estimate of the mean of the parent Poisson distribution and of its variance. The corresponding relation for count rates, r, is
(r/t)‘,
s, = M&/t = (rt)yt =
(3-35)
where M is the accumulated number of counts in the measuring time, t. A consequence of Eq. 3-34 is that the estimate of the relative variance, s~M*=l/M, can be reduced to any small value by increasing t and, thus, the number of the counted events. For not too low numbers of counted events (say above M = 50, Hilaire, 1973) the Poisson distribution may well be approximated by the normal or "Gaussian" distribution. In this case, the latter, normally characterized by two parameters (JJand o) can be used with a single parameter, by means of the Poisson relation, p = 02, or M/t2 = s',. But before this approximation can be made, tests should be made to determine whether the Poisson distribution is appropriate. Otherwise, the two-parameter normal ("Gaussian") distribution must be used, which is often the case in low-level measurements (Hilaire, 1973). 3.4.2.3. Combined uncertaintv:
"error oronaaation"
Let us return to Eq. 3-27, where the variance of a linear function,
of the n random variables, xJ, is described. Let us further consider the more general case where z is replaced by some differentiable function f(x,,x,,...%) and see what happens to us(f) if each variable, xJ, varies by a small amount which is of the order of its statistical uncertainty. Any such function can be developed into a power series, in the neighbourhood of a given reference point, e.g. the point defined by the mean values, T. If each variable changes from T to si, + Axj, the beginning of a Taylor expansion may be written as 6f f(x,,x,,
,‘h) = fG,,x,,
,51”) + c” j=l
where terms of second and higher compared with the associated 4's.
Axj +
,
order in Axj can be neglected Thus one has
Af = f(xl,x,,...) - f(TI,,S;,....)=
(3-36)
6xj
n 6f 1 Axj j=l 6x,
if the Axj's are small
,
which has nearly the same form as Eq. 3-27. Therefore, we can now write propagation law for uncertainties, also called the error-propagation law, as
02(f) =
6f 2 c" &Xj) j=l (16x,
+
2 1 6f 6f j>k dx, 6x,
Apart from the partial derivatives of at least approximately, the only quantities products and power functions, the use of For the most frequently great advantage.
COV(X,,Xk)
(3-37)
the general
(3-38)
the function f which can always be calculated, needed are the corresponding sample values. For estimated relative variances, sz(x)/x2, is of encountered functions of one or two variables,
Radioactivity
788
measurements:
principles
and practice
The first experimenter measures x3 by comparing it with 1, + .& = 25 mm, and, ignoring any uncertainty arising from his own measurement, he computes the variance of xj to be var(x,) = var(P,) + var(P,) = 0.0013
(3-39)
pm2
The second experimenter measures xJ as the difference x2 - x1, where xz = 1, + I3 = 60 arising in his own measureand x1 = 1, - 1, = 35 mm, and, again ignoring uncertainties ments, calculates the variance of xg as mm,
var(x,) = var(x,) + var(x,) = 0.0063
pm2
,
using
var(x,) = var(ll) + var(P,) = 0.0034
pm'
,
and
var(x,) = var(P,) + var(P,) = 0.0029
pm’
(3-40)
(3-41)
would have given an Combining these last two results, in equations 3-41, in quadrature The reason for the discrepancy between the results overall variance equal to 0.0069 pd. of the two experiments lies in the fact that the second experimenter used the gauge blockI, to obtain both of the values x1 and x2, which causes he taken this into account, he would have obtained var(x,) = var(x,
a correlaion
that he neglected.
Had
- xz)
= var(x,) + (x2) - 2Cov(x,,x,) = 0.0029
+ 0.0034
= 0.0013
/Xl? (
Thus because Cov(x,,x,) = var(P,). the same as that by the second.
the uncertainty
2 x 0.0025
, (3-42)
obtained
by
the first
experimenter
is
experimenters should report with their results, not only variances, but Therefore, At least, the reported uncertalso covariances or correlations, where this is possible. This is only ainty components should be separated into uncorrelated and correlated ones. possible if the experiment is described in detail, especially with respect to measurements Cases similar to the above example are frequent in radiohaving certain parts in common. in measurements of decay constants and coincidence nuclide metrology, as, for example, If the experimental data are used for large-scale evaluations (e.g. of neutroncounting. capture cross sections), possible correlations between all data must be considered. Such evaluations are in general made using matrix ents are then assembled in a variance-covariance matrix with the individual variances of the measured variables as off-diagonal terms.
3.4.2.4.
Statistical
The uncertainty componcalculus. (usually called covariance matrix), in the diagonal and the covariance
testing
results of It is often useful and necessary to test the soundness of experimental radioactivity measurements by statistical procedures. A decision is then sought whether are compatible with theoretical predictions at a given level of the observed data Such tests may concern the randomicity of a set of repeated measurements, the probability. significance of a measured count rate above background, the assignment of two independently measured mean values to the same population ("Student's t test"), or the identification of two variances, differing in value, with the same population ("F test"). In each cause a characteristic "test parameter" is derived from the data and compared The underlying distributions are generally the with the theoretically expected value. Poisson or the normal (Gaussian) distribution, and the theoretical predictions for various If the value of the degrees of probability are reported in tables (see e.g. CRC, 1985). experimental parameter exceeds the expected value, the data must be rejected. in the so-called "analysis of variance" or of Both F and t tests are involved "covariance". If this interesting procedure is to be applied, the measurement scheme should laboratories) can be be designed so that component variances (e.g. within and between studied. (Also see Paule and Mandel, 1982). As important as being able to analyse results by statistical methods, is the need to to such analysis. design an experiment in such a way that the data are best suited experimental design are the Latin, Graeco-Latin and orthogonal Examples of such And an expert in the creation of such designs was W. J. Youden squares (Fisher, 1949). who coined the phrase that an experiment was a considered course of action aimed at Examples of his design are the Youden answering one or more carefully framed questions. three quantities against each other in every combination. diagram and his measuring describing such experimental designs have been reprinted by H. Eleven of his publications H. Ku (1969).
Radioactivity
measurements:
principles
and practice
789
In the statistical analysis of data, if the number of independent experimental data is test (Pearson, 1900) is often the limited, but not too small, the so-called chi-squared This test is a special application of the most suitable.
) nx
for u = n - 1 degrees
(3-43)
i=l
of freedom.
from the estimator The numerator in this equation differs only by the factor n/(n-1) is equal to X, the estimator of sz of the variance (I' , which for the Poisson distribution if the observed data follow a Poisson distribution, the value of the mean p. Therefore, L2 (= sz/X) should tend to unity as the number of observations, n, increases. Any large and deviation from unity is a measure of non-Poissonian, or, in the case of radioactivity (non-"Gaussian") behaviour. n large, non-normal is a rather complex function that allows the The Pearson chi-squared, x2, distribution where 0 < x < mn to be calculated as a probability of the values of x2 exceeding x, with the distribution. function, only, of the number of degrees of freedom associated Values of the probability for different values of x2 can then be computed for different degrees of freedom and tabulated (CRC, 1985), or plotted (Fig. 3-6).
5
10
15
20
25
Chi-squared , X2, for different probability levels, Fig. 3-6 dependence on the number of degrees of freedom, Y .
P,in
namely, the sum of In the same paper Pearson (1900), derived a simple statistic X2, the quotients of the squares of the residuals divided by the expectation value, that is distributed as chi-squared, i.e.
(0,
- Ei)*
x2 = 1 i where Oi is the ith assumed distribution classes.
(3-44) E,
and E, is the experimental observation, of the experimental data, and the sum
expectation value for the is over all i groups, or
Radioactivity measurements: principles and practice
790
As an example of the chi-squared test for the goodness of fit, we will explain its application to a series of measurements of the number of counts, xj, observed a large number of times from a long-lived radioactive source, during the same, and suitable, fixed intervals of time. If j = 1, 2, . . . ..M. and the frequency fj is the number of times that each number xj was observed, then n. the total number of intervals is
and N, the total number of counts registered, is
Let us now compare the frequency distribution fj of xJ of a Poisson distribution, -x $2 e E(f,) = nP, = Xj!
with the expected frequencies
(3-45)
of counts, N, and that has the same expectation value (mean), and the same total number CPj = 1. We then enter these values into the statistic X2 (Eq. 3-44) of the chi-squared distribution, to give
x2=
M [fj- E(fj)12 1 j=l E(fj)
(3-46)
Table 3-7 gives a simple numerical example of the application of the chi-squared test in which the calculations are explained step by step. Table 3-7 - Example of a x2 test 1 j
XI
fj
1
5
1
5
0.038
1.48
-0.48
2
6
0
0
0.063
2.46
-2.46
3
7
3
21
0.090
3.51
-0.51
4
8
4
32
0.113
4.41
-0.41
5
9
6
54
0.125
4.88
1.12
6
10
10
100
0.125
4.88
5.12
7
11
7
77
0.114
4.41
2.59
8
12
5
60
0.095
3.71
1.29
9
13
2
26
0.073
2.85
-0.85
10
14
1
14
0.052
2.03
-1.03
11
15
0
0
0.035
1.37
-1.37
n
=
N =
Xjfj
Pj(p=lO)
E(fj)=nPj
fj-E(fj)
39 389
j = index for classes
xj = number of counts for j-th class fj = frequency of intervals with Xj counts in a total of n intervals Pj = Poisson probability for observing Xj, given its mean p, estimated by X = N/n = 389/39=10 "
=M-2=9 -51
-5
E(fj) = n X
x2= x,!
M [fj 1 j=l
_
E(f,)l' = 12.47
E(fj) + P = 0.20 (see Table 3-6)
Radioactivity measurements: principles and practice
The range of xj should be between 5 and 20. If it is much to pool the data in a more convenient number of intervals.
791
larger, it is preferable
Further, the number of degrees of freedom, u, the only parameter of the X2 distribution, must be determined. It is equal to the number of classes, M, minus the number of restrictions placed upon the empirical data, here equal to two, due to the estimation of the mean and the common value of the total number of counts. Thus v = M - 2. Finally, the "experimental" test parameter X: can be compared with "theoretical" values xi,r (Fig. 3-6), and the hypothesis (e.g. Poisson behaviour) is rejected with probability P, if X$ > X:,,. Alternatively, the probability P that the hypothesis can be accepted may be derived from Fig. 3-6 by noting the value of P at the point where X$ = Xg p. P can also be regarded as the probability that Xf will exceed its theoretical value in a repeated measurement. In practice, a hypothesis is usually accepted, if 0.1 < P < 0.9, and rejected strongly for 0.02 > P > 0.98. 3.4.2.5. Further statistical problems in radionuclide metrolopv 3.4.2.5.1.
Consequences of the Poisson distribution and its distortions
As radioactive decay is governed by the Poisson law, all properties of the latter In particular the sole (Haight, 1967) can also be applied to study radioactivity. parameter of the Poisson distribution, the mean count rate ii, can be measured by several methods different from the usual counting of the number of disintegrations in a given time interval. For example, the fluctuations of the output current of an ionization chamber can be used to measure the current itself (variance = mean), thus avoiding problems from high direct currents (Oda et al., 1976; Lux and Baranyai. 1982). Also the measurement of the mean time interval, 2, between pulses is equivalent to the measurement of the mean decay rate (B = l/6). Other relations involving the Poisson distribution that could conceivably be used to measure decay rates are those between adjacent probabilities such as, for examor the different moments about the mean M, = ii, M, = ii, M, = ii +3ii2, ple, nP, S = FP"_iB or about the origin, ma = ii + ii2 (Miiller, 1978). But, in addition to the Poisson frequency distribution, other distributions can or must also be used for the description of radioactivity phenomena. This is expecially the case for the Poisson interval distribution, that is, the distribution in size of the intervals between successive events. This follows from the probability-frequency distribution, based on the probability of no event occurring in the time interval from zero to t, combined with the probability of one event occurring in the time interval between t and t + dt. This combined probability, dP,, equal to the product of the two separate probabilities, is -zit iidt = [(Tit)'e /O!] Kdt dP, = P,,,,ii =Tie -ntdt
.
Radioactivity
792
measurements:
principles
and practice
To understand this, consider an experiment in which a detector is used to record the counts, Na+b for a time f,+b from a source "a" plus background, and then to record the for a time 4; that is, with the source removed, and probably an background count, N,, inactive dummy source in place of the active source in order to reproduce the scattering of environmental radiation into the detector by the source. And let ta+b + tb = T. Suppose 2 s,, si are the estimated variances of the source and background count rates, ra and r,,, and Thus st is let si be the estimated variance of the source "a" derived from Na+b and N,. the unknown "true" variance of L-,, of source "a", and s"d = s=il+ + szb which is equal to B So that, in general, si must be greater than s,, and especially so when Na+b/t'.+b + N,/t’,. r, and rb are of comparable magnitude. Thus the background radiation will tend to broaden the frequency distribution of the net count rate. In general it is, however not important to distinguish between s, and sd, particularly bearing in mind the large uncertainty associated with the standard deviation, referred to in ~3.4.2.1. Therefore, in order to avoid unnecessary confusion we will only consider s,. If the total measuring time, T = f.+b + tb, is limited, measurements of low levels of activity, then we may ask how subdivided in order to minimize the variance, sf of the net sample answer, consider the summation of the component variances of sza as sza
=
=
as it may well be in that time may best be count rate, ra ? For an given by
sza+b + SZb
(3-48)
N a+b -*-
Nb (3-49)
t:+b
tzb
By differentiation 2s, ds,
=
N a+b Nb - 2 dt,, - 2 dt,
and, by above
setting
question
ds, = 0
and
dta+b + dt, = dT =O,
is then obtained ta+b -=-
(Knoll, ra+rb
(3-50)
t3b
t:+b
as T is
constant,
the answer
to the
1979) as
r, (3-51)
(
tb
Tb )
This relation is also derived in NCRP (1985, p. 306), and its use is there illustrated by means ofa nomogram devised byR.Loevinger and M.Berman,from which an optimum division of counting times between source and background can be chosen in order to give a desired level of uncertainty in a minimum total time of counting. If it is possible to vary certain parameters of the counting experiment, such as the kind of detector, the source configuration, the impurity rate, and the pulse-height discrimination, one may want to measure r, to within a given relative uncertainty, u, equal to It then = sz - (N,+J/t' a+G)
NJ/t'b
(l/T)[r,+, (1 + tb/t.+b)
= (l/T) [ra+&+(@,+b)‘) =
(l/T)[rF+,
r,(l
&+b)/tbl
+ rb(l+(rs+b/&
Radioactivity
measurements:
principles
and practice
793
sample treatment (impurity reduction, etc.), and selectivity, volume ( etc.), radiation A similar, but more complex figure of merit can also be defined for spectrometric price. methods (Knoll, 1979). It should also be mentioned that background subtraction present particularly complex problems (see 74.11.4.1.1).
in spectral
analysis
may often
Another statistical concept concerning background is the "minimum detectable activity" For many applications simple which is defined in different ways in the literature. definitions are sufficient, as, for example, the minimum detectable activity is one that give.s rise to a count rate of three times the background standard deviation (ICRU, For low-level measurements and some 1972b); or to one tenth of the background count rate. 1983; refined statistical definitions are needed (Sumerling, applications more other Currie, 1984). The statistical investigations above are valid for any digital pulse-counting system. But they are also valid, in a somewhat modified version, for analogue systems, especially These are connected, for current-measuring devices such as ordinary ionization chambers. to a current-measuring instrument, and the via an integrating RC filter, in general, statistical fluctuations of the measured current can be described by the root-mean-square (rms) deviation, which is equivalent to the standard deviation in digital measurements. Thus analogue and digital measurements are statistically equivalent (Weise, 1971), but each of them has advantages for particular applications. 3.4.3.
Corrections
3.4.3.1.
for svstematic
Dhvsical
effects
General
The accurate measurement of radioactivity is always a complex procedure. In general, applied to the directly measured data. This is especially many corrections have to be But the same, although mostly true for direct (sometimes called absolute) measurements. if the unknown and the much smaller, corrections must be applied in relative measurements, The individual corrections can be very different reference source are not exactly alike. counting, coincidence counting and for the various methods, especially for single-channel Therefore, only the general aspects of the different corrections peak-area measurements. referred to the simplest will be discussed in this report, and it is, where possible, The subdivision into physical and instrumental analytical method described in 73.4.1.1. because they may involve overlapping corrections cannot always be completely consistent, effects. 3.4.3.2.
Backpround
and interfering
radiations
the presence of a radioactive source. Every counting system yields counts without is normally measured under exactly the same conditions as for the This "natural background" In general, source of interest, using an inactive but otherwise identical dummy source. any interfering radiations, e.g. from impurities, are added to the natural background and For singlethe sum, the "extraneous counts", is treated as a second radiation source. it is simply subtracted from such as defined-solid-angle counting, channel measurements, For coincidence measurements and spectrometry, the definition and the source count rate. The possibly different coincidence treatment of the backgrounds can be very difficult. (and the behaviour of the background and the sample, and the peaks in the backgrounds background below the peaks in spectrometry) cause serious problems (Jorch and Campbell, (See later in this section.) 1977; Miiller, 1983). environmental radiation (especially The components of the natural background are: of the r3'U and 232Th series), radiation from zzzRn, 'OK, e5Kr, and from the radionuclides rays (minimum-ionization muons, high-energy and cosmic from the detector material, Different measures must be taken to reduce nucleons, and wide photon-electron showers). these different background components. In general, also any kind of electronic noise and but one always tries to set the discriminpick-up is included in the natural background, For some systems this could be a ation level high enough to eliminate any noise influence. The root-mean-square noise is, in such delicate problem (e.g. proportional gas counters). This and the cases, best described by the equivalent number of electrons and their energy. discriminator-threshold adjustment can then be controlled with a low-energy-radiation source, e.g. 3'Ar or 55Fe. the effect of which must be subtracted together with the The interfering radiations, Nearby accelerators and neutron natural background stem from several different sources. sources (up to several hundreds of meters away), or sample changers can cause direct disturbing radiation, and both, as well as the sample itself, can induce activation in the and subsequent radiation (e.g. detector (e.g. "Na or lzsI in NaI(T1) and its environment, Especially important can be radioactive contamination of the sample, reactions). (n,% and also possible contamination both initial and any introduced during sample preparation, With care and modern high-resolution spectrometry these effects can be of the detector. corrected for satisfactorily. The backgrounds
of individual
counting
systems
vary
strongly,
depending
upon
the kind
Radioactivity
794
measurements:
principles
and practice
and size of detector, and the shielding. Therefore, only very approximate general figures Some very special detectors, such as a thin layer can be given. of ZnS(Ag) on a thin plastic disc, when unshielded, show backgrounds in the energy range from 0.1 to 6 MeV of from only one to a few counts per minute; ordinary, small, gaseous counting tubes can have background counts of several tens to several hundreds of counts per minute; NaI(T1) and other scintillators a few counts to several thousands of counts per minute depending on the measuring conditions (a 3" x 3" Na(T1) detector, shielded by 5 cm of lead, could register about 10 s-l above 10 keV, and semiconductors about an order of magnitude greater, per unit volume). Proper shielding reduces these backgrounds by one to two orders of magnitude and special procedures, especially anticoincidence shielding, again by a similar factor. Several measures must, or can, be taken to reduce backgrounds. First, the electrical installation must be designed adequately. One single efficient (5 to 10 ohms) ground connection without loops is absolutely essential, and the insertion of an efficient wide-frequency-band filter at the output of the main power supply is strongly recommended. Furthermore, the electrical shielding of the whole equipment should be complete, Also shielding against other atomic or nuclear radiations is, in general, essential. Usually the detector and the counting chamber are placed inside a lead enclosure (e.g. Fig.5-2). The optimum size of this enclosure and the thickness of the lead shielding depend on the use of the detector. Larger enclosures show smaller wall-scattering effects, but smaller ones are cheaper. The thickness of the lead does not, in general, need to be greater than 4 to 8 cm (99-percent reduction of 2-MeV gamma rays at 8 cm), because greater thickness contributes only little. The lead shield could be supplemented by the addition of some neutron-absorbing material, e.g. boron-loaded concrete or plastic, at its outside. And at the inner surface, the shielding could be improved by a lining of lower-Z materials, e.g. 0.8 mm of cadmium and 0.5 mm of copper or steel, in order to improve the absorption of low-energy x rays. For further background reduction anticoincidence and coincidence procedures must be applied. The most common is anticoincidence shielding, in which the detector is surrounded by guard counters operating with electronic circuits that reject counts that are in coincidence with guard-ring counts. The procedure can reduce the background by 2 or 3 orders of magnitude. Further reduction by 1 or 2 orders is possible by selective coincidence counting (of radiations that are coincident due to the decay considered). Finally, pulse-shape discrimination (PSD) can be rather widely used for the elimination of extraneous counts (ICRU, 1972). This method is based on the differences between the rise times of pulses from different detectors or radiations and discards pulses with "wrong" rise times. The statistical problems with backgrounds are discussed in aJ3.4.2, and background Variable backgrounds, e.g. when measuring problems in spectrometry, partially, in 74.11. more detailed treatment. near accelerators, need a 3.4.3.3.
Effects
influencirw
the efficiency
The efficiency of a counting measurement or system can be defined as the number of (corrected for background and instrumental effects) per number of detected counts Consequently every interaction of the disintegrations in the source (see, also, 73.4.1.1). radiation occurring between its origin in the source and its detection as an electrical This is indicated pulse at the output of the detector system can influence the efficiency. for the defined-solid-angle counting by the correction factors in Eq. 3-6, and is similarly valid for every counting method. The largest correction is, in general, the geometry factor, the ratio of the full The latter is the solid angle solid angle, 4~ sr, to the effective solid angle, neit. subtended by the area of the detector at the point of the source from which the radiation defined for strongly absorbable radiations (nucleons, is emitted. It is, in general, electrons and low-energy x rays) by a circular diaphragm in front of the detector and for gamma rays by the detector dimensions. Mostly, the geometry factor can be calculated very Practical problems are accurately from the measured dimensions of the counting chamber. sometimes encountered because of source dimensions, source positioning and source-activity For the most frequently used geometry, namely a circular diaphragm, with a distribution. diameter of Za, and an axial source, at a distance z from the diaphragm, and for an arimutsimple analytical half angle 0 (Fig. 3-7a), the following ha1 angle 4 and a subtended expression holds
neff
8eff =
=
dn
/ 2n
SJ 0
= 2n(l =
O,ff sin
0
- co* 0,,,)
2s(l - z/(22 + ar)b)
zz na=/z=
(3-57)
Radioactivity measurements: principles and practice
No analytical expressions are known, except for special cases such as a = z, for axially-extended and non-axially-extended sources, but very accurate approximations are available for these cases (Jaffey, 1954).
r'
1-1
,top detector
f
I ’
I . ‘\bottom
I detector
Fig. 3-7 Defined-solid-angle counting; a) usual arrangement, b) doublecounter system, c) possible disturbance by scattering, d) baffles for reducing c). Complex corrections must, in general, be applied for absorption and scattering effects individual between source and detector. These can be subdivided into parts: self-absorption and scattering (especially backscattering) in the source; absorption in the media between source and detector (e.g. p-ray absorbers in y-ray measurements); scattering at the walls of the counting chamber (including the diaphragm); and scattering and Self-absorption in the source is of great importance absorption in and at the detector. for strongly absorbed radiations and can modify the peak forma recorded (Tq4.11 and 5.3.5.4). Backscattering in the source and at the source support can also be of crucial importance. For instance, for beta particles in 2a geometry the backscattering coefficient (the ratio of the backscatteredto incident radiation) varies between about 0.3 and 0.6 for saturation-thick backings of atomic number 7. between 10 and 80, respectively. For o particles the strong low-angle backscattering makes 2a measurements relatively inaccurate. Absorption in media between source and detector can, in general, be kept negligibly small (e.g. by evacuation, replacement of air by H, or He, or use of calculable absorbers), and scattering at the chamber walls can be minimized by proper construction and choice of materials. For CI particles, for example, the energy of the particles scattered from the walls into the detector can be kept so low, by the choice of low-2 material, that the scattered radiation is not contained in the full-energy peak (Fig. 3-8). Similarily, the height of 4ra counters for coincidence systems should be kept as low as possible, in order to minimize l-ray self-coincidences due to Compton scattering. Also the circular diaphragms defining the geometry can be constructed to minimize transmission and scattering (inner height about equal to the range of the measured radiation). The absorption and scattering in and at the detector, expecially the backscattering at its surface, are taken into consideration by the detector-response function. This describes quantitatively the spectrum at the detector output as a function of the incident spectrum. As this is a very complex function, it is usually approximated by a single parameter, the detector efficiency, defined in 115.?.1.5. An important correction, to which adequate attention is often not given, is that for the energy discrimination. In every piece of counting equipment there is either a deliberately incorporated or unintended threshold circuit, or discrimination level, which prevents pulses below a certain amplitude from being transmitted. This can influence the detector efficiency considerably (and under certain conditions can even make the detector ineffective). In general, the discrimination threshold can easily be set high enough to eliminate all instrumental noise, and possible physicalandinstrumental spurious pulses (see Campion, 1976). But it may sometimes be difficult to correct for small genuine pulses that are lost, especially at high count rates with considerable pile-up. Therefore, it is very useful to observe the direct detector output and to use additional low-energy radiation sources, such as "Ax- or "Fe, for the calibration of the discrimination threshold. Several other effects can alter the efficiency of radioactivity measurements strongly. Rather large corrections may be necessary for nuclides decaying in a complex way, especially corrections for the detection of other than the investigated radiations. For non-coincident radiations the individual efficiencies must be added, but for coincident radiations, terms proportional to(1 - *,)(z must be considered. For coincidence measurements (see q5.5),
795
796
Radioactivity
measurements:
principles
_ .~.~ +- ~--+
-0.1
I
and practice
‘4-M,S(Be)
I I
30"
60
90
120
150
Elastic scattering of alpha particles into an angle 0 ; ratio Fig. 3-8 of the energy after scattering, E(B), and the initial energy, Eo. the correction for the counting of “unwanted” radiations (e.g. gamma rays in the beta chanAlso angular correlaLions can influence the outcome of coincidnel) may become a problem. ence measurements. 3.4.3.4. Secondary radiations. second- and hipher-order effects Radioactive decay and the subsequent absorption of the emitted radiations are much more complex than described by the simple (first-order) decay or absorption schemes. Low-intensity secondary radiations and effects often interfere with, and may sometimes dominate, the detection process. This especially can be important for external bremsstrahlung, internal conversion and annihilation radia?rion. Electromagnetic bremsstrahlung, also named continuous Rantgen radiation, is always produced when charged particles (especially electrons) are accelerated or decelerated. It is always present, when radiation of any kind is absorbed, because absorption finally involves the deceleration of electrons. Consequently, every gamma-ray spectrum has a low-energy excess (with a spectrum proportional to approximately due to l/E) bremsstrahlung. This external bremsstrahlung is produced in the field of external nuclei, in contrast to internal bremsstrahlung which originates in the field of the nucleus producing the primary effect (electron capture, etc.). The intensity of the external bremsstrahlung is about 10-Z to 10m3 times that of the primary effect (beta-ray absorption, etc.), and is proportional to the 2' of the absorber material, while the intensity of the internal bremsstrahlung is still one to two orders of magnitude smaller and independent of the surrounding matter. Nevertheless, in many cases, bremsstrahlung may be the only measurable radiation (A. Spernol et al., HN, 1973, p, 169). Pure beta-ray emitters with high end-point energy, e.g. 32P, can be conveniently measured by means of the bremsstrahlung that they generate, especially if the beta particles are completely screened. Under certain conditions, this applies also to low-energy beta-ray emitters, such as tritium (see Curtis, 1972). The most frequently-assayed type of radioactive decay, that can only be detected and measured via secondary radiations, is electron capture by the nucleus (EC). Here the undetectable captured electron leaves a vacancy in the electron shell of its origin, and the central nuclear charge is reduced by one unit. The resulting rearrangement of the whole atomic electron cloud, which happens within 1O-12 to 1O-'3 s, leads to the emission of a cascade of detectable x and Auger radiation (see 72.4.5). Similar effects accompany every radioactive decay involving charged-particle emission, but here the secondary radiations are usually negligible compared with the main decay products, although the energies can be rather high; note, for example, that the binding energy of K electrons in high-Z atoms is of the order of 100 keV. Somewhat smaller energies are transferred to the recoiling residual daughter nuclei of the decaying parent atoms. But recoiling daughter nuclei from a-particle decay can cause more serious trouble, such as satellite peaks, ejection of some source substance with the recoil, and possible implantation into the detector. Another secondary radiation which can be more easily detected than the original radiation is the radiation following the annihilation of positrons. Annihilation photons are mainly produced when a positron at the end of its path, at rest, captures an electron and annihilates by emission of two 511.keV photons in opposite directions. Because a few percent of the annihilations also occur in flight (AiF) the 180° angular correlation between the two annihilation quanta, is, however, never perfect. The proportion of annihilation in flight to that at rest is greater the higher the atomic number of the can also cause material in which it occurs. Annihilation in flight some problelr,s in
Radioactivity measurements: principles and practice
797
Thus in the calibration of a %r-sZRb generator Hoppes et al. the assay of ,9'emitters. (1987) report a five-percent discrepancy between the results obtained using solid-state and liquid-scintillation detectors, which they ascribe possibly to uncertainties in the large corrections for annihilation-in-flight losses. Many other secondary and higher-order effects can influence radioactivity measurements, but they are, in general, negligibly small. Examples include one- and three-quanta annihilation, internal ionization and, or, excitation (with EC, IC and beta decay), and double and multiple processes such as double-beta decay, double Compton scattering, exotic decay (72.4.2; Rose and Jones, 1984) and environmental effects (B. Crasemann,HN, 1973, p. 33; Harbottle and Maddock, 1979). 3.4.3.5. Radioactive-decav
correction
Every radioactivity measurement is referred to a certain time, the reference time, in order to allow corrections to be made for radioactive decay. In this context the term "correction" may not be entirely correct, but it is in universaluse. The radioactive-decay law is a law of nature, as immutable as that of our own aging to which we may adjust but for which no correction is yet in sight. But because of radioactive decay, it is necessary, especially when measuring a short-lived activity, to adjust or normalize by calculation to a specific point in time, usually described as the "reference time". Most often, either the starting time (t,) or the midpoint time (t,) of the counting interval is chosen as the reference time. If the counting time is short compared with the half life, the source activity can be regarded as constant during the counting time, and no "correction" for decay during the measurement needs to be applied. For the calculation of the activity at any reference time (t,) the simple exponential formula must be used, i.e. ntr = where n
and n L
tr
nt, exp [-0.69315(t,-t,)/Tti] ,
(3-58)
are the count rates at, respectively, t, and
t,.
If the counting time is not negligibly short compared with the half life, TS, the This is a difficult problem, decay during the measurement must be taken into account. because in general the background (usually assumed to be constant) and count-rate-dependent Often background and dead-time losses must be combined with the decay calculation. In this case the midpoint of the counting interval (t,) dead-time losses can be neglected. is most advantageously taken as the reference time, and a simple decay computation can be If the counting interval is 8, the measured count rate n in the interval 8, must be made. multiplied by the factor D (Eq.3-6) to obtain the count rate at the reference time t,, i.e. %,
=
?iD @/2 exp(-Xt)dt _I-e/2
=
ne
=
Z(O.69315 S/T,)&xp(O,69315S/2T$
- exp(-0.69315 0/2TQ].
(3-59)
The factor D has relatively little effect; even for 6 = Th, it is only 0.981. Exact formulae for the combined "correction" for decay and for extending and Formulae for the combined non-extending dead-time losses are given by Miiller (1983). correction for decay and background (for negligible dead-time loss), have been proposed by many authors and discussed, e.g., by Kalantar (1983) and in NCRP (1985). Both approximate and exact formulae for combined corrections for decay, dead-time loss background have been derived by Axton and Ryves (1963), for extending and for nonextending dead times. Approximations must be adapted to the conditions considered. Of these, the relation that is used most frequently is and
"0 = [n'/(l - n'r)
--xt, / (1 - e-XB) B] e
,
(3-60)
for the reference time t, at the beginning of the counting interval of duration 8, n' the measured count rate, T the dead time, x the decay constant of the nuclide measured, and B the background count rate. Still more complex is the combined correction for decay, background and dead time in These problems are reviewed by A.P. Baerg in NCRP (1985, 73.2.5) coincidence counting. references (also see 75.5 in this Report). Difficulties also arise with many relevant This problem is always present in measurements with particle from variable backgrounds. accelerators.
4.
DETECTORS
4.1. INTRODUCTION radioactivity such as atomic and The previous pages deal with the peripherals of nuclear theory, the stochastic nature of radioactivity and the laws of radioactive decay, exposure to it), and so radiation and its interaction with matter (including man and his The rest of this manual will deal with the measurement of radioactivity in its on. various modes of decay, with the measurement of the various parameters of nuclear decay, and with the instruments and measuring systems required to effect such measurements. in their interactions Radiations, of different nature and different energies, can, with matter, produce both intranuclear and extranuclear (atomic) effects. Thus alpha particles or gamma rays of sufficient energy can produce nuclear transmutations, and they of light in the visible can also, in common with all radiations (including photons region), remove extranuclear electrons from atoms to create positively charged ions. Neutrons can interact elastically with the nuclei of atoms to produce energetic recoil nuclei, and energetic nuclear recoils also occur as a results of alpha-particle decay. provide Free electrons and positive ions or positive holes the modus operandi for all methods of electrical detection of radiation in gases, liquids and solids. The higher mobilities of electrons govern the speed of counting successive radiation events in such detectors, and the energy required to create one electron-ion or electron-hole pair in the substance of the detector determines the resolution between events of closely the same energy. The higher the mobility, the faster can events be counted; the greater the number of pairs from a given expenditure of energy, the better the resolution. The measurement of radioactivity is not limited to measuring the radiations emitted by the atoms of radioactive elements. The number of radioactive atoms can themselves be measured and related to activity by means of the radioactive decay law. Such measurements, however, usually involve rather specialized methods such as, for example, mass spectrometry, accelerator mass spectrometry, and selective laser excitation of individual species of atom. None is yet widely used in the measurement of radioactivity. 4.2. REFERENCES Nearly all of the methods, and their principles, to be considered in this section have been treated in far greater detail in other recent texts. That to which reference has been most frequently made in this Report, in order to avoid unnecessary elaboration, is the National Council on Radiation Protection and Measurements Report No. 58 (NCRP, 1985) A Handbook of Radioactivity Measurements Procedures published originally in 1978 and as a revision in 1985. This second edition contains decay-scheme data, for some 270 biomedically important radionuclides, from the evaluated-data and reference nuclearstructura files of the Oak Ridge and Brookhaven National Laboratories, from which, also, the 13 examples shown in Table 2-4 have been provided. NCRP Report 58 also lists around 750 references covering many aspects of radionuclide metrology not covered in the present Report, which is concerned more with the establishment of new radionuclide metrological laboratories. But in such an enterprise the proceedings of the First International Sumner School on Radionuclide Metrology held in Herceg Novi, Yugoslavia, in 1972, and published as a special issue of Nuclear Instruments and Methods in 1973 (HN,1973), could be of the greatest value. These proceedings contain 56 papers by outstanding experts in the field that cover practically every aspect of radioactivity measurement as practiced today, with the exception of the methods of selective sampling, anticoincidence counting, and the counting of the numbers of radioactive atoms instead of their decay rates, In these proceedings there are some 1,500 references (some of which, however, are bound to be redundant), going back as far as 1908 in the case of Campbelling (q.v.). Following the Herceg Novi Summer School and to perpetuate its aims, members of the organizing committee, with strong support from Y. Le Gallic and B. Grinberg, of WI, and the national and international laboratories active in the field, founded the International Committee for Radionuclide Metrology (ICRM). As a sequel to Herceg Novi, ICRM sponsored a seminar on Applied Radionuclide Metrology that was held in Geel, Belgium, on May 16 and 17, 1983, the proceedings of which ware published in a special issue of the International Journal of Applied Radiation and Isotopes in August 1983. These proceedings provide a vary valuable source of information on the developments in the field of radionuclide metrology that had occurred in the decade following Herceg Novi. 4.3.
The different kinds of radiation have been described in 72.4. The types of radiation arising from spontaneous atomic disintegrations are generally alpha, beta, gamma and x radiations, extranuclear electrons, neutrinos, neutrons and protons, and fission products, Measurements of radioactivity normally involve the first five of these. The detection of
799
800
Radioactivity
measurements:
principles
and practice
of ionization, neutrons and protons is also their loss of energy in matter by the process Radioactivity is an atomic other nuclei. either directly or indirectly by the recoils of and the total energy available in a radiophenomenon, involving the whole atom (72.3.21, equation, to the difference in active decay is always related, by the Einstein mass-energy Decay rates can be measurably of the daughter atom. mass of the parent atom and that altered, for example, by altering atoms or their compounds.
the state of ionization
or chemical
composition
of some
Charged corpuscular and energetic electromagnetic radiations dissipate energy in their passage through matter by ionization either directly by producing positive ions and electrons (usually free but sometimes bound to electronegative atoms), or indirectly through recoils or, in the case of photons with energies in nuclear recoils, Compton-electron excess of 1.022 MeV, by the creation of electron-positron pairs. When radiation is absorbed, an amount of heat equivalent to the energy absorbed is When free electrons, or electrons in the outer shells of atoms, return to lower produced. atomic energy levels, electromagnetic radiation is emitted either as x rays or as photons in the visible or ultra-violet range of frequencies. Radiation can therefore be detected calorimetrically as well as by measuring electrical currents or light generated in gases, liquids or solids. Energetic particles travelling in a transparent medium with velocities exceeding the velocity of light in that medium, also emit visible radiation, known as Eerenkov radiation Detectors based on the observation of Cerenkov after its discoverer. radiation have physics of nuclear reactions and the been developed, but find application mainly in the search for new elementary particles using high-energy accelerators. Accelerated or decelerated electrons also emit radiation known as bremsstrahlung. Such are the x rays that were found, by RGntgen, to be emitted when cathode rays were decelerated in solid targets. Bremsstrahlung finds some, but rather few and unimportant, applications in the measurement of radioactivity. The properties of all the foregoing types of radiation and their interaction processes rather fully in the previous sections of this report, in with matter have been discussed Knoll (1979), Mann, et al., (1980), NCRP (1985), and in many other texts. The earliest detectors of radiation were the photographic plate, crystals of zinc The grains of a photographic emulsion became sulphide and the gold-leaf electroscope. A crystal of zinc sulphide, a solid scintillator, emitted a developable on irradiation. flash of light in the process of stopping an energetic alpha particle. The gold-leaf gas-ionization chamber, the voltage on the leaves dropping electroscope was the prototype rate that was correlated with the rate of production of positive-ion-electron pairs at a The photographic plate still finds use in the detection of nuclear-particle in the gas. autoradiography but is not otherwise significantly used in measurements of tracks and in Liquid- and solid-scintillation detectors and ionization detectors, both radioactivity. are very widely used in the measurement of activity and of the gaseous and solid-state, 1980, or NCRP 1985). energies of the radiations emitted. (See Knoll, 1979, Mann et al., In order to characterize a radioactive species (radionuclide) completely one must number, the activity and decay constant, the nature of its specify its atomic mass, atomic and electric moments of it radiation or radiations, spin, parity and the nuclear magnetic level of the state of its progeny to which decay occurs, and also of the excited or ground difference in mass between parent and daughter atoms (or total energy available for the and transition probabilities of all its possible the transition; or Q value), the energies conversion electrons, such as alpha particles, x and gamma rays, and Auger and radiations and a spectral distribution and mean energy in the case of beta particles and bremsstrahlung. The instruments and processes involved in such characterizations include non-energyof various kinds of radiation and discriminating and energy-discriminating detectors nuclear photographic emulsions and accurate timing devices, macro- and micro-calorimeters, and beta-ray spectrometers, mass radiation-track recording plastic films, alpha-particle spectrometers, mass (or "isotope") separators, and a host of nucleonic instruments such as amplifiers and multichannel analyzers. cathode-ray oscilloscopes, satisfied to know their For most purposes the user of radioactive materials is specific activities or activity concentrations and purity, their decay constants and the Rarely, however, would a of their radiations, including the energy of each. nature secondary standardizing laboratory be called upon to measure or verify more than the calibrated activity and purity, and the former would usually be measured with equipment regional laboratories; and the latter using activity standards supplied by national or could often involve half-life and radiation-energy measurements. Purity (chemical and radionuclidic) should be the responsibility, however, of a reputable supplier, and nuclear specialized laboratories and published in nuclear-data data are usually produced by tables.
Radioactivity
4.4. DETECTION 4.4.1.
OF RADIATION:
measurements:
principles
and practice
801
PRINCIPLES
Ionization
was The photographic plate, in use in 1896 time for the recording of x radiographs, More sensitive the detector at hand to Henri Becquerel when he discovered radioactivity. detectors in the form of simple ionization chambers were used by Pierre and Marie Curie and The Curies used a parallel-plate air by Ernest Rutherford in their early experiments. condenser connected to an electrometer to measure the relative activities per atom of various chemicals and rocks spread in the form of a layer of powder on the lower horizontal Rutherford in his early work used the simple plate of the parallel-plate condenser. invented in 1777 by Abraham Bennet (Phil. Trans. Roy Sot. 77, 26) gold-leaf electroscope, The gold-leaf for the purpose of investigating the properties of static electric charges. in the early electroscope, in its use as an ionization chamber, found elegant expression 1930's as a measuring instrument of very adequate precision in the form of a quartz-fibre Much of the pioneering work at the electroscope designed by Charles and Thomas Lauritsen. Radiation Laboratory in Berkeley in identifying new radioactive species was carried out that has access to Any laboratory using the Lauritsen electroscope (see Fig. 4-l). calibrated standards and also has a good balance and plastic pycnometers could distribute in the range of 1.5 to 3.0%, relative radioactivity standards, with random uncertainties using the quite inexpensive Lauritsen electroscope as its comparator (Mann et al., 1980). Quartz-fibre electrometers of greater precision were developed in the late 1940's by Hugh Carmichael at the Chalk River Laboratories of the present Atomic Energy of Canada Limited.
View of a Lauritsen electroscope used for internal measureFig. 4-l ments of sources emitting a or fl particles or external photon sources (after Hunter and Mann, Nat. Res. Council of Canada Report CRM-409, 1948). radiation traverses a volume of gas it produces If electromagnetic or corpuscular In the process of ionization ionization and excitation of the gas atoms and molecules. together with free electrons. In an atomic and molecular positive ions are formed electronegative gas such as oxygen the electrons may attach to neutral gas molecules to form negative ions. radiation field is confined in an enclosure If the volume of gas in a constant containing two electrodes between which an electrical potential difference is maintained, then positive ions will move towards the cathode and negative ions and electrons towards the ionization current, flows across the gas and current, the anode, and an electric Such a device is known as an ionization chamber and the through the external circuit. value of the ionization current observed in the external circuit is a measure of the number of gaseous ion pairs created inside the chamber and therefore also of the amount of the The configuration of the chamber can vary particular radiation that is traversing it. considerably to suit the experimental requirements, but is more often than not either the former consisting of outer cylindrical and inner axial cylindrical or rectangular, electrodes, and the latter of parallel plates or grids. Positive-negative ion pairs formed in a gas will, unless drawn apart, recombine. On introducing a small voltage difference between the electrodes of the ionization chamber the ion pairs will be separated and start drifting to the respective electrodes, but at low On increasing the voltage, and therefore the still voltage recombination occurs. occurs until a maximum current, the velocities of the ions, less and less recombination saturation current, is achieved (See Fig. 4-2).
Radioactivity
802
measurements:
principles
and practice
z e
2 --_---I
E ._ 5
I
Plateau region
.; 0
Applied voltage
Saturation Fig. 4-2 chamber. 4.4.1.1.
Pulse-ionization
curve as obtained
with a typical
ionization
mode
If the ionization chamber is provided with an external RC circuit similar to that ions of electrons towards the anode and positive shown in Fig. 4-3, then the movement the high resistance R, towards the cathode will induce a pulse of voltage V, across where V, is a function of time t. The shapes of these pulses are illustrated in Fig. 4-4. The electron mobilities are some lo3 times greater than those of the positive ions so that the initial sharp negative slope shown is due to the movement of the electrons away from the cathode, and the slower return of the pulse tail is due to the inductive effect of the The larger R, the smaller is the slower movement of the positive ions towards the cathode. current flowing in the external circuit. 0
Td
T
t 00
i
IX
I
I
t*
I
I
I
=
Principle of a parallel-plate ionization chamber. A single ion pair is assumed to have been formed at time t = 0 (after
Fig. 4-3
Mann
et
al.,
1980).
Typical pulse shapes obtained with a parallel-plate pulse Fig. 4-4 ionization chamber, as a function of time, t. The dashed line is for a single ion pair, the solid lines for a number n of ion pairs, where RC>> RlCl > RxC2 . The ionization chamber is thus able to generate a steady current output in a constant radiation field, or to operate in a pulse mode to detect separate ionizing events. For the purpose of understanding the operation of the ionization chamber as a proportional or Geiger-Miiller counter it is convenient to consider such a chamber having a cylindrical configuration operating in the pulse mode. In the direct-current mode, resistance R (as shown in Fig. 4-3) would be zero (capacitance would merely represent that of the chamber and residual capacitances), and a current-measuring device would be placed across AB. In the pulse mode, R would be large and a cathode-ray oscilloscope or (as in the case of the calibration of samples of ZZ2Rn) a pulse-recording nucleonic circuit would complete AB.
Radioactivity measurements: principles and practice
The questions considered above have been discussed in somewhat more detail in Mann et al. (1980). 4.4.1.2. Gas multinlication If. after achieving saturation, the voltage applied to the ionization chamber is increased still further, we reach a condition where the electrons accelerated towards the anode achieve velocities between collisions with neutral molecules, and therefore energies, sufficient to ionize these molecules and to create more ion pairs, and multiplication of the ion pairs, over and above those created by the incident radiation, occurs. The onset of such multiplication will occur at lower voltages in a cylindrical ionization chamber than in a parallel-plate chamber containing a comparable mass of a given gas because of the very much greater electric-field strength in the neighborhood of a rod or wire anode of relatively small radius. As a result of this multiplication of ion pairs the current flowing in the external circuit again increases with increase in applied voltage. In addition to the direct-current mode of operation, the ionization will also give rise to current or voltage pulses in the external circuit. Thus consider the situation in which a single 01 particle of, say, energy equal to 5 MeV dissipates all its energy in the gas of the ionization chamber. The average energy, W, expended by a, ,9 or -r radiation in creating one ion pair when traversing the gas a gas-ionization chamber is a quantity that has been measured for a variety of gases for different radiation energies (ICRU, 1979a; Niatel et al., 1985). For such gases, W lies in the range of from 25 eV to 35 eV per ion pair, so that a 5-MeV a particle that expends all of its energy in the gas will create of the order of 1.5 x lo5 ion pairs in the chamber. The application of the principles of gas multiplication to the development of detectors capable of recording single radioactive events can best be considered in terms of a cylindrical ionization chamber with an anode of wire having a small cross-sectional radius. A voltage is applied between the outer cylindrical cathode and the wire anode by means of a circuit similar to that shown in Fig. 4-2 and the chamber is filled with a pure electropositive gas so that any primary ionizing event occurring in the chamber will give rise to positive ions and free electrons without the formation of negative ions. We "ill suppose that N ion pairs are formed within the gas filling of the chamber when a single ionizing event occurs within it, and will consider the number of electrons and positive ions that will be collected at the electrodes for different values of the applied voltage V. For zero voltage V applied to the chamber, the N electrons and N positive ions will either recombine in the track of ionization or move randomly until they are neutralized within the chamber. If the primary ionizing event occurs when a voltage is applied to the electrodes that is less than that necessary to give the saturation current in the steady state, then a fraction of the ion pairs will be collected and a voltage pulse V, would be detectable across AB. When the voltage V is greater than that which would promote a saturation current from a constant source of radiation, then essentially all the N ion pairs from a single primary event would be collected and a voltage pulse similar to those shown in Fig. 4-4 for the two shorter time constants, R,C, and R,C,, would be detectable across AB. This functional relationship between the number of collected ion pairs and the applied voltage is illustrated in regions I and II of Fig. 4-5, for two cases in which ionizing events forming respectively 10 and lo4 ion pairs have been hypothetical primary assumed. In Fig. 4-5 region I is that region of applied voltage where recombination occurs, and region II is that of saturation where essentially all of the initially formed ion pairs are collected. 4.4.1.3. Voltare nulses from sinele radiative events The boundary between regions II and III in Fig. 4-5 represents the onset of gas multiplication which has already been discussed rather generally for the case of the direct current arising from a constant source of radiation, for either a parallel-plate or cylindrical geometry. In more detail, however, one must remember that the electric field, E, is constant between parallel electrodes, but is inversely proportional to the radius, r, from the axis in the case of the cylindrical geometry. The field gradient, the rate of change of E with r is therefore proportional to l/t. Thus E becomes very large as r becomes very small. In other words the electric-field intensity in a cylindrical detector with a fine-wire anode can become very large close to the wire anode. Thus secondary ion pairs, formed by collision, will be mostly generated in the immediate vicinity of the anode wire. 4.4.1.4. The nronortional region In a cylindrical detector with a wire anode, multiplication will begin on entering region III from region II, with increasing applied voltage V, and it will further increase
803
Radioactivity measurements: principles and practice
804
Applied voltage,V
Number of electrons collected vs applied voltage in a gasFig. 4-5 ionization detector. (I) recombination, (II) saturationl (III) proportional, (IV) Geiger region. The lower curve is for Nl = 10, the upper curve for N2 = lo4 ion pairs formed in a primary event. The dashed ordinate L indicates the onset of limited proportionality (see text). (After Mann et al., 1980). with increasing voltage as the electric field becomes sufficient to impart enough to free electrons at greater values of the radius r to cause secondary ionization.
energy
In the lower-voltage part of region III the numbers of electrons and positive ions to the number of ion pairs, N, formed collected, n, at any given voltage V is proportional in the primary ionizing event. Thus n = MN where M is known as the multiplication factor, and region III is known as the proportional region. Pulse detectors operating in counters, this region are called proportional The higher-voltage part of region III is known as the region of limited proportionality because the number of ion pairs collected is no longer proportional to the number of ion pairs produced in the primary ionizing If we consider two primary ionizing events the one resulting in N, and the other event. in N, ion pairs, where N, is about 10 and N, about lo", then it can be seen that above a certain applied voltage L (Fig. 4-5), n1 and n2, the numbers of collected ion pairs corresponding to N, and N,, tend to equality. At a voltage A (Fig. 4-5), the ratio nz to n1 is closer to 10 than to lo4 for N, and N, equal to 10 and 1,000, respectively. The gas multiplication of region III contrast with no gas amplification in region where the multiplication of proportionality change in applied voltage, V.
amplification, in is sometimes called gas Region II is also, of course, a region II. factor M is unity and remains constant with
Because the amplitude of the output pulse is proportional to the number of ion pairs formed by a primary ionizing event in the saturation or proportional regions of a gasenergy operating in the pulse mode, such detectors can be used for ionization detector completely in the sensitive region of spectrometry provided that the radiation is stopped The output-pulse amplitude is slightly modified, however, if the primary the detector. ionizing track is not parallel to the wire or electron-collecting plate of the detector. The secondary electrons may be collected at the anode in the order of 1 /bs, but the thousand times longer to reach the cathode. If the positive ions take of the order of a ionizing track is oriented at a considerable angle to the cathode then there may primary collection of the positive ions that are also be a considerable lapse of time between the The induced potential at the anode due to cathode and further away. formed close to the the positive ions moving away from it will therefore be smeared out in time and the To overcome this in the case of a particles in distorted. electron pulse correspondingly wire grid intermediate a parallel-plate chamber, Otto Frisch placed a fairly transparent anode in such a manner that all the a-particle in voltage and between the cathode and SOUL-ce on the cathode ended on the cathode side of the grid. In this tracks from a manner the electrons reached the anode in a very short time to give a short voltage pulse the grid from the inductive effect of the receding and the anode was also shielded by Good a-particle energy spectra were then obtained. positive ions. This device, known as the Frisch-grid pulse-ionization chamber, is now only of passing interest because a-particle spectrometry can be more conveniently carried out using surface-barrier for a particles detectors silicon detectors and solid-state operation of silicon detectors for electrons. The the gridded lithium-drifted is discussed more fully in Knoll (1979) and Mann et al. (1980). pulse-ionization chamber The cylindrical pulse-ionization chamber is, as mentioned above, used for the detection and assay of radon in air, but in that application it is essential to remove the electronegative oxygen from the air. 4.4.1.5.
The Geieer
region
1n the proportional region the chain multiplication process in which one electron can produce large numbers of ion pairs is known as a Townsend avalanche. A primary ionizing
Radioactivity
measurements:
principles
and practice
805
length along event will normally produce a cluster of such avalanches whose magnitude and This the anode wire will be determined by the size and disposition of the primary event. cluster of avalanches is also generally limited to a short length of the wire for low that the primary event does not values of the applied voltage in region III, provided extend for much of the length of the cylindrical chamber, and the cluster will spread along the wire with increasing applied voltage. As the applied voltage is increased up to the threshold of, and into, the region of field increases in the proximity of the anode wire limited proportionality, the electric Campion (1968) has also shown, using and the Townsend avalanches increase in magnitude. them, that the number of photons emitted by an electron-multiplier phototube to observe deexcitation of the atoms and molecules in the ionized plasma near the anode wire also the ion sheath, or plasma, increases with increasing voltage (i.e., with the size of from the cathode photons, in turn, release photoelectrons around the anode wire). These and anode of the wall, and these photoelectrons again traverse the gas between cathode avalanches, and secondary pulses ("after ionization chamber to cause further Townsend pulses") at the anode wire. Some four or five such photon pulses of diminishing amplitude were detected by the phototube in a time that "as of approximately the same duration (2 to 3 +z) as the duration of the electronpositive-ion pulse illustrated in Fig.4.4. is increased through the Concomitant with these developments, as the applied voltage region of limited proportionality, is the creation near the anode wire of a positive space charge that will wipe out the high electric field near the wire and terminate the process of gas multiplication. As the positive ions move away from the anode the high-intensity region will be restored. lower-voltage Thus in the true proportional region (in region III of Fig. 4-5 on the side of L) the Townsend avalanches are relatively small and photon emission is not so great as to destroy the proportionality between the primary ionizing event and output pulse. As the applied voltage is increased through the region of limited proportionality more and more photons are emitted from the Townsend avalanches near the anode wire, with more photoelectrons emitted practically simultaneously from the cathode (c = 3 x 1O1' cm s-l), and The the Townsend avalanches begin to spread along the whole length of the anode wire. but the more slowly moving positive ions form a electrons are quickly collected, positive-ion sheath around the anode wire and the induced pulse on the anode terminates as When the applied the positive ion sheath moves out towards the cathode and is collected. voltage is so high that the electron-ion sheath envelopes the whole length of the wire, This region is the ionization chamber is said to be operating in the Geiger region. When operating in the Geiger region, at a given illustrated by region IV in Fig. 4-5. applied limits, primary more.
chamber are, within statistical voltage, the output pulses from the gas-ionization all equal in amplitude, irrespective of the number of electron-ion pairs in the ionizing event whether it be one electron-ion pair or many orders of magnitude
On raising the applied voltage above that corresponding to the upper limit of region IV, the ionization chamber will begin to develop multiple pulses, not necessarily related to any applied voltage, a ionizing event occurring within it, and, on further raising the continuous electrical discharge with the emission of light can occur. For complementary 4.5. GAS-IONIZATION COUNTERS
details
DETECTORS:
see Mann
et al.
IONIZATION
(1980)
CHAMBERS.
PROPORTIONAL
AND GEIGER-MijLLER
radionuclide metrology. Gas-ionization detectors have been the "work horses" of They can be divided into two broad types of instrument, namely those with steady-current and outputs. those with pulse In the former there is a great diversity of instruments, while in the latter there are grid-shielded pulse-ionization chambers, and proportional, GeigerMuller and spark counters. These last the spark counters find no application in routine radionuclide metrology and are used mainly for high-energy-particle detection. And pulse-ionization chambers, as mentioned in 74.4.1.4, have been largely replaced in metrological applications by solid-state ionization devices. 4.5.1.
Ionization
chambers.
As mentioned earlier, the gold-leaf electroscope was one of the first ionization instruments to be used for quantitative measurements of radioactivity. This instrument was the precursor of a great many other instruments such as the Lauritsen electroscope, the Carmichael electrometers, pocket dosimeters, free-air chambers, cavity chambers, reentrant chambers (on which the present radionuclide calibrators or "dose" calibrators used in the assays of photon-emitting radiopharmaceuticals are mostly based), and also pressurized ionization chambers, and internal ionization chambers into which radioactive gases such as can be introduced for assay. tritium r:in the form of [3H]-HzO) or 14C (as [%-CO,) Many of these chambers and their applications have been discussed extensively and in detail in NCRP (1985, 77 3.11, 4.4, and 6.4.3.2.3). In particular the evaluation and use of the calibration "K factors" (activity per saturation current) for different photon-emitting nuclides is discussed in those sections.
806
Radioactivity
measurements:
principles
and practice
Almost every application of a gas-ionization chamber to radionuclide metrology is as a relative-calibration instrument. In other words, the chamber must be calibrated in terms of a radioactivity standard sample and the K factor measured for a given radionuclide. The only exception is the activity calibration of a photon-emitting nuclide using a cavity ionization chamber of known volume, that is generally air-filled. This method is described in NCRP (1985, 83.11.2). But its use requires a knowledge of the emission probabilities per decay for all photons emitted by the radionuclide in question, and the difficulties in constructing and maintaining such a chamber places it more in the purview of a national laboratory. Gas-ionization chambers are operated in a region of applied voltage such that the value of the ionization current is saturated (region II in Fig. 4-5). In this region of saturation current the exclusion of electronegative gases is not necessary, so that Lauritsen and Carmichael electrometers, and gas-ionization chambers at atmospheric pressure, are normally filled with air. However, in national and international laboratories the calibrations of activity, for many photon-emitting radionuclides. are normally maintained, or checked, using reentrant ionization chambers containing argon or nitrogen at a pressure of about 20 atmospheres (= 2 MPa) (see 74.4.3 and Figs. 74 and 75a in NCRP, 1985). Direct activity calibrations of radionuclides which emit, say, beta particles and gamma rays are obtained using a fundamental, or direct, method such as @-y-coincidence counting. If the radionuclide is short-lived (e.g. 1311, with 8.02.day half life) the calibration is preserved, or maintained, by measuring the saturation current when a known volume of a solution having an activity A of the radionuclide, usually contained in a flame-sealed glass ampoule, is placed in the reentrant finger of a pressurized-argon ionization chamber. Saturation ionization currents range from 10.' to lo-l3 A and must be measured by one of several methods available (NCRP, 1985, 74.4.6). If R is the measured readout due to the saturation ionization current, I, then the calibration "K factor" is defined as K = A/R. or response, R, (The readout is normally proportional to the saturation current I.) The "K factor" is inversely proportional to R and is in the nature of a reciprocal efficiency. As long as the current response of an ionization chamber is stable over long periods of time, then any other solution of that radionuclide with activity A’ can be calibrated by measuring the saturation current obtained on placing an eaual volume of solution, in a comuletelu similar ampoule, in the fame position within the reentrant finger of the ionization chamber, and measuring the new response R’. The activity A' of this second solution of the same radionuclide is then equal to AR’/R, or KR'. For assurance of reproducibility over extended periods of time, the stability of measuring its of an ionization chamber is usually checked (or monitored) by response to a long-lived reference source (or sources) at the same times that R and R’ responses Such long-lived reference sources may consist of sealed sources of "Co or are measured. with its 7. la7Cs, but are most frequently well-sealed metal capsules of z26Ra inequilibrium in terms of a radium-226 reference for convenience, ray-emitting daughters. Continuing, source, then if the responses to the long-lived source are RRa (at the time of measuring R) source or for and R;, (at the later time of measuring R', either for the old radionuclide are the respective (but not a new batch of the same radionuclide), and if AR,, and 46 necessarily known) activities at the earlier and later times, a "K factor", KRa, can be And defined for the reference source such that KRa is equal to A&RR. or to A ka/Rka (i.e. the ratio of ionization currents), should be equal R&JR,,, the ratio of responses making the two measurements on the to As',/&,, the ratio of activities at the times of reference source. function of the decay But the decrease in the ratio A&/A,, is a simple, calculable, If *=Ra, in equilibrium with its r-ray-emitting constant of the reference nuclide. If the is the reference material, then its decay amounts to 0.05% per annum. daughters, ratio Ak,/A,,, then good is found to decrease in like proportion to the ratio R;,/RR, stability and reproducibility of the ionization-chamber system can be presumed. of calibrations of short-lived radioactivity Another approach to the maintenance standards by means of an ionization chamber is to define a "relative K factor", KR, equal where R and R are still the observed responses (ionization currents) for the to AR&R, of interest (of activity long-lived reference source and for the short-lived radionuclide subsequent date it is desired to calibrate one or more new If at any A), respectively. only necessary to obtain samples of the radionuclide of interest (e.g. lJII), then it is calibration sample and to the old, long-lived, and R.& to the new the responses R’ In this when placed in the same geometry in the same ionization chamber. reference source to be calibrated means the same context, the same geometry with respect to the new sample volume and density of solution in an exactly similar glass ampoule. The activity (or activity interest is then given by A’
concentration)
A' of the new
sources
of the radionuclide
= K,R’/R,,
Apart from any calculable radioactive decay the value of R/R’ will be equal decay, will reflect some departure from unity, other than for radioactive
of
(4-l) to unity. A"Y instability or
Radioactivity
measurements:
principles
and practice
ionization-chamber system (inclusive of geometry or source characteristics) change in the investigated. In effect therefore, the activity calibratshould be and, if significant, in terms of ions of shorter-lived radionuclides, such as '"'I or even %o, are preserved the application of this method in the ionization chamber and the reference source. In the ionization chamber could be uncertainties can be tolerated, cases where larger "chirper" which, in pocket dosimeter or even a pocket replaced by an electroscope, device. conjunction with a timer, can be used as a radiation emission-rate-response 4.5.1.1.
Quality
4.5.1.1.1.
control
In national
usinp
an ionization
chamber
laboratories
long-lived reference source Not only can an ionization chamber in conjunction with a standards from previously made calibrations, but such a be used to prepare new batches of to check new direct ("absolute") used in national standardizing laboratories system is Thus standardizations against previous direct standardizations of the same radionuclide. batches of s°Co solution standards might have been prepared by a national standardizing both 1970 and 1980. In the laboratory using the method of coincidence counting in, say, amount of the solution can be flame-sealed in a standard glass first calibration a 3-ml ionization chamber in terms of a ampoule and its "relative K factor", Ks: measured in an encapsulated, sz6Ra reference source, or in terms of two or three such s2sRa well-sealed, Likewise in 1980, K, can again be measured for the new batch of "Co standards sources. that has been prepared by coincidence counting, using 3 ml of the new standard in a similar glass ampoule in the same ionization chamber and in terms of the same szaRa reference sources.
If the ratio of the 1980 to 1970 values of KR is in the same proportion as the 1980 to measured by coincidence counting, then there is 1970 values of activity concentration that have there is consistency amongst all the dilutions and measurements assurance that been made in preparing the two batches of standards. laboratories is normal use in standardizing the ionization chamber in The pressurized-argon ionization chamber (see NCRP, 1985, 74.4), in which the mass of the gas clearly remain constant. Open-air filling the chamber should (in a robust chamber) Such chambers have chambers have, in the past, also been used in national laboratories. but their response must be corrected for small given long-term satisfactory performance, changes in temperature and atmospheric pressure. The procedures
described
above
for the preservation
of a direct
calibration
(sometimes
"absolute" miscalled an calibration) for the calibration of successive batches of relative activity standards (sometimes called "secondary" or "tertiary" standards), can be applied in terms of a long-lived reference source, constant source-to-detector geometry, radiation rate-of-response (e.g. an ionization-current-measuring) and any detector that gives an output signal that is a linear function of the amount of radiation detected. 4.5.1.1.2.
International
quality
control
In the late 1960's discussions took place at the Bureau International des Poids et Mesures (BIPM) and at the International Atomic Energy Agency (IAEA) with a view to establishing international reference systems, based on ionization-chamber measurements, for the quality control of national-laboratory activity standards for both consistency within and between national laboratories. Details of the method as it was finally adopted IAEA and BIPM are given in papers by Houtermans (1970) and Rytz (1983). The latter by publication gives a detailed description and valuable discussion of the SIR programme. Soon after the death of Hans Houtermans, the IAEA international quality-assurance program was brought to a close, but that at BIPM, known as the Systeme International de Reference (SIR) program that was started in 1972 by A. Rytz (1983), continues to give the most valuable service to the national radionuclide-metrology laboratories. From the periodic data sheets issued for each radionuclide, national laboratories can learn if their calibrations agree with those of other laboratories in the international community, and, further, any major discrepancies between laboratories that become evident in the activity calibrations of any given radionuclide can indicate the need for a special distribution of split solutions, having the same activity concentration, for international intercomparitive measurements under the aegis of BIPM. The basis of the SIR program, as described by Houtermans in 1968 (Houtermans, 1970), is the measurement of equivalent activity (see below) of a photon-emitting radionuclide in reentrant ionization chamber in terms of a long-lived reference source (also see ;5.4.6.5). The reference sources adopted by IAEA and BIPM consisted of szsRa in equilibrium with its y-ray-emitting daughters contained in well-sealed metal (usually platinum-iridium) capsules.
case or, (or,
the
The quantity on the right-hand side of Eq. 4-l h as the dimensions of activity; in the of a solution standard this would be activity concentration multiplied by the volume preferably, mass of solution. This quantity is known as the eauivalent activity, A,, where sz6Ra is used as the long-lived monitor, as the radium eauivalent activity) of radionuclidic source in the ionization chamber. As Houtermans (1970) pointed out
Radioactivity
808
meaSUrement8:
principles
and practice
"the essential quantity is A,, i.e. the activity of the nuclide, which gives the same instrument response as the long-lived standard when measured under standard conditions, Of course, care must be taken to keep all conditions such as ampoule dimensions, absorption in the liquid, etc., "constant". (also see 75.4.6.5.) 4.5.2.
Prouortional
and GeiPer-Miiller counters
and Geiger-Miiller counters Proportional are gas-ionization detectors operating, respectively, in the proportional and Geiger regions (Fig. 4-5). Their cathodes are often cylindrical, but can have different shapes to suit different requirements, and their anodes, often of stainless steel, usually consist of a fine straight or looped wire of the order of 0.02 mm to 0.1 mm in diameter. The gas filling, contained within the cathode and anode insulators, usually consists of a pure electropositive gas such as argon, to which has been added up to ten percent of a multiatomic gas such as methane in proportional counters and ethyl alcohol or a halogen in the case of Geiger-Miiller counters. The function of the multiatomic gas is to absorb photons and to dissipate the energy from excited molecular levels rather than as photoelectrons. This inhibits after-pulsing in the case of proportional counters and, as "quenchers", the initiation of continuous discharge in the case of Geiger-Mtiller counters. In the Geiger region, however, alcohol molecules also expedite the spread of the positive-ion sheath along the anode wire,because the photons arising in the initial Townsend avalanche while being highly absorbed by the alcohol molecules also have enough energy to ionize a significant fraction of the alcohol molecules, thus creating a positive-ion sheath, and space charge, that helps to quench the initial discharge. Because of the creation of this positive-ion sheath the output pulses from a Geiger-Miiller counter are, apart from statistical fluctuations, all of the same size irrespective of whether the detected ionizing event in the counter consists of one ion pair or many orders of magnitude more. The ions of the main electropositive gas filling can also be neutralized on their way to the cathode, exciting molecular levels in the multiatomic gas additive, in both the proportional and Geiger regions. Also, in the Geiger region, the alcohol and halogen ions tend to dissociate as they are neutralized at the cathode instead of emitting further photoelectrons. Thus it is that a Geiger-Miiller counter with an alcohol quenching additive has a limited life, whereas the halogen atoms can recombine into molecules. Geiger-Miiller counters can also operate when filled only with a pure electropositive gas but it is then necessary to incorporate electronic quenching of the applied voltage, in the external circuit, to give reduced voltage for a time that is somewhat longer than that Proportional counters used in reach the cathode. required for the positive-ion sheath to dating are also operated with a gas filling of only carbon dioxide, but this radiocarbon must be highly purified. An argon (90%) and methane (10%) mixture is the gas filling most commonly used in gas-proportional counters, but for more penetrating radiation the higher atomic-number noble gases, krypton and xenon, may be used. D.R. Carson and R.R. Wilson in their 1948 paper on Particle and Quantum discussion of the modus operandi of gas-filled a detailed and comprehensive
Counters, give detectors.
1n typical proportional counters with a distance of a centimeter, or so, between anode collected in microseconds and the positive ions in and cathode, the electrons can be moderate But at after the detection of an ionizing event in the counter. milliseconds applied voltages, because of the limited size of the Townsend avalanche and the absence of (see large positive-ion space charges, the counter is able, with a short time constant Fig. 4-4), to record a subsequent ionizing event in the order of one microsecond. space charge there is a large positive-ion In a Geiger-Miiller counter, however, created by the positive-ion sheath that stretches along the whole length of the anode wire. longer to This can give an output pulse of several volts, but it takes correspondingly where a further ionizing event in the counter can be clear the space charge to a point In a counter of typical dimensions this inoperative time can amount to as much recorded. as 500 milliseconds. counter is the detector of choice. Therefore, for high count rates, the proportional record successive "fast" external circuitry, ionizing events It can, with special counter at rates of the order of lo6 per second. occurring in the 4.5.3.
Special
aoolications
of pas-ionization
detectors
Direct-current-reading reentrant ionization chambers operating in the saturationcurrent region normally constitute the detection systems of the so-called "dose" calibratused in the assays of radiopharmaceuticals. The output ors or radionuclide calibrators, circuitry to give a direct reading current in these instruments is digitalized by special or multiples of the becquerel, of the radiopharmaceutical or in submultiples of the curie, the chamber. other radioactive preparation placed in the reentrant cavity of and Geiger-Miiller, counters can be made in different configurations for Proportional, Many are cylindrical in design and may have special thin alumindifferent applications. Other counters ium or beryllium windows to enable low-energy radiations to be recorded. mounted to fill an aperture in the cathode may be "windowless" with the radioactive source
Radioactivity
measurements:
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809
One very widely used "windowless" design is that in which two of the counter. identical windowless counters are joined so as to form an air-tight seal around an cr- or p-particle Source mounted between them, in such a way that each counter subtends a solid Such a configuratangle of effectively 2n steradians at the source on either side of it. Either half of such a 4n counter can be used with a source ion constitutes a 4rr counter. on a solid backing to count in 2rr geometry. Examples of both types of counter are illustrSuch ated in Knoll (1979), Mann, et al. (1980), NCRP (1985) and many other publications. used almost exclusively in counters have been operated in the Geiger region but are now the proportional region in order to measure high count rates. The counting gas, usually argon (90%)/methane (lo%), is ordinarily flushed through the counters from a tank of the Specially designed 4a counters operate at pressures up to 75 atm compressed counting gas. purpose of detecting j3 particles, conversion electrons and x rays with (7.6 MPa) for the These are described by A. P. Baerg in NCRP (1985) and in the publicathigh efficiency. ions by him and his colleagues that are referenced in that report. These counters are also used extensively in the method of efficiency-extrapolation coincidence counting, also described in papers by Baerg and his colleagues that are also referenced in NCRP (1985), and later in this Report. wall
Proportional counters of cylindrical geometry are also used for internal gas counting. In this method a radioactive gas such as 3H in carrier hydrogen or 14C02 in carrier carbon gas, is admitted into dioxide, mixed with a suitable proportional-counting the counters (See 75.4.4, and also for activity measurements. NCRP, 1985, and publications referred to therein.) Because the detection and energy characterization of gamma rays depends very largely on their interaction with electrons in the Compton and photoelectric processes, it is desirable to use ionization-chamber gas fillings with high electron densities. With this end in view, work has been in progress since about 1970 on the use of noble gases in condensed These provide the only known condensed nonconductor in which form, both liquid and solid. the ion pairs created by ionizing radiation can be collected as in gas-filled ionization chambers. Of particular interest was xenon with its high atomic number. Knoll (1979) describes, with references, the stage of development, at that time, of such detectors, and presents an interesting table of some of the pertinent properties of liquid argon and xenon The cryogenic requirements for this method could clearly and of liquid and solid argon. constitute a limitation for many laboratories. 4.6. LIGHT-EMITTING.
ELECTRON-EMITTING
AND
SOLID-STATE
DETECTORS
For the reasons stated in the immediately preceding paragraph it is of interest to use detectors that have both high electron density and large stopping powers (i.e. those in the loss of energy of the radiation per unit length of path travelled is which M/h, devoted to the development of radiationFor this reason much research has been large). Of those in current use there are two detecting materials in the liquid and solid states. excited by radiation namely liquids and solids that emit light when broad categories, and the group of semiconducting crystals in which radiation can create (luminescence), and and positive holes that are collected, respectively, at the anodes mobile electrons cathodes attached to the crystals, as an ionization current. Although there has, in the past, been no Luminescence can be prompt or delayed. is now generally termed fluorescgeneral agreement in the literature, prompt luminescence and delayed luminescence is termed phos"x-ray fluorescence", ence, analogously to There is a fundamental difference between the functioning of organic and phorescence. light emission derives from the deexcitation of inorganic scintillators in that the of excited molecular energy levels of organic molecules, whereas most of the deexcitation Lattice vibrations inorganic crystals is from energy levels of the whole crystal lattice. and deexcitation from one level to another is assumed to quantized, are assumed to be bring about the emission of a quantum of elastic-wave energy known as a phonon (Hughes and Pooley, 1.975). A phosphorescent pulse decays exponentially. Because of the difference between the organic and inorganic responses a phosphorescent pulse decays in times that are of the times shorter in organic crystals than phosphorescent pulses in order of a thousand The time decay constant (the time to decay to l/e of the initial inorganic crystals. The rise time amplitude) is of the order of 10 ns for the former and 10 JLS for the latter. of such a pulse to maximum amplitude in either type of crystal is of the order of one nanosecond. 4.6.1.
Organic
Scintillators
of Organic scintillators are mostlv polycrystalline substances (i.e. consisting is stopped or scattered in such a If a, p or 7 radiation randomly oriented crystals). crystal, energy is deposited in its substance by the a or B rays, or by secondary electrons molecular levels of the constituent produced by the 7 rays and this energy can excite organic molecules that reemit the energy in the form of photons in the visible or ultraH. Kallmann in 1947 was the first to use crystals of violet regions of the spectrum. naphthalene to detect ionizing radiation by the scintillation process, and he was followed by P.R. Bell in 1948 who used crystals of anthracene for the same purpose. Because
the
reemission
of the energy
deposited
by
the radiation
event
is through
the
81 0
Radioactivity
measurements:
principles
and practice
can act as scintillators when deexcitation of single molecules, anthracene and naphthalene dissolved in organic fluids or in solid-plastic solution. The former is an example of the widely used method of liquid-scintillation counting in which the radiation energy is dissipated in the solvent and transferred to the dissolved molecules of the scintillator. added substance known as a wavelength shifter is often used to absorb Also another higher-energy (high-frequency) radiation from the prime scintillator and to reemit it at lower frequency in a suitable range of wavelength to match the sensitivity of an electron-multiplier-phototube detector. In plastic solution the energy is again dissipated in the solid material and transferred to the molecules of the scintillator. Many organic More detailed discussion of this method is given in fluors are now available. Birks (1964), Knoll (1979) and NCRP (1985). 4.6.2.
Semiconductors
and thermoluminescence
Semiconductors are crystalline materials with resistances intermediate between those and insulators. of conductors Their resistivities are also logarithmic functions of (1971) comments that the resistivity (specific electrical temperature. C. Kittel resistance) of a pure metal can be of the order of 10“' ohm cm at low temperature and that of a good insulator may be as high as 1022 ohm cm. He quotes a remark by E.M. McMillan that this range of 10z2 in resistivity may be the largest of any common physical property of solids. The properties of semiconductors are best described in terms of the band theory of insulators solids, developed from Bloch's (1928) collective electron model for crystalline 1948-49). In this theory it is assumed that in a crystal the valence (see Garlick, electrons, that bind the atoms together in the lattice, occupy electron-energy levels in a valence band, while free electrons that can move freely through the lattice occupy higher-energy levels in a conduction band. Between these two bands, as illustrated Electrons in the valence band can, in Fig. 4-6, is a forbidden region devoid of electrons. acquire enough energy from ionizing radiation, thermal agitation, or phonon however, interactions to be excited from energy levels in the valence band into energy levels in the conduction band, through the forbidden region where no electron states are allowed. Such a forbidden region is called a band gap or energy gap, the increment in energy of which is This energy can vary from less than 1 eV for semiconductors to more than 5 designated E,. eV for insulators. The excitation of an electron from the valence band to the conduction band is completely analogous to the process whereby radiant (including thermal) energy can excite extranuclear electrons in lower-energy atomic shells to higher-energy shells, or to complete freedom (ionization), through the forbidden regions between the atomic electron It is also analogous to the process postulated in the Dirac theory by which a shells. negatively charged electron in a universal "sea" of negative-energy states is excited through an energy gap equal to somewhat greater than 2mocz to occupy a positive-energy level, and the vacancy or "hole" left in the "sea" of otherwise completely filled negative-energy states has all the attributes of a positively charged electron. In the band theory, if the valence band is completely filled and the conduction band is empty the crystal will behave as an insulator. On the other hand, in a conductor, such as a metal, the valence band is filled and the conduction band is partially filled, so that on application of an electric field to the conductor the electrons are free to move and a current flows. In contrast to insulators and conductors, a semiconductor at ambient temperatures around 300 K may have the valence band almost completely filled and the conduction band almost completely empty except for the few electrons that are always being excited by thermal agitation into the conduction band. In the simplest case exemplified in Fig. 4-6 the concentration of electrons elevated by thermal agitation into the conduction band (and therefore the conductivity) is governed by the Boltzmann distribution law and is proportional to exp(-E,/kr), where E, is the energy gap between the valence and conduction At room temperatures kT is equal to about 0.025 eV bands, and k is the Boltzmann constant. while E, ranges from 0.2 eV for indium antimonide to 6 eV for diamond (in graphite E, = 0). In a high-purity crystal the simple representation of Fig.4.6 holds, but impurities and crystal defects contribute extra allowed electron states at a variety of energy levels in the forbidden region. Conduction
Donor
level
Electron
Hole
band
traps
traps
Acceptor level
Valence band
Band-gap energy-level Fig. 4-6 (after Mann et al., 1980).
diagram
for an
inorganic
crystal
Radioactivity measurements: principles and practice
811
But for a high-impurity crystal at 300 K with a low value of E,, electrons can be excited by thermal energy available in the lattice into the conduction band and, on application of an electric field, a small leakage current will flow in the crystal. Moreover, for every electron raised to the conduction band, a vacancy or "hole" is created in the valence band in the form of a missing valence electron. This hole can also act as a positive-charge carrier by virtue of accepting a valence electron from a neighbouring lattice bond which creates a hole in that bond that can accept another nearby valence electron, and so on. This movement of electrons in one direction is equivalent to a positive hole moving in the opposite direction. Under the influence of an applied electric will move to the anode and holes in the valence field electrons in the conduction band Kittel (1971) has made the following cogent comment: "If the band towards the cathode. band is filled except for an electron missing from the state E, we say that there is a hole in the state E. The physical properties of the hole follow from those of the totality of electrons in the band. This sentence is the key to the understanding of holes." With decreasing temperature E,/kT becomes larger, and its negative exponential becomes rapidly smaller. Thus, as the temperature decreases the numbers of electrons being excited into the conduction band rapidly decreases and semiconductors tend to become insulators at extremely low temperatures. The resistivities of high-purity semiconductors are proportional to p_exp(w/kT), where p. is the limiting resistivity at very high temperatures, and w is an excitation energy. Thus the resistivities of semiconductors decrease with increasing temperature whereas the temperature coefficients of metals at ambient temperatures are predominantly positive. suppose that a semiconducting crystal, at a reduced temperature such that the conduction band is devoid of free electrons, is exposed to ionizing radiation the energy of which would normally be considerably greater than E, (Fig.4-6). The radiation is scattered around the crystal lattice to which it imparts energy directly by ionization and by such secondary processes as Compton scattering, phonon scattering and the photoelectric effect. Free electrons are therefore excited to the conduction band and those with residual energy will move through the lattice and rapidly dissipate such energy in further interactions with the atoms of the lattice creating more free electrons in the conduction band. Every electron excited to the conduction band will leave a hole in the valence band, and the numbers of free electrons and holes created will be proportional, within statistical fluctuations, to the amount of energy imparted to the crystal by the ionizing radiation. Moreover, if a voltage is applied across the crystal the electrons will be collected at the anode and the holes at the cathode, and a current flows in the external circuit. In this respect therefore, the semiconducting crystal is operating as a solid-state ionization "chamber"; also single ionizing events will give single current pulses in the external circuit. Unfortunately, however, even the purest crystals are rarely free from small traces of impurities or from defects in their structure, and such impurities create electron and hole absorption-and-emission energy levels intermediate between the energy levels of the valence and conduction bands. Such impurity and defect energy levels are called electron traps and hole traps, and can exist, respectively, as little as a few hundredths of an electron volt either above or below the valence and conduction bands. As electrons can now be excited, with relatively little thermal energy, into such traps from the valence band (leaving holes in that band), or from such traps into the conduction band, even very pure crystals will give rise to leakage currents that militate against the use of such semiconductors as high-efficiency absorbers of radiation energy. But fortunately three methods have been developed to reduce the leakage current in such crystals to a minimum, namely by creating a semiconductor rectifying diode, by purification or by compensation. These three methods will be discussed later (84.6.3.3). In the early days of solid-state physics, the purest crystals were designated as intrinsic but with the introduction of the method of compensation the term "intrinsic" was extended to include both very pure material and also that in which compensation had reduced the number of uncompensated charge carriers to less than about 1O'O cme3. But very pure material is now mostly referred to as high-purity, or HP, and that in which the charge carriers have been reduced by compensation as compensated or drifted. 4.6.2.1. Semiconductor imuurities and douing Diamond, germanium and silicon crystals with tetrahedral bonds.
all are quadrivalent
and form
face-centered-cubic
If there are present in any of these crystals small numbers of pentavalent impurity atoms, such as atoms of phosphorus, they will substitute in various lattice locations. But in satisfying the valence requirements of the surrounding quadrivalent atoms, each phosphorus atom will find itself with a loosely bound electron which requires less energy to set it free. Such atoms are called donor atoms and, if solely of one kind, will exist in an elevated energy level about 0.01 eV below the conduction band as illustrated in Fig. 4-6. Such an impurity is termed an n-type impurity because it can contribute negative electrons readily to the conduction band.
Radioactivity
812
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principles
and practice
If, on the other hand, the impurity atoms are trivalent (e.g. boron), they will also replace the quadrivalent atoms at many lattice locations, but the lattice structure calls for a quadrivalent atom. Thus the one trivalent atom in the otherwise quadrivalent tetrahedral lattice in closest proximity around it will be quite ready to accept the missing electron that the lattice would otherwise normally accommodate. This location with its non-negligible probability of accepting a loosely-bound extra electron is called a" acceptor site. The energy levels of such acceptor sites are of the order of 0.01 eV above the valence at ambient temperatures, band. Therefore, kT being equal to about 0.025 eV, electrons in the highest-energy levels of the valence band can readily be excited by thermal agitation to the acceptor-energy level (Fig.4.6). With the great number of electrons available in the upper-energy levels of the valence band, most of the acceptor sites will be filled by thermally excited electrons from the valence band. Impurities that create acceptor sites in a crystal lattice are called p-type impurities because the vacancies, or "holes", created at lattice sites throughout the crystal can The natural impurities that occur in most crystals of act as positive-charge carriers. germanium and silicon are such as to render them p-type. Selected impurities can also be diffused into high-purity crystals of germanium and silicon at elevated temperature a process know" as doping. If thin films of aluminium or gold are evaporated on to opposite faces of such a ptype crystal to form electrodes to which a voltage is applied, there will be a leakage current due to electrons moving from vacated site to adjoining vacant site in the valence band, from cathode to anode, across the crystal. Such a current in p-type material is, as mentioned earlier, equivalent to positive charge being transported across the lattice by the movement of positive holes from anode to cathode where they are neutralized by electrons from the external circuit. In n-type material,free electrons that have been elevated to the conduction band from donor sites move freely (apart from collisions that may generate phonons and, or, heat) through the crystal lattice from cathode to anode under the influence of the applied electric field. The drift velocities of electrons and holes in semiconductors are more nearly in which the drift velocities of electrons can be equal than in gas-ionization detectors, of the order of lo3 times greater than those of the positive ions. Thus in germanium and silicon detectors, having applied electric fields of 250 V.cm-l at a temperature of 300 K: the drift velocities in germanium are of the order of lo6 cm se1 and 5 x lo5 cm s-l, for the electrons in the conduction band and holes in the valence band; in respectively, silicon the respective figures are of the order of 5 x lo5 cm s-l (electrons) and lo5 cm s-l (holes). I" majority material
material the holes are the dominant carriers of charge and are called p-type carriers, and electrons in the conduction band are minority carriers. I" n-type electrons are majority carriers and holes the minority carriers.
4.6.2.2.
Traps. recombination and luminescent centers, and thermallv-stimulated exoelectrons
thermoluminescence.
in semiconducting crystals create traps for electrons and Impurities and defects The behaviour of some semiconductors such as diamond and thermoluminescent holes. materials can only be understood, eve" if imperfectly, by assuming that electrons and around the crystal lattice, encounter such defects where they holes, in their movements Such electron and hole traps occur can remain trapped for various intervals of time. within the energy gap, E,, between the valence and conduction bands, and some of them can occur at a relatively large fraction of E, from either band. One of the earliest semiconducting materials to be experimented with as a detector of ionizing radiation was diamond. Such radiation created electron-hole pairs in the crystal and, under the influence of a" applied electric field, a flow of charge could be detected Diamond was in fact found to operate satisfactorily as in an external electrical circuit. except that with continued use its output signal a detector of ionizing radiation, due to the build-up of space charge caused by the decreased in magnitude apparently trapping of electrons in its lattice. This space charge could however be removed by heating the crystal so that the traps could be emptied by the thermal excitation of the electrons into the conduction band, whence they could return to the valence band. Such thermal deexcitation underlies the phenomenon of thermoluminescence described overall below. Many semiconducting crystals, combined with a variety of dopants, have electron traps some 0.04 to 0.05eV (corresponding to a value of kT at about 500 K) below the lower limit of the conduction band (Fig. 4-6). Ionizing radiation interacting with the crystal can deposit sufficient energy in it to excite electrons from the valence band into these even when the energy is insufficient to excite an electron into the electron traps, conduction band. Free electrons in the conduction band, if not removed by a" applied return promptly to the valence band with the emission of electric field, will normally radiant energy.
Radioactivity
measurements:
principles
and practice
813
However, in many doped materials the trapped electrons have no way of escaping unless fortuitously excited by further incident radiation into the conduction band, whence they They can also be elevated to the condution band by heating deexcite to the valence band. to above about 500 K, from which they return to the valence band with the emission of This is usually accomplished by raising the temperature of the semiconductor at a light. rate of about 1 K 5-l by means of which procedure a "glow curve" of light intensity vs. This observation corresponds to more and more temperature (i.e., also time) is obtained. energetic photons being emitted as the increasing value of the energy kT reaches traps that are at deeper and deeper energies below the lower energy limit of the conduction band. This phenomenon is known as thermoluminescence. in semiconducting crystals is fundamental to the The concept of electron traps their photoconductive and thermoluminescent properties. When a understanding of the conducting or thermosemiconducting crystal is irradiated with high-energy photons, luminescent response persists for varying lengths of time after the source of radiation is removed. In some thermoluminescent crystals the incident radiation energy is stored for years. Such is the principle underlying the well-known thermoluminescent dosimeter (TLD) and the use of thermoluminescence in dating ancient pieces of pottery. In some cases that have indicated that thermoluminescent discordant results have been observed deexcitation may occur by the emission of phonons (thermal quenching) rather than photons; also long decay lifetimes, ranging up to one-hundred million years for calcite, have been For a discussion of these properties, an article by M.J. Aitken in Oberhofer and quoted. Scharmann (1981) may be consulted. Thermoluminescent dosimeters made from a variety of materials can be used for photon, neutron and charged-particle dosimetry (see Christensen et al., 1982). A few typical materials (and their dopants) are lithium fluoride (P, Mg, Cu and Ti), calcium sulphate (Dy and Tm), calcium fluoride (Mn, Dy and undoped CaF,), and magnesium silicate (Tb). Typical maximum emission wavelengths of the radiation and fading times are also given in the above review by Christensen et al. The fundamental role of electron traps in phosphorescence and thermoluminescence has been discussed very fully by Randall and Wilkins (1945). Briefly, they consider the case of a trapped electron at an energy level E below the conduction band, that must absorb at least an amount of energy E before it can escape from the trap. As the electrons in the traps have a Maxwellian distribution of thermal energies the probability, p, of an electron escaping at temperature T is given by p = &E/kT
)
(4-2)
where s is a constant (with the dimension frequency). If the trap is in the nature of a potential well, then these authors point out that the constant s should be the product of the frequency with which an electron strikes the side of the well and of the reflection coefficient (also see Mott and Gurney, 1964). Randall and Wilkins quote a value for s of the order of lOa s-l in phosphors that had been studied. It had also been observed experimentally, as mentioned above, that if certain crystals were exposed to radiation at room temperature for a given time and were then heated so that their temperature increased uniformly with time, light was emitted during the heating process. This effect was referred to as glov and the plot of intensity of light emission as a function of temperature attained gave the glow curve. Such a glow curve could moreover consist of a whole series of glow peaks, indicating the existence of electron traps at different discrete energy depths E. Randall and Wilkins then proceeded from the above equation by assuming that n was the number of electrons in traps at a given energy depth E and temperature T at time t, so that dn/dt = -r~se-~'~~ provided warming,
(4-3)
that there was negligible retrapping. then they derived the expression E = T,
where
,
f(s,p)
[l
+ f(s,p)]
<< 1, and To is the temperature
k log s
If
P,
equal
to
dT/dt,
is
the
,
of maximum
rate
of
(4-4) glow
Using this equation with some further assumptions and experimental data, able to calculate that a temperature of maximum glow equal to 340 K corresponded depth equal to 0.67 eV at the rate of warming normally used.
they were to a trap
More recent experiments show that different crystals used in thermoluminescent dosimetry may exhibit many glow peaks with very different lifetimes. Thus Pohlit (1973) has shown that lithium fluoride has five strong glow peaks at temperatures ranging from 332 K to 427 K with corresponding trap depths between 1.41 eV and 3.62 eV and half lives at 298 K ranging respectively from 2 minutes to lo4 hours. Two weak glow peaks were also observed at higher temperatures. The energy of 3.62 eV corresponds to kT for a temperature of about 4 x 10" K. This trap level is however drained by electrons having velocities at the higher end of the Maxwell distribution as described above, following Randall and Wilkins (Lx. cit.).
Radioactivity measurements: principles and practice
814
The foregoing very brief outline is intended only to indicate why it "as necessary to postulate the existence of electron traps in semiconducting crystals. There are also corresponding defects that act as hole traps. And some traps can also act as recombination or luminescent centres. Thus an electron elevated to the conduction band, from either the valence band or from a trap, is free to move around the crystal (in the absence of an electric field) until it encounters a hole, that is either moving freely in the crystal or is located in a recombination or luminescent centre. In the process of recombination either a phonon or a photon is emitted. The mechanisms of the atomic processes involved in these centres is not always completely understood. Moreover another interaction can occur because of the Coulomb attraction existing between a free electron and a free hole; when they meet in the crystal they can form a stable bound state, somewhat analogously to the formation of positronium. Such a bound state is called an exciton. An exciton can decay into a free hole and free electron, or by the electron falling into a lower-energy hole state with the emission of a photon or phonons. Another mode of escape is also possible for a trapped electron that receives sufficient energy to elevate it into the conduction band, with enough residual energy to overcome the surface work function, and traverse the interface. Such energy can be imparted in diverse ways such as mechanical deformation of the crystal or by heating it, provided that the electron is also close to the crystal surface. This phenomenon "as first described in 1902 in the Philosophical Magazine by J. C. McLennan in an article entitled On a kind of radioactivity imparted to certain salts by cathode rays. The title itself implies that McLennan noted the delayed emission. According to Becker (1973; chapter 3) this phenomenon of electron emission had been known by a number of different terms, of which the following (and their abbreviations) were still then extant: Exoelectron emission (EE) for "cold" or spontaneous emission; optically stimulated exoelectron emission (OSEE); and thermally stimulated exoelectron emission (TSEE). The last of these, TSEE, is of interest because of its potential for radiation dosimetry, by detecting electrons instead of photons (see Becker, 1973, and Kriegseis et Electron detectors that are used include current-reading or pulse-counting al., 1985). and closely-packed channeltron multipliers gas-ionization devices, electron multipliers, Many suitable semiconducting media are also described by (74.6.6 and Becker, 1973). Becker, and detailed information is given about the use of thin Be0 films by Kriegseis et al. Beryllium oxide can, for example, be thinly coated on to graphite discs which can then be heated rapidly with a halogen lamp, and dose readout can be accomplished within 30 s using microprocessor-controlled equipment. The low mean energy of about 0.2 to 0.3 eV of TSEE from thin films of Be0 necessitates the use of electron multipliers with the Be0 in Such dosimeters have a dose response that vacuum, or of sensitive proportional counters. is almost independent of photon or electron irradiation energy, and that covers a linear dose range from 10 pGy to 10 Gy. Systems using ionization chambers and counters, with the semiconductor in many configurations (including deposition upon the internal surface of a Auger-like cylindrical-counter cathode) are described and referenced by Becker (1973). the surface acquiring sufficient transitions are also possible, with electrons close to energy to escape, when other electrons in the crystal deexcite to lower-energy states. Becker and Kriegseis et al., may be consulted for further information and for very many references. 4.6.3. Semiconductor detectors From the foregoing sections it may be seen that it should be possible to use an ionic crystal as a solid-state ionization detector, closely analogous to its gaseous forerunner. Ionizing radiation incident upon the crystal creates electron-hole pairs, each free electron and free hole moving through the crystal under the influence of an externally applied electric field, the electrons to the anode where they are collected, and the holes As in a gaseous ionization chamber any leakage to the cathode where they are neutralized. current must be reduced to a minimum for satisfactory operation. 4.6.3.1. Resolution The average energy to create one electron-hole pair at 77 K is about 3.8 eV for This is inclusive of energy dissipated in competing silicon and 3.0 eV for germanium. processes, and is considerably less than the average energies ranging between 25 eV and 35 eV in producing an electron-ion pair in gaseous ionization detectors. The ability to resolve ionizing events of proximate energy, which is proportional to the number of charge carriers formed and collected per ionizing event, is therefore considerably greater in solid-state than in gas-filled detectors. 4.6.3.2. LeakaPe currents Leakage currents occur for different reasons in gaseous-ionization and solid-state detectors. In the former they are limited to poor insulation of the high-voltage electrode including surface leakage across the insulator; in the latter they can arise from surface derives from the close proximity in energy the principal problem leakage, but (approximately of the order of 0.01 eV) to the valence and conduction bands of the donor and acceptor levels created by impurity atoms. Surface-leakage currents can be reduced by
Radioactivity
measurements:
principles
and practice
815
the inherent leakage and, as has been previously mentioned, etching the crystal surfaces, acceptor and donor impurities can be reduced to satisfactory levels briefly by caused by or by compensation. two basic methods, namely by high purification 4.6.3.3
Purification
and comoensation
Because the acceptor and donor levels can be easily populated and depopulated at room temperature (kT - 0.03 eV) from the valence or into the conduction bands, respectively, an If NA and N, are the impure ionic crystal always has an abundance of charge carriers. then NA + N, is the cubic centimetre, numbers of acceptor and donor atoms present per carriers and it is essential that this be reduced to less than number of potential charge levels. Up about 10" cmm3 in order that leakage currents may be at acceptable operational it has been found possible to purify only germanium crystals to such an to the present, Such crystals have been called intrinsic, but there has been acceptable level of purity. some tendency also to apply the term to crystals in which the total charge-carrier density It is has been reduced by the method of compensation, without removing the impurity atoms. therefore preferable to refer to high-purity germanium detectors (HPGe), when such are the detectors being described. is applicable to silicon and germanium The second method, that of compensation, but that still have too high a density of impurity charge crystals of good purity, It is based on a method described by Pell (1960) in which he drifted positive carriers. most residual impurity atoms lithium ions into p-type crystals of silicon and germanium In this method a layer of lithium in pure crystals of silicon and germanium being p-type. is deposited on to a face of the crystal maintained at a temperature of about 4OO'C in an After a short time the lithium will have diffused several tenths of a evacuated enclosure. is then millimetre into the crystal, to which an electric field of from 500 to 1000 volts applied, at temperatures ranging from 0°C to lOO'C, for times ranging from several days to The positive potential is applied to the a month, depending on the size of the crystal. lithium-coated face and the negative to the p-type crystal, at locations depending on the crystal shape. through Under the influence of the electric field, lithium ions drift interstitially the crystal lattice forming neutral (zero-charge) loosely-bound chemical complexes with the If one plots lithium the lithium boundary advances. impurity acceptor atoms as concentrations, N,,, against depth of drift, d, as in Fig. 4-7, then at some short distance Complexed acceptor atoms in the lattice behind the interface N,, will be equal to NA. (phonon) excited valence structure, such as calcium, no longer readily accept a thermally electron from a silicon or germanium atom and will therefore have a much lower probability hole in that region of the of contributing to the creation of a free, charge-carrying,
c
Lithium concentration YS depth, d in e p-type crystal, Fig. 4-7 1980). before, end b) after drifting (after Mann et al.,
a)
After the lithium has been drifted through the desired volume of the crystal, the temperature is lowered and the distribution of lithium is allowed to equilibrate by further "self-adjusting" diffusion, without an externally-applied electric field (see Fig. 4-7). In this condition, in any region of the crystal where NLi > NA the resulting positive space charge will tend to move excess lithium ions out of the region, and into regions where Excess lithium ions will be squeezed back into a relatively thin layer on the NL, < NA. face (n+) at which the drifting was initiated, and at the other boundary there will be a residual layer of uncompensated p-type material. With the latter coated with an evaporated layer of gold, both bounding surfaces serve as the electrodes for the compensated region; the linear drift distance, d, can be of the order of about 2 cm. Both the n+ layer and the p layer will contain negative and positive charge carriers, respectively, which between them will cause a small drop of potential acros.s the "intrinsic" or compensated region. Although the lithium compensating atoms are interstitial, they are nevertheless referred to as acceptors and the bounding layer of lithium atoms designated n', denoting a substantial excess of donors. In its use as a detector of ionizing radiation an external source of potential is applied in opposition to the space-charge potential, i.e. a reverse
Radioactivity
816
measurements:
principles
and practice
bias, with the positive pole of the external source connected to the n+ layer and the negative pole to the p layer. In this configuration the lithium-drifted detector acts as a rectifying junction, and no current will flow across the highly resistive compensated electrical breakdown occurs. But, if the external polarity is interchanged, region until free electrons supplied by the n+ layer (in the conduction band) and free holes from the p layer (in the valence band) will flow unimpeded. The mobilities of the electrons and holes pairs in a gas, about the same are, unlike electron-ion order of magnitude. In diamond, silicon and germanium, respectively, at 300 K the mobilities are 1,800, 1,600 and 3,800 cm2 V-' 5-l for electrons, and 1,200, 400 and 1,800 cm' VW' 5-l for holes (Kittel, 1971). At 77 K the electron and hole mobilities for high-purity and compensated germanium are of the order of 4 x lo4 cm' V-' 5-l and lo4 cm' V-' s-l, respectively. However, when an energetic photon deposits energy in the depleted region, producing Compton electrons or a high-energy photoelectron, their energy will be dissipated in further interactions with lattice atoms, creating many free electrons and free holes that will be collected respectively at the anode (n+ layer) and cathode (p layer). The operation of a lithium-compensated germanium, Ge(Li), detector is illustrated in Fig. 4-8 which could equally well represent the functioning of a high-purity germanium detector; nowadays the latter is more generally available and the most frequently used.
n+Layer
p-Layer
i /--lntrmsic
reQion----_ti
Electron~hole Ge-2.96 St-3
1
pairs
&/pair 76
elrlpsir :
Illustration of a p-i-n planar semjconductor detector, showing a typical photon interaction with the detector, and the movement of electrons and holes (after Mann et al., 1980).
Fig. 4-8
4.6.3.4.
The ~-n
iunction
Many ionic crystals with various dopants, both natural and added in carefully controlled melts, exhibit the phenomenon of semiconduction and delayed phosphorescence. In radiation physics germanium and silicon are the best-known detectors, and cadmium telluride that has recently become available is also of interest in that it is relatively dense and can operate at ambient temperatures. Then there are many devices displaying delayed phosphorescence used as thermoluminescent dosimeters (see, for example, P. Braunlich, 1979, and M. Oberdorfer and A. Scharmann, 1981.) In carefully controlled growing of crystals, by adding different dopants to the melt at different stages, or by subsequent diffusion, both n- and p-type crystals of silicon and in a single germanium can be produced and in which n- and p-type regions are present crystal, or even a combination such as a pnpn sequence in a four-layer diode. Two further designations that are used to specify the type of crystal are ?r and u, meaning respectively slightly p and slightly n. Thus a high-purity germanium detector that was still slightly p-type, and which had an nf layer of lithium on one surface and a diffused p-type layer on the other serving as contacts for the external circuit, could be designated as a p-n' junction. Contacts and p- or n-type layers can also be created by bombarding a surface of the crystal with an accelerated beam of positive ions. Typical p-type (acceptor) impurities that can be incorporated into crystals of silicon or germanium are oxygen, phosphorus, calcium, arsenic and antimony. Some n- type (donor) impurities that can be incorporated into these crystals are lithium, boron, aluminum, gallium and indium. Two of the earliest semiconducting devices used to detect and quantify ionizing radiation were the p-n junction and the surface-barrier detector. Both are fundamentally the same as the lithium-drifted detectors, differing primarily in the thickness and nature of the charge-free region which is not compensated but deuleted of charge carriers. To form a p-n junction one can take a thin disc of a highly doped p-type crystal of silicon and germanium and expose one face of it to phosphorus vapor. On heating the crystal wafer phosphorus atoms diffuse into it forming a heavily doped n+ region about 10-3-mm deep. Thin films of aluminum or gold can be evaporated on to both surfaces of the wafer to form so-called ohmic (i.e. non-rectifying) electrical contacts. This is the p-n The contacts might equally well be achieved by lightly junction, or p-n+ in this instance. implanted ions; it is important that whatever material is used should not diffuse into the substance of the material thereby creating a rectifying junction so that the current is no
Radioactivity
longer
mea.surements: principles
the same for a given voltage
applied
in either
and practice
817
direction.
In considering the functioning of a semiconducting crystal it is important to remember that the territory of a free electron created in the n region is the whole crystal. It is also convenient to remember that a donor atom in the lattice constitutes a charge-neutral site with a loosely bound electron which, when excited into the conduction band, leaves a In like manner an acceptor atom is one positively charged site in the lattice structure. that constitutes a charge-neutral site in the lattice that however "needs" an electron. When it binds one loosely to itself it becomes a negatively charged site in the lattice. As phosphorus donor atoms begin to diffuse into the p-type crystal, electrons, populating the conduction band from the donor (n+-type) energy level, will move across the advancing phosphorus interface into the p region and combine with free holes. This in distribution, will populate more acceptor sites in the turn, by virtue of the Boltzmann acceptor energy level with electrons, which sites become negatively charged fixed sites in There is thus established across the nf-p interface a space-charge potential the lattice. donor sites on the n+ side and a corresponding caused b) a surplus of fixed positive surplus of negative acceptor sites on the p side. This condition is illustrated in Figs. 9(e) and 9(f). The space charge thus created across the p-n+ junction opposes the movement of further electrons into the p region or of holes into the n+ region, and thus constitutes a rectifyin such devices as the Zener diode and the field-effect ing diode, that finds expression It also tends to drive electrons back into the n+ region and holes into the p transistor. region and thus creates a region at the junction that is devoid of charge carriers and is called the deuletion repion. If a reverse bias is now applied to the p-n+ junction by means of an external circuit, as shown in Figure 9(g), it will act to reinforce the space-charge field and electrons will be used to combine with more holes in the p region and Some electrons donated to the conduction band by the donor atoms will be removed. The equilibrium will therefore shift to an increase in the numbers of positive donor sites in the n+ region and negative acceptor sites in the p region, and a consequent increase in the depth of the depletion region; i.e. an increase of the volume on either side of the interface that is depleted of charge carriers. In semiconductor parlance, electrons from the n+ layer and holes from the p region will diffuse across the junction to create more negatively charged acceptor sites on the p side of the junction and more positively charged donor sites in the n+ side. The size of the depletion region is thereby increased. The depths of the depletion region can vary from very thin up to about 20 mm depending on the value of the reverse bias. voltage is increased no current will flow until a break-down occurs and the current increases.
As the rapidly
If the polarity of the externally applied voltage is, however, reversed to give a forward bias no current will flow until the externally applied potential exceeds that created by the space charge at the junction. At this point electrons injected into the conduction band from the external circuit will be driven across the junction, and a current This is the basis of the semiconductor diode or transistor. will flow around the circuit. In semiconductor parlance, electrons and holes will be driven into the depletion region, neutralizing the positively ionized donor sites on the n+ side and the negatively ionized acceptor sites on the p side of the junction. 4.6.3.5.
The surface-barrier
detector
This is essentially another form of p-n junction with a very thin entrance window to facilitate the detection of low-energy photons and charged particles. If a wafer of an n-type silicon or germanium crystal is exposed to air for a few days a thin oxide layer is formed. Oxygen is electronegative and therefore an acceptor, so a p-n junction is formed. Contacts to the crystal are established by evaporating a very thin layer of gold on the front oxidized surface and an aluminum layer on to the back. 4.6.3.6
Semiconductor
detector
configurations
DifEerent configurations of Ge(Li) and HPGe cylindrical annular and semi-annular detectors are shown in Fig. 4-9. These various configurations, and their particular advantages are discussed fully in rather NCRP, 1985. The reversed-electrode n-type HPGe configuration shown in Fig. 4-10 has a boron ion-implanted p-type electrode of the order of only 0.3-pm thick. One of its characteristics is also worthy of note, that is its reduced sensitivity to the effect of radiation damage caused by fast neutrons that results principally in the production of hole traps. This is due to the fact that, in such a cylindrical geometry, increments in volume, dV. with radius r from the axis are proportional to rdr. It is therefore clear that more of the substance of the detector is closer to the outside than to the inside. Thus holes moving towards an outer electrode will on average have a shorter distance to go and therefore less chance of being trapped.
Radioactivity
818
measurements:
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and practice
Non-quantitative diagram of a p-n junction; a) depletion Fig. 4-9 in an unbiased junction of 8 acceptors, region; b) distribution, 8 donors, a electrons, and o holes; c) concentration of electrons
and holes; d) concentration of acceptors and donors; e) dipole layer produced by the net charge distribution; f) electrostatic potential distribution corresponding to e); g) distribution of acceptors, donors, electrons and holes in a reverse-biased p-n junction (after Mann
et al.,
1980)
__ n . typ.
F: HPGa
500 pm .+
n-type contact
100-200
mpm
n-typ.
pm COntlCt
b4;:::t K-twe core
-.._---___J
coaxial
HPGa
true co.xI.I
Ge,LI,
Different configurations of cylindrical high-purity germanium and lithium-compensated germanium detectors (after NCRP, 1985).
Fig. 4-10 4.6.3.7.
Other
semiconductor
developments
So far, it has sufficed to discuss the operation of the semi-conducting class of radiation detectors only in terms of crystals of silicon and germanium. It is desirable to keep or operate both types of detector in a cryostat near the temperature of liquid nitrogen. But in many cases, as in space, nuclear medicine or for environmental monitoring it is convenient to have such detectors that can be operated at ambient temperatures. For such operation it is necessary to use a semiconductor that has so large a band gap that negligible numbers of electrons can be thermally excited into the conduction band. To achieve this it is necessary for E, to be greater than about 1.4 eV (NCRP, 1985). Three such substances under development are HgI, (Es = 2.13 eV), CdTe (Es = 1.47 eV) and GaAs (E, = 1.43 eV). For further information and references NCRP, 1985 may be consulted. 4.6.4.
Inorganic-crvstal
scintillators
Activated crystalline sodium iodide, cesium iodide and calcium fluoride are amongst the oldest scintillators in use, with thallium-activated sodium iodide being probably the best known. Pure sodium-iodide crystals scintillate very efficiently at 77 K with very fast response, but their responses at ambient temperatures are greatly diminished. Sodium iodide is very deliquescent and has to be sealed in an aluminium can with a transparent window. Cesium iodide is less deliquescent and is of value because of its higher density, and calcium fluoride is nonhygroscopic. Silver-activated zinc-sulphide crystals were shown by W. Crookes in 1903 to scintillate when bombarded by alpha particles, and they have been used as alpha-particle detectors ever since, usually as thin films on thin plastic discs or glass discs or bell jars (e.g. for the assay of radon and its daughters). But it was not until 1947 and 1948
Radioactivity measurements:
principles
and practice
819
H.Kallmann and P.R.Bell next showed, respectively, that single crystals of naphthat thalene and anthracene could be used as scintillators to detect ionizing radiation. In 1948, R. Hofstadter also found that thallium-activated sodium-iodide crystals scintillated when exposed to ionizing radiation. Furthermore, as the density of sodium iodide was about three times that of anthracene it was better suited to the detection of gamma radiation. Today, thallium-activated sodium iodide is probably the scintillator that is most widely used for photon detector. Pure sodium-iodide crystals are also very efficient photon detectors at 77 K, but are about ten times less efficient at room temperature. Their useful thickness is also limited to about 1.3 cm because they strongly absorb their own fluorescence radiation in a narrow band of wavelength at about 300 nm. The principle of operation of NaI and of NaI(T1) as dissimilar to that of a semiconductor, in that it is presumed scintillators is not wholly that the photon irradiation creates energetic Compton recoil electrons, photo-electrons or electron-positron pairs that in their progress around the crystal suffer inelastic collisions in the crystal lattice thereby raising electrons to the conduction band, leaving The energetic electrons in their progress around the crystal holes in the valence band. can create more electron-hole pairs and also impart energy to the crystal lattice, this In fact, energy being then dissipated as quantised lattice vibrations (phonons) or heat. 90 percent or more of the absorbed energy is emitted in this form rather than as light. The holes left in the valence band can now act as ionizers of luminescence centres, by means of which electrons in the conduction band can deexcite. when they encounter them, with the emission of fluorescent radiation. The introduction of an activator, such as thallium, creates many more luminescent centres in the forbidden region between the valence and conduction bands, thus facilitating This is achieved in practice by the deexcitation of electrons in smaller decrements. adding thallium to the NaI melt, at a concentration of about 0.2 percent of thallium by mass, prior to growing the crystal. The thallium atoms form chloride complexes within the If a series of crystals with crystal lattice and these act as luminescence centres. different concentrations of thallium is examined, it is found that, as the concentration of thallium increases, so does the intensity of the NaI fluorescence (a band centered around 300 run) decrease and that of NaI(T1) (a broad band centred around 430 run) increase. An increase in wavelength of the fluorescence corresponds to differences in energy level between the activator sites (luminescence centres) within the forbidden region between the This fact also explains why NaI(T1) is, unlike NaI, valence and conduction bands. transparent to its own luminescence. Crystals of NaI(T1) emit a wide band of fluorescent Light ranging in wavelength between about 330 run and 550 nm, with a maximum at about 430 nm. The lower wavelength, 330 run corresponds to an energy of about 3.8 eV, and that of 550 run to about 2.3 eV. In this connection, it is useful to remember that the 589-m wavelength of the well-known D lines of sodium, is equivalent to an energy of 2.106 eV. NaI(T1) detectors are available in a wide variety of shapes and sizes, the latter from thin discs 1 or 2 cm in diameter up to cylindrical well detectors 20 cm in diameter There are also cylindrical geometries where the cylinder and 10 cm or more in depth. length is greater than its diameter, and they are available with "pin" wells, or widerWell-type or hollow- cylinder NaI(T1) detectors are diameter wells, or no wells at all. also used for scattered (Compton) photon elimination and for cosmic-ray or environmental background reduction. NaI(T1) crystals can also now be heated and moulded into a variety of shapes and extruded, for example, into long rods for use in airport x-ray security systems (see NCRP, 1985). Within the last ten years two high-atomic-number scintillators have been developed, namely bismuth germanate, Bi,Ge,O,,, often referred to as BGO, and cadmium tungstate, These have about double the density of sodium iodide, and about four times its CdWO,. linear absorption coefficient at 150 keV (see NCRP, 1985, for references). 4.6.5, Electron-multiolier
uhototubes
As gaseous-, liquid- and solid-scintillation detectors came into more and more general use it became necessary to devise a means of converting their extremely weak fluorescent responses into electrical pulses that could be amplified to a level that would permit of the output data being stored, processed and analyzed. Fortunately, two physical phenomena ware available that, when combined, served to provide an answer to the problem. The first was the photoelectric effect that is at least as old as the quantum theory, in association with the names of Planck and Einstein. The second was that of secondary-electron emission. The first of these effects was used to make a photoemissive -? cell more usually known as a photocell, that was described by Elster and GeiteL in 1910. Then in the Late teens of the century, secondary-electron emission was suggested by J. Slepian as a means of amplifying small currents of electrons. Next, in the 1930's multistage electron multipliers were developed commercially, presumably to meet the needs of the "talking movie." These consisted of a semi-transparent photocathode followed by a number of stages of electron-emission multipliers.
Radioactivity
820
measurements:
principles
and practice
and to the present time, the development of the 1940's, late Beginning in electron-multiplier phototubes has been pushed ahead to meet amongst other requirements those of the great variety of scintillation detectors that has been developed. A typical with a NaI(Tl)-crystal detector is ten-stage electron-multiplier phototube, in combination The individual electrodes of the accelerating system are called illustrated in Fig. 4-10. in a "Venetian-blind" configuration, and are also dynodes, and they are often arranged focussing of the secondary electrons electrostatic shaped, in order to give satisfactory from one dynode on to the next. The yields of emitted secondary electrons from a dynode surface are functions of the energies of the incident electrons (i.e. the inter-dynode accelerating voltage) and of the Depending on this nature, between four and six secondary nature of the dynode surface. electrons could be typically emitted for primary electron energies of a few hundred The corresponding gains for a ten-dynode tube would be 4" electron volts (Knoll, 1979). for, say, a single and 61°, i.e. lo6 and 6 x 107. The output pulse from the phototube photoelectron incident upon the first dynode will be sufficiently large for further amplifThe operation and statistics of electron-multiplier phototubes is ication and processing. probability in the case of discussed well by Knoll (1979), and their zero-detection liquid-scintillation counting will be further discussed in Chapter 5. Further details and references are to be found under Secondary emission of electrons, and Photomultiplier tubes in the Encyclopaedic Dictionary of Physics Electron multipliers, that electron-multiplier phototubes in the (Pergamon Press, 1962), which also notes This physically correct term seems to be in general use in "preferred IRE terminology". with the terminology of this the literature of exoelectron physics and is concordant report. 4.6.6.
Channel
electron
multiuliers
Channel electron multipliers (CEM) are similar to electron-multiplier phototubes in electron emission to provide the principle in that they use many stages of secondary They consist, however, of glass or ceramic tubes coated on the inside amplified output. surface with a high-resistance semiconducting layer, along the length of which a suitable difference in voltage is maintained by means of electrodes deposited on each end of the The device is contained and operated in an channel, as shown in Fig. 4-11 (Kurz, 1979). A somewhat similar principle had been suggested by McGee and his evacuated vessel. This consisted of an colleagues in 1960 (see McGee, 1960) for use as an image intensifier. array of metal tubes cut into short lengths, with ends at 55' to the tube axes to give and reassembled to form a matrix of short dynodes. No correct electrostatic focusing, operating results are, however, given.
4
Illustration of the various processes contributing to the Fig. 4-11 _ output from an electron-multiplier phototube by the InteractIon oI gamma-rays from a point source with a NaI(T1) scintillator detect?1 (after Heath,
1964, and Mann
er a1.,1980).
Radioactivity
measurements:
principles
and practice
821
As with the electron-multiplier phototube, the linear CEM can give spurious counts due to positive ions being accelerated in a direction opposite to the electrons and giving rise to secondary-electron emission from the next lower dynode. These positive ions usually arise from ionization of the residual gas between the last dynodes where the number of electrons per pulse is very large. In the case of the phototube the solution is usually to achieve and maintain the lowest possible gas pressure, but in the case of the GEM is to add a fairly large curvature to the channel so that the positive ions strike the walls travelling only a very short distance (see Fig. 4.12, also Kurz, 1979, for references). The CEM is, as its name implies, an electron multiplier, but it can be used to detect both positive ions or photons provided that the incident radiation has sufficient energy to liberate at least one secondary electron as it enters the opening of the CEM (Fig. 4.12). Some CEM have a funnel-shaped opening for improved collection.
mcomlng wmary
/
eiectron
’
--mwlg
wmary
electron
Cutaway views of channel electron multipliers (Cm's); left: Fig. 4-12 straight channel; right: curved channel. These channel multipliers are not yet widely used as detectors of radioactive-decay application in mass spectrometry, instrumentation in products, but find fairly extensive They space, and as detectors of spallation products in high-energy accelerator physics. are therefore probably of no more than academic interest at the present time to a burgeoning regional radioactivity metrological laboratory. 4.7. EERENKOV
RADIATION
DETECTORS
If a charged particle is propagated in a transparent medium, by energetic beta decay or as an energetic Compton recoil, with an initial speed in the medium that is greater than the speed of light in that medium, then it is observed to emit visible radiation in the Many will have range, in the case of its discoverer, Cerenkov radiation (Cerenkov, 1937). observed this bluish radiation surrounding the fuel assembly of a swimming-pool reactor. shock waves that are It is, in fact, produced somewhat analogously to the supersonic As the high-velocity created when a flying object breaks the so-called sound barrier. particle traverses the transparent medium it leaves in its trail a wake of electrically polarized atoms that emit electromagnetic radiation as they depolarize. The refractive index of water, n, is equal to 1.33 at ambient temperatures, so that If a high-energy charged particle the speed of light in water is equal to about 3c/4. traverses water with a speed equal to a fraction p of the speed of light then the tLrenkov radiation can only be emitted as a coherent wavefront in a cone of half angle ti where cos B = l/PI-L. For a particle that has a speed approaching that of light the value of B tends to unity and the angle 0 approaches a maximum value equal to cos-1 (l/n). Conversely, as the angle 0 approaches zero, fl tends to l/n, and c/n represents the threshold speed for the production of Cerenkov radiation in that medium. Eerenkov radiation has rather limited uses in radionuclide metrology but has usually applications in high-energy physics. It is detected by means of and electron-multiplier using liquid-scintillation-counting techniques phototubes, equipment. Colour quenching is a problem common to both methods of detection, but t?erenkov radiation is, from its very nature, not subject to chemical or ionization quenching. Gelsema et al. (1975) have enhanced the efficiency of the Cerenkov effect for the detection thereby of energetic photons by adding high-2 salts, such as sodium iodide to water, increasing the probability of observing high-energy Compton-electron recoils. The Eerenkov radiation produced by high-energy principally in the higher-frequency range of the visible for electrons
having
For further may be consulted
energies
information
between
275 keV and 2 MeV
and references,
Jelley
electrons spectrum, (Ross,
(1958),
in water is emitted between 250 and 600 nm
1970).
Franfois
(1973)
and NCRP,
1985
Radioactivity
a22
measurements:
principles
and practice
4.8. CALORIMETRY To the extent that radiation energy can be absorbed by matter, so can the quantity of radiation be measured in terms of the amount of heat generated in the process. In the case of a radioactive source, this is usually achieved by confining the source within an enclosure that is thick enough to absorb all the radiation (or much of it for relative measurements), and by measuring the rise in temperature of the enclosure as a function of time, or by balancing the rise in temperature against that due to a known source of power (often electrical power) contained in a second similar enclosure, maintained under identical conditions. The enclosure is often called a -1 thermel and its temperature is usually measured by means of thermistors or thermocouples. In the case of the well-known Bunsen ice calorimeter, the temperature is constant and the balancing source of power is provided by the latent heat of melting ice in a given interval of time. There are three broad classes of calorimeter, namely adiabatic with practically no loss of heat to its surroundings and its increase in temperature is measured, isothermal in the equilibrium condition of which the heat loss to the surroundings is equal to that generated by the source, and twin-cur, in the equilibrium condition of which the power generated by the source in one thermel is balanced against a known source of power in a second as-identical-as-possible thermel in similar surroundings as the first. Calorimetry, utilizing both calorimeters and very sensitive microcalorimeters, has been used since 1903 for the measurement of radioactivity. (For references between 1903 In recent years the uses of calorimetry have been largely and 1958, see Mann 1962.) limited to the assay of special nuclear materials such as 241Am and the isotopes of In this application the calorimeter designed by Jordan and Blanke plutonium (ANSI, 1975). (1959; also Jordan, 1967) and the Bunsen ice calorimeter (Ditmars, 1976) have been those of In the last paper, Ditmars describes his use of the Bunsen ice calorimeter to choice. measure the power of two sources comprising mostly z38Pu of nominally 0.23 W and 1.4W. The sensitivity of the Jordan-Blanke calorimeter is such that the magnitude of the half life of 'H, using a 2-kCi source, can be clearly discerned from the recorded power-vs-time graph in a period of from 2 to 4 hours. The preparation of standards of 63Ni was also carried out at the National Bureau of Standards in 1968 using a twin-cup microcalorimeter (Barnes, et al., 1971). Otherwise this method currently finds few applications to radionuclide metrology. For further extensive references NCRP (1985) may be consulted. A very
remarkable
development in cryo-microcalorimetry has recently been achieved by and their colleagues (see Moseley et al., 1984, and McCammon et al., 1985) using etching techniques developed by Downey (1980). Their calorimeter consists of a very small and thin doped silicon wafer (0.5 x 0.5 mm x 80 pm; Moseley et al., 1985) At these temperatures all with an ion-implanted transistor operating at less than 0.3 K. small. carriers are trapped and, by the Debye T3 law, the heat capacity becomes vanishingly Their calorimeter is therefore sensitive to a single "Mn x ray, for which they have obtained photopeaks with resolutions of 35 eV or less.
D.MCC~INIIO~and S.H. Moseley
4.9. COUNTING
RADIOACTIVE
ATOMS
Much more sensitive methods of measuring the activities of radioactive substances have of measuring the numbers of been developed in the last decade, based on the principle radioactive atoms in a sample before they decay instead of counting the numbers of atoms The earlier method was that of accelerator mass suectrometry, and decaying in unit time. the latter, based on the method of selective laser photoionization, is also known as resonance-ionization spectrometry. In the tandem Van de Graaff method (Bennett et al., 1978) negative ions are injected into the accelerator operating at about 10 MV. They pass through an electron-strippng foil in the high-potential electrode, and are accelerated Both before and after the ions through another 10 MV as they return to ground potential. undergo charge-to-mass selection in the manner illustrated in Fig. 4-13, they are finally In the case of 14C dating the sensitivities are identified by range and energy detectors. such that measurements can be carried out with samples of milligrams rather than grams, but The methods of accelerator-mass-spectrometry dating are possibly at some reduced accuracy. such as "Be not, however, limited to 14C, but may be applied to long-lived radionuclides and others produced by by cosmic radiation. Neither of these methods measures activity directly; the former method of high-energy mass spectrometry requires an appropriate standard of activity to calibrate the system, and the latter requires a knowledge of the value of the radioactive decay constant in order to calculate the activity of the sample. However in contrast with the direct method, the sensitivities may be as much as lo3 times greater but their accuracies are not yet as high. 4.9.1.
Accelerator
mass
suectrometrp
This method is based on the use of a cyclotron, or a system of deflecting magnets and Historically, probably filters with a tandem Van de Graaff accelerator as an ion source. the earliest published use of the cyclotron as a mass spectrometer was given in papers by in which they described the separation of 'He from 'He and Alvarez and Cornog (1939), the discovery of tritium using the 60.inch Berkeley cyclotron. The cyclotron itself has a
Radioactivity measurements: principles and practice
023
mass resolution that is considerably greater than that of a mass spectrometer, and the background of unwanted atomic ions with the same charge-to-mass ratio can be reduced by differential linear energy absorption in range filters and particle-identifier detectors. They also operate in the case of 14C to remove the otherwise overwhelming background contributed by residual atmospheric 14N. (Also see Bennett et al., 1968, and Fig . 4-13.)
principle of 14C-atom counting with the tandem-accelerator Fig. 4-13 mass spectrometer. 4.9.2. Selective laser ohotoionization Following the development of lasers operating at a variety of frequencies it became possible to photoionize selected individual atoms of an isotope of a given nuclide by means of a two-step photoionization process. This method of measurement selects any one atomic species from the rest of a sample by excitation of the atoms of choice, using laser radiation of an appropriate frequency, to an intermediate energy level (below the ionization potential), whence it can again by excited by laser radiation into the ionization band. For this second excitation the same laser frequency can be used, when appropriate. Such ions can then be electrostatically accelerated into a detector and counted. The development and applications of this method have been described in an excellent review by V.S. Letokhov and C.B. Moore (1977) entitled "Laser Isotope Separation". This has a wealth of useful technical detail (146 pages and 367 references). In their Preface the authors make the comment that the "laser enrichment of uranium Fromises to be the first major chemical applications of lasers in industry" and this forecast is given considerable substance by reference, later in their review, to the work of Tuccio et al. (1974) and Snavely et al. (1975), at the Lawrence Livermore Laboratory. These last authors subjected a collimated beam of zJsU and 23aU atoms to the radiation of a tunable dye laser that, at a wavelength of 591.54 nm excited the 235U atoms. Simultaneously the beam was irradiated with radiation from a mercury lamp in the wavelength range of 210 to 310 nm, which ionized the excited 235U atoms. These latter were then separated from the beam of neutral atms by a transverse electric field. In the work reported by Snavely et al., a Z35U+-yield rate of 20 mg h-' was obtained. G.S Hurst and his co-workers (1979, 1980) have developed many experimental systems and procedures for the application of this method. In the latter publication (1980), schemes are tabulated for photoionizing all known elements except helium and neon. An interesting and informative review of the development of high-energy mass spectrometry, with many references, has been written by Muller (1979), and some more recent reviews, with references, are contained in Currie (1982). An also interesting, but initially disappointing, attempt has been made by Hutchinson et al. (1987) to apply the method of resonance-ionization spectrometry to environmental samples by measuring trace uranium concentrations in soil. They concluded that, although the concentration of 238U could not be measured by this method, the ratio of 235U/238 U spikes (in about equal parts) could be measured with an accuracy of about 16%. 4.10. OTHER RADIATION DETECTORS More than 600 pages of the total of over more than 800 pages of Knoll (1979) are devoted to radiation detectors and to the subject of detector electronics and pulse processing. Furthermore, Knoll gives references to publications describing investigations carried out with many different kinds of detectors and giving details concerning their operational characteristics. There are also many other available references that describe different types of detectors ranging from solid-state detectors of small size (weighing fractions of a gram and used for in viva intracavitary detection) to the detector system, weighing 2 x lo3 kg, at the European Center for Nuclear Research (CERN), in Geneva, that is designed to detect and identify the particle showers produced by the collisions of very energetic protons and antiprotons. (This latter, with its ancillary equipment, is operated by technicians wearing contruction-workers' hats!)
824
Radioactivity
measurements:
principles
and practice
Very few detectors at either end of this scale will be used for routine radionuclide metrology, but for often very specialized and esoteric applications that are far beyond the limited scope of this Report. But for those who have an interest, academic or otherwise, reference could, for example, be made to England (1976), Kamitsubo et al. (1982) or Barth and Neuhofer (1983). Many further references will be found therein. 4.11.
RADIATION
ENERGY
General
remarks:
4.11.1.
4.11.1.1.
Enerev
SPECTROMETRY Detectors
nroblems
of choice
and the need
for enerev measurements
A rough energy spectrum is often sufficient for the spectroscopic identification of radionuclides and possible impurities. If a more definitive answer is sought, a precise spectrum must be registered and analyzed (spectrometry) by which activities can be measured or compared via peak-area evaluation; decay-scheme parameters may be determined, as well as detection limits or cut-off energies for counting devices. It is advisable to use standard geometries for such measurements, such as 76-mm x 76.mm (3" x 3") NaI(T1) scintillation detectors and sources at 25- or lo-cm distance, or 25-m& Si surface-barrier detectors. The source-detector distance for the latter should be at least 2 cm in order to avoid significant coincidence-summing effects. 4.11.1.2.
Characterization
of spectra
The energy of particles or photons emitted by a radioactive source is distributed in a way more or less characteristic for the source substance. The observed energy spectrum, i.e. the number of particles or photons per unit energy interval as a function of energy, is often modified by the material and geometry of the detector and by the source configuration, depending on the nature and energy of the radiation. As was explained in 72.4, energy continuous, and a distinction is made spectra,
spectra between
may be discrete ("line" spectra) differential spectra n(E) and integrzt
N(E) = s&E E
as functions of E’ (see Fig. 2-S). A single spectral "line" is broadened by the detection process and by interactions in the source itself and becomes a "peak" with a definite width. Peak shapes can often be fitted to normal ("Gaussian") distributions (see Fig. 2-3 and Eq. 3-28) and have their characteristic width (FWHM, FWTM, etc.) at one half or one-tenth of the maximum. The smaller the width, the higher is the resolution. The latter is often expressed by the quotient of FWHM by peak energy. In a photon spectrum the peak positions correspond exactly to the peak energies, provided the peak is symmetrical. However, the tail from another peak or from Compton scattering or "scattered radiation" may render a peak asymmetric, so that the maximum ordinate no longer corresponds to the real peak position. In This applies also, of course, to secondary peaks (escape, etc.), an o-particle spectrum, the peak position does not correspond to the full energy, whereas puse (i.e. free of conversion or Auger electrons) B-ray spectra have no peaks and extend as far as the full disintegration energy. Further peak-to-total, 4.11.1.3.
detectors may characterization of sources and peak-to-valley and peak-to-Compton ratios (see Fig.
Spectral
be expressed by 3-9 and q4.11.5).
the
distortions
The radiations emitted by the atoms of a source undergo a series of interactions on their way to, and inside, the detector by which the shape of the spectrum gets distorted in more or less important ways, depending on the nature and energy of the radiation, the source properties, and the construction of the detector, including its electronic system. its support and any surrounding matter cause absorption (self- and The source itself, foil-absorption) and scattering. Further scattering occurs in the detector material and its envelope. Counting statistics and detector response can be an important cause of distortions: pulses created by particles or photons may add randomly (pile-up) or by coincidence (sum peaks) or secondary radiations and peaks are produced (see 74.11.1.4). 4.11.1.4.
Secondary
radiations
and peaks
All the effects mentioned in y4.11.1.3 are unwanted but often unavoidable. Therefore, they must be recognized as such and taken into account. Bremsstrahlung (bremsen = to brake), originating from the stopping of charged particles, can be regarded as part of the background, and annihilation of positrons yields pairs of photons each of energy equal to 511 keV, and consequent single or double escape peaks. (These occur when one or both of the annihilation photons escape without interacting with the detector forming peaks mOc2 (0.511 MeV) and Zm,,c' (1.02 MeV), respectively, below the photopeak. With positron emitters, annihilation in flight, between source and detector, can cause errors (73.4.3.4) but this is not, of course, a factor in liquid-scintillation counting.) Internal conversion and the photoelectric effect ("external conversion") give rise to electrons and
Radioactivity
measurements:
principles
and practice
Backscattering of Q or 0 particles, x or 7 rays avalanches of x rays and Auger electrons. can modify a spectrum considerably and confuse its interpretation (see Fig. 4-15). Satellite peaks and higher-order effects may have similar consequences.
200
0
BOO
500
400
Fig. 4-14 Characteristic parameters of a spectrum: E,= Energy at maximum count rate, FWHM = Full width at half maximum, FWWl = Full width at one-tenth maximum, Nmax/Nmio = Peak-to-valley ratio, N,,,/NCE = Peakto-compton ratio, Np/Nt = Peak-to-total ratio = photofraction.
0.05 Fig. 4-15 Energy energies, Ey 4.11
.1.5. Instrumental
01
0.2 03
0.5
1
2
of Compton edge and backscatter , of incident radiation.
345 peak for different
considerations
The experimenter will choose the detector and associated electronic system according to the nature and energy range of the radiation to be measured. Low-noise preamplifiers are recommended in many cases and data processing with pulse shaping must be adapted to the detector on the one hand and to further data processing on the other. Complete systems are available commercially but may not be sufficiently flexible for the task at hand. Pulse-shape discrimination can often be used to distinguish between different kinds of radiation, e.g. 1 rays and neutrons. A multichannel analyzer of at least 1,000 channels is almost indispensable for all kinds of spectrometric work, whereas advanced systems such as anticompton and pair spectrometers, magnetic or curved-crystal spectrometers are not really needed in everyday radionuclide metrology. Spectrum stabilizers (based, for example, on electronically maintaining a high-energy peak in the same analyzer channel) are also available. 4.11.2.
AlDha-Darticle
4.11.2.1.
Suitable
sDectra
ener.ev-resuonsive
detectors
and their Drouerties
Many different types of detector, such as the following, can be used for the detection of 01 particles: Pulse-ionization chambers, gas proportional counters with thin windows or internal source, scintillation detectors (liquid scintillation, pure or activated NaI,
a25
Radioactivity
a26
measurements:
principles
and practice
activated CsI and ZnS, and plastic), and semiconductor detectors surface-barrier detectors, and diffused junction diodes).
(Si(Li),
Ge(Li),
HPGe,
Si
However, when a detailed energy spectrum is required, surface-barrier detectors and diffused junction diodes are superior to other types in most respects. We will therefore concentrate the discussion mainly on these two types and on their properties and merits. For further study the following references may be useful: Glover (1984), and Sze (1984). 4.11.2.2.
Silicon
surface-barrier
and ion-imolanted
detectors
The sensitivity of silicon surface-barrier (SiSB) detectors (74.6.3.5) to (I particles is much greater than it is to ,9 particles or 7 rays. Similar thin-layer detectors, both n+ and p', can now also be obtained by ion-implantation of appropriate dopants. Their responses are fully linear and the resolution is excellent (FWHM of 14 to 20 keV are current; 11 keV is obtainable with selected detectors, but usually for only a few months). The energy needed to produce one electron-hole pair is 3.62 eV at room temperature. The pulse height does not vary with count rate, and the pulses have a fast rise time of 10 ns The gold-layer entrance window may be as thin as 10 nm, corresponding to an or less. particles of 5 MeV. energy loss of 10 to 20 keV for a The sensitive volume (depletion Their small size makes them depth) ranges from 2 pm to 5 mm, depending on bias voltage. easy to use, but they are sensitive to light and relatively fragile. Irradiation by 10" (I particles per cm2 is likely to impair the detector irreversibly. Silicon surface-barrier detectors should be used in vacuum (5 10 Pa) in order to The gold surface must not be touched. However, prevent damage by surface-current leakage. Al-coated surface detectors have recently been developed that are not damaged by careful cleaning of the surface. Diffused-junction-diode detectors may be used where ruggedness is essential. The but the depletion region has been obtained in a operation is the same, in principle, different way and the dead layer is thicker. The surface may be wiped and the cost, in general, is less. The background pulse rate of fresh SiSB detectors is very low and negligible in the Therefore, sources of 208~209~210Po,a beginning, but may increase due to contamination. notorious "creeper", should not be measured without a cover foil. The energy range for a-particle spectra extends from 3 to 9 MeV, but mainly from 4.5 to 7 MeV. The pulse heights are in general large compared with electronic noise, the latter being due to "shot noise" from the detector-leakage current and from the preamplifier and amplifier circuits. The numbers of counts per channel in the peak is often several thousand times larger than that in the low-energy tail. Therefore, for detectors are very powerful tools the measurement of surface-barrier a-particle-emitting impurities and isotopic admixtures. Silicon surface-barrier detectors are produced in a large variety of configuration and specifications by many manufacturing companies, whose catalogues should be consulted. 4.11.2.3.
Other
a-uarticle
soectrometers
Such comprise gas proportional counters, scintillation detectors and Frisch-grid Owing to the energy of 28.2 eV necessary for producing an ion pulse-ionization chambers. pair in argon, FWHM values for 5-MeV a particles using proportional counters are about 100 considerably higher than those of about 15 keV that can be obtained with keV, which are With scintillation detectors efficiencies of 5 to 100 % (e.g. surface-barrier detectors. with CsI(T1)) can be obtained. Frisch-grid ionization chambers have an efficiency of up to Sources of a diameter up to 80 mm can be 40% and fairly high resolution (FWHM t 25 keV). The background rate is very low and the detector is easy to decontaminate. used. It is insensitive to j3 and 7 rays and is nearly indestructible. A proportional counting-gas mixture of high-purity Ar/CH, (in the ratio 9 to 1) is normally used, and the chamber must be vacuum tight, so as to be able to evacuate it rapidly to 10e3Pa, before filling. It is claimed to provide a good introduction to practical a-particle spectrometry (Glover, 1984). 4.11.2.4.
Shaoes
of a-uarticle
snectra
Alpha particles from radioactive substances always have sharply defined energy values corresponding to the mass-energy difference between parent and daughter atoms (see q2.4.2. On traversing the electron cloud that surrounds the parent atom, an (II and 2.5.2.). particle loses small amounts of energy which results in a slight broadening of the otherwise nearly infinitely sharp line. However, this natural line width is too small to because of the be observed, even with the highest-performance magnetic spectrometers, unavoidable self-absorption and back scattering. In surface-barrier detectors, additional broadening is produced by statistical incomplete charge collection and variations of energy loss in the phenomena (scattering, Geometrical effects are important and may necessitate a compromise between dead layer). source-detector distance, count rate and solid angle.
Radioactivity measurements: principles and practice
PO-215
6.4
6.6
6.8
7.0
7.2
24
PC.-214
76
7.8
8.0
8.2
8.4
8.6
8.8
Typical alpha-particle spectra measured with a conventional Fig. 4-16 surface-barrier-detector system with an overall FWHM of 12 to 15 keV. Numerical data are given in Table 2-6. Table 4-1 - Recommended energy and intensity values for selected a-particle emitters (see Fig. 4-16)
1, (%)
El2 (kev) 235"
4 599 4 556 4 502 4 414 4 400 4 365 4 344 4 325 4 218
(1) (2) (1) (2)
5.0 4.2 1.7 2.1 55 17 1.5 4.4 5.7
234u
4 774.8 4 722.6 4 603
(9) (9) (2)
72.3 27.4 0.3
239PU
5 156.70 5 143.9 5 105.1
(14) (8) (8)
73.3 15.1 11.5
222RKl
5 489.52
(30)
99.92
244Clll
5 804.82 5 762.70
5) 5)
76.4 23.6
252Cf
6 118.1 6 075.7
5) 5)
84.5 15.5
21bPo
6 778.3
( 5)
=lOO
215P0
7 368.2
(8)
=lOO
214Po
7 686.90
(6)
=lOO
213Po
8 376.3
(26)
=lOO
212P0
8 784.92
(12)
=lOO
(2) (2) (2) (4)
027
Radioactivity measurements: principles and practice
a28
A few typical spectra obtained with silicon surface-barrier detectors are show" in The corresponding energy and abundance values are presented in Table 4-1, in Fig. 4-16. Most spectra are complex and, for emitters with eve" the order of increasing energy. neutron and proton numbers, the line "intensities" decrease rapidly with decreasing energy. For even-odd or odd-even nuclides, this is not ordinarily the case, and the highest-energy It should also be noted that the particles often have very low emission probabilities. peaks stemming from the same nuclide have all the same shape. The thinner the source the However, there is always a more or less pronounced more "Gaussian" are the peak shapes. This is important in low-energy tail for which a hyperbola may be a good approximation. analysing complex u-particle spectra of isotopic mixtures. 4.11.2.5. Calibration enereies Direct a-particle-energy measurements are reserved to specialized laboratories and high-precision equipment, and have been carried out for nearly 30 different a-particle The large majority of energy values have been measured with respect to these emitters. high-precision standards which thus constitute the basis of a consistent system of recommended values (Rytz, 1979). Some of those are reproduced in Table 4-2. Table 4-2 Calibration energies for a-particles (in keV)
DECAY CHAINS
SINGLE EMITTERS 3 182.71 4 013 3 954
(3)" (3) (8)
238"
4 197 4 150
(5) (5)
235"
4 4 4 4
599 400 374 368
(2) (2) (4) (3)
4 687.7 4 621.2
(15) (15)
234U
4 774.8 4 722.6
(9) (9)
231P,
5 5 5 4
(1) (1) (I) (1)
230Th
239Pu
059 028 014 952
5 156.70 (14) 5 143.9 (2) 5 105.1 (2)
2IOPo
5 304.38
24IAlll
5 485.60 (12) 5 442.90 (13)
238PlJ
5 499.07 (20) 5 456.3 (2) 5 721.00
(8) (10)
244Clll
5 804.82 5 762.70
(5) (5)
*42cm
6 112.77 6 069.42
(8) (12)
253E*
6 632.57 6 591.4
236PLl
5 767.66
(7)
228Th
5 423.20 5 340.31
(22) (15)
224R,
5 685.42 5 448.7
(15) (12)
212Bi
6 089.94 6 050.83
(4) (4)
2%OR"
6 288.13
(10)
216Po
6 778.3
(5)
212Po
8 785.08
(12)
227Th
6 038.06 5 977.71 5 756.96
(15) (10) (IO)
223R,
5 5 5 5
(4) (29) (30) (9)
211Bi
6 622.9 6 278.8
(6) (6)
21gR"
6 819.1 6 553.0 6 424.7
(3) (3) (3)
215Po
7 386.2
(8)
226~3
4 784.38 4 601.7
(25) (2)
22%"
5 489.52
(30)
218Po
6 002.40
(9)
214Po
7 686.90
(6)
(5) (5)
Data taken from Rytz (1979)
*Uncertainty
in units of last digit(s)
747.2 716.16 607.34 539.8
Radioactivity measurements: principles and practice
4.11.3. Beta-Darticle and
eleCtrOn
829
SDeCtra
4.11.3.1. Suitable detectors and their main orooerties Electron energies can be measured by means of gas proportional counters (operated over a wide range of suitable pressures), scintillation detectors (inorganic, organic, plastic or liquid scintillators) or by semiconductor detectors (Li-drifted Si and Ge, HPGe, or surface-barrier detectors, and many others). In gas proportional counters about 30 eV (35 eV in CH,) is needed to produce one ion pair. The detector must be larger than the path length. Such counters of 30.cm diameter have been used successfully for measuring spectra of conversion electrons (see NCRP, 1985). 4a gas proportional counters operated at pressures of up to =7 MPa (70 atm) have also been used for the same purpose (see A.P. Baerg HN, 1973, p. 95; J. Legrand et al., HN. 1973, p. 101). Lithium-compensated silicon detectors are preferred for electron spectrometry and have They have a calculable been well investigated for energies between 0.015 and 5 MeV. response and a good resolution if the thickness is greater than the maximum penetration At 300 K, the distance. The low atomic number of silicon favours low backscattering. energy needed to produce one electron-hole pair is 3.6 eV. Si(Li) detectors are generally used at liquid-nitrogen temperature, but they do not seem to deteriorate when it is necessary to let them warm up to room temperature, from time to time. Ahmad and Wagner (1974) report I!WHM values of 0.88, 1.06, 1.50 keV for electron energies of 115, 194. 624 keV, respectively. The dead layer was 0.6-pm thick, corresponding to an energy loss of about 20 keV. 4.11.3.2. Shaoes of B-oarticle and electron soectra Beta-particle energy spectra are continuous, and extend from zero to the maximum A spectrum with superimposed lines from conversion electenergy E,,, (see also 12.4.3). rons and subsequent Auger electrons is represented in Fig. 2-7. Such spectra can in principle be used for activity comparisons, but it is important to account for the various disturbing effects, among which scattering and self-absorption are prevalent, especially at 1OW energy. As scattering and backscattering increase with atomic number, silicon detectors are superior to germanium detectors. A spectrum may be further disturbed by electromagnetic radiations and secondary effects. 4.11.3.3. Some imoortant calibration enereies There are not many suitable calibration standards for monoenergetic examples are given in Table 4-3.
electrons.
Table 4-3 - Calibration energies for electrons
Source 1251
55Fe
keV 3.7 4.9 to 5.2 5.7 to 5.9 6.3 to 6.5
Intensity, percent of source decays
Radiation
79.3
Ce-K
48.5 11.0 0.9
Auger-K
133Ba
17.2
10.6
ce-K
125I
21.8 to 23.0 25.8 to 27.4 29.8 to 31.7 30.5 to 31.2
13.1 6.0 0.8 10.7
Auger-K
ce-L
133Ba
45.0
45.2
ce-K
131I
45.6
3.5
ce-K
'99Al.l
125.1
5.5
Ca-K
'03Hg
193.6
13.5
Ce-K
lJlI
329.9
1.5
ce-K
207Bi
481.7
1.6
ce-K
13'CS
624.1
8.1
ce-K
Data taken from NCRP (1985) and Lagoutine et al. (1975)
Some
Radioactivity
830
4.11.4.
Snectra
4.11.4.1.
of electromagnetic
Suitable
detectors
measurements:
principles
and practice
radiation
and their urouerties
For photon spectrometry, detectors made from high-2 material are essential in order to obtain the greatest possible absorption of energy within the detector. This explains why the thallium-activated NaI crystal is by far the most frequently used detector for photon spectrometry above about 50 keV. But for high resolution semiconductor detectors must be used. (For higher resolutions, semiconductor detectors are used.) 4.11.4.2.
Thallium-activated
sodium-iodide
detector
The relatively high atomic number (2=53) of iodine ensures high photoelectric absorption, high photo-fraction (ratio of the photopeak area to that of the whole spectrum) and high detection efficiency. Response functions have been calculated for many different photon energies and crystal dimensions. These theoretical spectra reproduce many features of the experimental curves, except for low energies. The detailed study of a response curve gives a deep insight into the various phenomena of photon interactions with the detector material, and helps to determine the most favourable conditions as to the choice of detector dimensions and measuring geometry. The almost exclusive aim of photon spectrometry is the measurement of the photopeak area for each single line of a spectrum. The precision with which this can be accomplished depends on the energy resolution, defined as R = AE,/E,, where E, is the -/-ray energy and AE, is the full-width at half-maximum (FWHM) value of the number-of-events peak (see Fig. 4-14). For any specific detector, the resolution as a function of photon energy is given by
h (a+bE,) RZ-----
(4-5)
E, where E, is the photon energy, and a and b are constants that can be measured experimentally for every specific detector assembly. The intrinsic resolution of a scintillation crystal is of the order of 1 to 2%, for excellent light-reflection conditions. Because a scintillation crystal is always used multiplier phototube (see Fig.4-11), loss of resolution l l l l l
in combination with an depends on the following
electronfactors:
the statistics of photoelectron collection (in the phototube); the electronic noise (almost negligible); the sensitivity variation over the active detector volume; gain fluctuations in the phototube; drifts.
By convention, the resolution is often expressed with respect to the 662-keV 7 rays from the decay of 13'Cs, For NaI(T1) of 76.2-mm diameter and height (3" x 3"), resolutions of between 6 and 7% may be considered very satisfactory. For 7 rays from the decay of a'Co (E, = 122 keV) current values are 10 to 11%. The quality of commercial NaI(T1) crystals is such that very reproducible efficiencies are obtained for specified geometries. The most frequently used configurations are the right cylinder with height equal to diameter, and the right cylinder with a reentrant cylindrical well. The latter is especially useful for the measurement of weak sources because of the large solid angle and the low dependence on source position inside the well. Efficiencies, so-called total and absolute, as well as intrinsic and peak-to-total, have been measured with high precision and presented in spectra, graphs and tables by various authors (also see 7 5.2.1.5). Good definitions of the first three of these four qualifiers of "efficiency" can be found in Knoll (1979). Background may be important, mainly in low-level activity measurements. External causes are cosmic radiation (that is normally dominant without shielding) and ambient l-ray sources. The remainder is due to photons from contamination and interactions in structural and shielding material. Besides cosmic rays the mo.st important sources of background radiation are 4oK (mainly in the phototube envelope), '*'Rn (in the air) and various contaminants of the shielding material. However, 5 cm of lead lined with 1 mm of Cd sheet (to absorb the K-shell photoelectrons from lead) is an adequate shield for many applications. In the event that a new laboratory is being built to house the counting equipment, particular attention should be paid to checking the aggregate of the concrete that is to be used in the foundations, walls and floors of the structure. This is of utmost importance when the laboratory is to be used for low-level mea.surements and environmental monitoring for radioactivity. When NBS moved to a new site just over 20 years ago, aggregates tested were found to have an appreciable range of activity, After the move the backrounds of solid-state detectors in the basement laboratory at the new site were found to be about half of what they had been in the basement laboratory at the old site probably largely due to the choice of a very inactive aggregate for the concrete used.
Radioactivity
measurements:
principles
Nowadays scintillation crystals are almost with phototubes. Further needed components are: l l l l l l
always
a stable dc power supply of 1 to 3 kV; a preamplifier mounted closely to the phototube; a linear amplifier; a single-channel analyzer or better multichannel a scaler-timer. optional: pile-up rejector; spectrum stabilizer;
Available consulting 4.11.4.3
and practice
purchased
The detectors lithium-compensated
detectors
and shapes
integral
analyzer
(at least
recorder
and xy plotter.
forms and sizes of crystals, and their prices, may manufacturers' brochures, announcements and catalogues. Semiconductor
as
831
of eamma-rav
best
assemblies
1000 channels);
be
determined
by
suectra
most frequently used for photon spectrometry silicon (2=14), germanium (2=32) and high-purity
are fabricated from germanium crystals.
Si(Li) detectors have photoelectric cross sections lower than those of NaI by a factor of about 50, but that is still sufficient for the detection of low-energy or x rays (LEPS, Such thicknesses of a few millimeter* are sufficient. low-energy-photon spectrometry); detectors give less prominent x-ray-escape peaks and smaller leakage current thdn Ge detectors. Cooling can be interrupted by warming-up cycles to room temperature, with no Below 55 keV the photoelectric process is more deterioration of detector performance. is complete (see probable than the Compton effect; below about 30 keV, charge collection Peaks due to x-ray Fig. 5-6) and produces single full-energy peaks of Gaussian shape. escape occur 1.8 keV below the photopeak, whereas in germanium they would be much larger and occur 11 keV below the photopeak. Above 3 MeV, pair production is not so overwhelming Dead layers in silicon as in germanium and the detection efficiency is normally adequate. are of the order of 150 nm. They are Ge(Li) and HPGe detectors are mostly used at medium energies (2 100 keV). commercially available in many different forms and useful sizes up to 100 cm3, and more. At low energies the peak width is dominated by electronic noise, to an extent depending on as a result of bias voltage. Therefore, small detectors are somedetector capacitance, times preferable. At an energy of 5.9 keV (55Fe x rays) resolutions (FWHM) of 150 to 250 eV are possible; typical best values at 122 keV and at 662 keV are, respectively, 400 to 500 eV and over 1 keV. The entrance window is about 400-1~~ thick. the resolution of a semiconductor It is very important to note that, bv convention, detector is given as AE, (the FWHM) at a specified energy E,. If it is assumed that the photopeak approximates a normal ("Gaussian") distribution, in which case AE, would be approximately equal to 2.350, i.e. extending above and below the mean, E,, by approximately 1.17717 (see Fig. 2-3 and Mann et al., 1980). Also,
if Ep is
the average
energy
AE, = 2.35
(E,E,)'
If the Fano factor is also taken becomes (Mann et al., 1980; NCRP, AE, = 2.35
required
to produce
one electron-hole
.
into account, 1985)
X- and ?-ray
the resolution
of a semiconductor
(FETE,)'
calibration
then
(4-b) detector
(4-7)
Examples of the shapes of y-ray spectra are given in Fig. 2-11 for a %o Fig. 4-17 for an lg21r source, each with NaI(Tl)and Ge(Li) detectors. 4.11.4.4
pair,
source,
and
in
energies
Recommended energy values for the calibration of photon detectors have been published by Helmer and van Assche (1979); also see Appendix 10 of Lederer and Shirley (1978). A 182 of NCRP (1985). comprehensive table of such energy values may be found on page 4.11.5.
Ouantitative
4.11.5.1
Aims,
spectral
possible
analysis
Drocedures
and problems
involved
Pulse-height equipment can reveal a large amount of spectra taken with modern information not only about the incident radiation but also about the performance of the detector. The aims of quantitative analysis of nuclear spectra are: l l l l
identification of the radionuclides in the source; activity measurements and impurity assays (with uncertainties); efficiency determination and estimate of detection limits; establishment of detailed efficiency functions.
Information-extraction required. They vary also
procedures depend on spectral quality and on the accuracy according to the radiation source, the radiation nature and the
Radioactivity
832
measurements:
principles
and practice
Fig. 4-17 Main part of the 19*Ir spectrum taken with a 76 x 76 mm NaI(T1) detector (WHM -8% at 1.33 MeV) and with a 50 cm3 coaxial Ge(Li) detector (FWIM ~0.15% at 1.33 MeV); numerical data from Heath (1964) and Heath (1974). detector type. It is not possible to discuss here the various procedures in detail, and we shall confine ourselves to just one kind of radiation (photons) and one type of detector (germanium detectors: Ge(Li) or HPGe). Single-channel analyzers (see Fig. 6-20) for differential counting are now almost completely superseded by highly sophisticated multichannel analyzers. The high stability of these very versatile instruments allows one to store very reliable pulse-height spectra directly on to magnetic tape or computer discs. Peak-area integration, a most important task, can be performed manually, for simple problems, or by computer, but the fullest analytical advantages of -(-ray spectrometry can only be achieved by means of elaborate computer programs. Many different programs have been developed and published which provide a completely automatic and detailed analysis of the identified nuclides and their with graphical and numerical print-out of a list Such an extensive treatment includes, of course, smoothing of activities or abundances. of background, peak search and identification, peak-shape analysis the data, subtraction and fitting, and peak integration for intensity calculation (also see g5.2.2.5). In can be evaluated and disturbing effects, such as sum coincidence or addition, uncertainties pile-up, can be taken into account (also see 75.2.4.3). 4.11.5.2
SiniDle peak
integration
methods
(manual or Commuter-aided)
The measurement of a differential pulse-height spectrum (dN/dH vs. H) involves the determination of AN/AH as a function of the pulse height AH, whereANis the whole number of pulses observed in a small but finite pulse-height interval AH, usually a whole-number channel width (but converted to energy by an energy/pulse-height scale calibration factor). in a spectrum with peaks of mean pulse height &,, if one It is, in general, convenient full-width at half-maximum height of a peak could occupy about 3 to 4 channels, and seldom Defining the detector resolution by R = FWHM/%, then, for R = 0.4% (i.e. more than 5. AE,'E = 4/100), the total number of channels to be provided for recording the full range of Similarly, assuming a quite realistic FWHM of pulse amplitude up to E, is 4/R, or 1000. On the other hand, 1.5 keV at 3 MeV, the multichannel analyzer should have 8000 channels. the total number of channels to be used also depends on the total number of counts that can be collected in a reasonable time. A simple example of the use of gamma-ray spectrometry is the measurement of the unknown activity of a source, A_, of a given radionuclide relative to the activity, Ak, of a standardized source of the same radionuclide by comparing the numbers of detected events, This can be done by adding up N, and N,., under the full-energy peaks (photopeaks) of each. channel contained within the limits of the "known" and the contents of every analyzer The background to be subtracted from the sum of events in the photopeak "unknown" peaks. channels is often obtained by taking the average content of the channels on either side of the pulse-height distribution that is estimated to represent the upper and lower limits of The activity of the unknown source is then given by %= A,N,/N,. A the photopeak.
Radioactivity
measurements:
principles
and practice
833
satisfying application of this technique was by Christmas and Cross (1983) in calibrating a relative to the U.K. sealed within a platinum-iridium needle, new radium standard, Hanischmid radium standard, using the 15%.abundant '14Bi 1.7645-MeV gamma ray in the decay chain of z26Ra. As all the radionuclides between "'Ra and 'lLBi are relatively short50-year difference in the dates of sealing of the two 226Ra lived, the approximately sources is immaterial and the high energy of the gamma ray reduces the significance of differences in attenuation or self-absorption by the source containers. For an ideal NaI(T1) crystal, the distribution to normal and can be written as
function
of the frequency
density
is close
N
P(x) = 4 (2x0)
exp
(-(x-x,)z/20z),
(4-S)
where x is the pulse height (proportional to the channel number, or energy of the detected standard deviation, and photon), x, is the pulse height of the photopeak maximum, o is the For a normal distribution the N is the number of pulses recorded in the photopeak maximum. full-width at half-maximum (FWHM) would correspond to the interval between x,-2.3550 and x,+2.3550, and the interval from x,-30 to x,+30 (= 1.3 FWHM) would contain 99.7% of the number of counts recorded in the photopeak; so that less than 0.3% lie beyond f30 from the In the foregoing discussion it photopeak and it has fallen practically to the background. has been assumed that the distribution of the frequency distribution is close to normal, but in practice the number of recorded events is finite and use of the estimated standard deviation s, would be more appropriate than 0. to a peak But, as a general rule, the interval corresponding may be of k+l channels above and below the peak channel, where k is the channel The total number of channels occupied by a recorded spectrum 1.3 FWHM. depends, of course, energy interval corresponding to a single channel) pulse amplification (also see 75.2.2.5). The simple facilitated with Inclusion used. also increase the 4.11.5.3
Computer
defined as that corresponding to (and thereby the on the selected
procedure for peak analysis just described can be accelerated and the aid of a small computer, whereby non-integer channel numbers may be of automatic smoothing and peak searching may not only save much time but consistency of the results. procedures
sophisticated computer programs have been developed and described (e.g. in Many Canberra, 1981; and by Helmer and McCullagh, 1983) by which a fully automated and complete Within the scope of this report it is spectral analysis can be performed (see 75.2.2.5). possible only to cover general principles, and not to keep up with the spectacular and To keep abreast with these the reader rapid developments in nucleonic instrumentation. should consult the literature, especially the very informative technical brochures that are available from the manufacturers. In these days of integrated microcircuitry, it is almost always easier to purchase a desired function than to create it from separate components. If one predicates that gamma-ray photopeaks follow a normal (i.e. "Gaussian" probability distribution P(x), with (for linear pulse-energy output) an underlying linear background, then a peak may be represented by the function N(x) = P(x) + Cx + B, where C and B are constants. But, instead of this theoretical and continuous function of the channel number x, the observations always comprise only the discrete and integral experimental values of counts in adjacent channels of equal energy increments, AE. Moreover, these values are subject to statistical fluctuations. Therefore, the existence, position and content of a peak can be determined only within certain limits of uncertainty that must also be evaluated. The following very abbreviated description of a detailed program given as an example of how the complete analysis of a pulse-height achieved: A.
Location
of peaks
(Canberra, spectrum
1981) is might be
of interest:
(a) (b) (c) (d)
Read experimental spectrum; Smoothing of the data read; Establish weighted first-difference spectrum; Search for possible peaks: zero crossings of (c) with negative slope, define regions where data increase above background in a statistically significant way; (e) Establish unsmoothed third-difference spectrum; (f) Peak-by-peak search for multiple peaks: zero crossings of (e) with positive slope and limits defined in (d); B.
Calculation deviation;
C.
Fitting of theoretical parameter uncertainties,
of peak
areas,
background
subtraction,
standard
peak shapes by non-linear evaluation of multiplet peak
least areas;
squares,
estimates
of
Radioactivity measurements: principles and practice
834
D.
Lower limit of detection, test whether a peak has a high enough probability to be "real";
E.
Detector calibration, using standard sources; (a) energy calibration and establishment of a relation of energy vs. channel number; (b) efficiency calibration;
F.
Peak identification by comparison with library data;
G.
Plotting and listing of identified radionuclides, output: energies, activities and uncertainties.
with their photopeak
5.
METHODS OF RADIOACTIVITY MEASUREMENT
5.1. INTRODUCTION 5.1.1. General The full description of a radioactive decay process would comprise all parameters of the initial state of the parent atom, the final state of the daughter atom, and the types Thus the metrology of radioand energies of all radiations in the process of decay. nuclides implies, in its broadest sense, a knowledge of the mass, charge, energy, magnetic dipole moment, electric quadrupole moment, half Life, spin and parity of the parent and daughter nuclei, and mass, charge, energy, intensity, spin, parity, polarisation, angular distribution, direction, and momentum of the emitted radiations. Many compilations of A narrower nuclear-decay data supply the latest known values of these paramaters. description of radionuclide metrology is restricted to measurements of activity (events par unit time) or radiation-emission probabilities. Radioactivity is usually measured in terms of the radiations that are emitted during Thus activity can the nuclear transition itself; but it can also be measured indirectly. This be derived from the mass, or number, of parent atoms if the half life is known. latter method has recently been used successfully in the method of accelerator mass spectrometry (74.9.1). Also, the activity of a parent can be derived from the numbers of daughter atoms (e.g. numbers of recoils produced in unit time). In this chapter the most frequently used methods, which are all based on electrical-pulse counting of the emitted radiations, are discussed in some detail, while the less frequently used special methods Some other methods that are less directly applicable to measureare treated only briefly. ments of activity in regional laboratories have also been mentioned in earlier chapters, and references made to appropriate texts where further information may be obtained (e.g. calorimetric and chemical dosimetry in 82.6, exe-electron and thermoluminescent dosimetry in 84.6.2.2, and resonant-ionization spectrometry, accelerator mass spectrometry and microcalorimetry in (1q4.8, 4.9 and 4.10. Other methods of detection based on excitation are the counting of tracks in photographic emulsions and autoradiography (Rogers, 1980); solid1975) and stimulated electrical discharges state track detectors (SSTD's; Fleischer et al., in spark and streamer chambers (Allkofer, 1971). The various measuring methods can be grouped into classes according to (i) the kind of radiation to be measured, (ii) the type of detector used (based on the physical principles involved, and (iii), the mode of measurement employed, such as pulse counting or current-reading, peak-area computation, single-channel or concidence counting (direct or by direct ("absolute") or relative (indirect) measurements, extrapolation techniques), source-detector geometry (external or internal source, lO", medium, 2s or 4n effective solid angle), physical state of source and detector (gaseous, liquid, solid; thin source or thick source), energy sensitivity, or position sensitivity. The physical principles involved and the many ways that they have been applied to radionuclide metrology are of basic importance; the principles have been discussed in some detail in chapter 4, and specific applications will be in the following sections. Many historical references to the early development of radiation detectors have been given by Spernol (HN., 1973). 5.1.2. Tvnes of radioactivitv measurement 5.1.2.1. Dieital. analoaue. peak counting. extrauolation The mostly used mode of measurement is single-channel (electrical) pulse counting (see The primary effect caused by the emitted radiation can also be integrated and Ch. 6). If the detector is energy sensitive and its measured as analog signal, e.g. a current. output signal proportional to the input, the number of counts in an energy interval, e.g. Further, measurements can be repeated under different under a peak, can thus be measured. The best mode of a conditions and the results extrapolated, e.g. to 100% efficiency. measurement is defined by many parameters and depends on the details of the methods used, as is discussed in the following sections. 5.1.2.2. Number of channels: coincidence and anticoincidence methods In single-channel measurements, electrical pulses induced in a single detector are counted in a single chain ("channel") of electronic instruments. But for certain purposes, two- or more-channel methods can be used with special advantage. Here, in general, two or more radiations and their coincidences are counted. These methods are restricted to nuclides that decay with the emission of two or more radiations and they need detectors that are each sensitive to one radiation only. These methods belong to the most accurate ones for the measurement of decay rates. This is due to the cancellation (in a first
835
Radioactivity
836
approxunation)
of the detector
measurements:
efficiences,
principles
and practice
c1 and Lo, in the coincidence
equations:
N, = N,N,/N,
= (~1N,)(~,N,)/(~1~2N,)
(5-l)
The coincidence method can not only be used for very accurate decay-rate measurements, but is also especially suited and powerful for the measuring of decay-branch probabilities or "intensities". If two radiations from a branch "a" of "intensity" (i.e. probability of emission), P,, can be measured separately and in coincidence, and N, (the activity of the nuclide itself) is known,then the value of P, can be computed from the classical coincidence equations, i.e.
Pa = NI,.Nz,./N,,.N~ where
(5-2)
9
N, 8 = P,al,,N,, N, a = Pa~z .N, and N, ci= P,e, acZ,.N,
Coincidence measurements can be extended to still more selective multiple-coincidence and anticoincidence methods. The latter have the additional advantage of the absence of any dead-time problems, but yield in general the same information as coincidence methods (see 75.5). Also, a comparison of single, double and multiple coincidence results can be used for the calculation of decay rates or branching ratios. 5.1.2.3.
Direct
("absolute")
and relative
(indirect)
methods
The great majority of applied radioactivity measurements are performed by comparison with a well-known standard. Such relative methods should be used wherever possible, because they are, in general, made much more easily, and cheaply, than direct measurements. They might even, be under certain conditions, more accurate than direct measurements. For example, the measurement of an 55Fe sample relative to standards of 54Mn and 51Cr is normally much more accurate than a direct measurement of 55Fe (see also 83.4.1). But finally all radioactivity measurements are based on some very accurate "absolute" or direct measurements. 5.1.2.4.
Use of statistical
laws
Pulse-mode counting, i.e. the measurement of the number of decays, within a certain time interval, is, statistically speaking, the simplest grouped-data-counting method. But other methods, some based on statistical laws and principles can be used to measure radioactivity. Such methods include Campbelling (Oda et al., 1976), multiscaling and correlation counting (Williams, Lewis and Smith, HN, 1973; NCRP. 1985, 73.2.4) selective sampling (SESAM; Miiller, 1981), module-Z counting (Mylon et al., 1983), time-of-event counting, and zero-probability counting. 5.1.2.5.
Suecial
auulications
Radioactivity-measuring methods are applied in quite different ways in as far-different fields as medicine and safeguards or mining and cosmology, etc. They are highly adapted to the individual problems and often extremely specialized, from protoninduced x-ray emission (PIXE) to extended x-ray absorption fine structure (EXAFS), and from wiping tests to flow-through methods, etc. These many special applications cannot be treated here. Thus, only the general principles and procedures of radionuclide metrology will be discussed. 5.1.2.6.
Most
freauentlv
used methods
While there are hundreds of special applications of different radioactivity-measuring methods, only a few of them are used frequently. These are the relatively simple and relatively accurate defined-solid-angle methods using modern solid-state detectors (NaI(Tl), Ge and Si(Li)). They are not only used for counting but also for identification of the nuclides emitting the detected radiations, These methods can be subdivided into relative methods for strongly scattered and weakly absorbed radiations (gamma rays of energies higher than about a few tens of keV) and direct methods for strongly absorbed and weakly scatterd radiations (mainly low-energy alpha-particles and electromagnetic radiation, but also electrons and fission fragments). The accuracy of the defined solidangle counting method in many cases is, however, limited by the accuracy with which the geometrical efficiency can be measured. For direct measurements, 4a methods, in which all the radiations from the source are emitted into the whole solid angle of 47r sr and counted techniques (T5.5), such as 4np-1 counting with efficiency extrapol(ll5.4), or coincidence ation, have been developed to a point where, in general, they are the methods of choice to results with low estimated uncertainties. But these methods when appropriately applied have been developed to give great accuracy, today of the order of 0.1 to 0.5%, and are in frequent use in national and international standardizing laboratories. Given an accurate direct standard of a suitably energetic gamma-ray-emitting nuclide, relative standards of low uncertainty can best be produced by means of a well-calibrated high-pressure ionization chamber, that can in optimum conditions give measuring reproducibility of the order of 0.1% or less.
Radioactivity
5.1.2.7.
Choosine
an optimum
measurements:
principles
and practice
837
method
If a certain radioactivity measurement has to be performed, several methods are often available, and a choice of the "best" method has to be made. Many parameters define what is "best", the most important ones being the desired accuracy which depends on the type of the decay and of the emitted radiation, simplicity, and price. It should be emphasized that, in cases where a good national or laboratory standard is available, relative methods of measurement are to be preferred. Optimum methods of calibration for some of the most frequently used radionuclides are indicated in Table 2-5. "Accuracy" figures given in Table 2-5 should be regarded as only rough estimates for "average" measuring conditions for various direct calibrations in column 1 and mostly relative measurements in column 2. The actual experimental conditions may vary considerably, and so too the attainable accuracies. For the establishment of a highly reliable system of radioactivity standards, that is traceable to national or international reference standards (see 72.2.3), and of reliable nuclear-decay data, it is necessary to make extremely accurate measuremeits. It is also important that these should be made using any available different and independent methods in order to reduce the probability of the presence of hidden systematic biasses (De Roost et al., 1972; Christmas et al., 1983). 5.1.2.8.
Characterization
of individual
methods
As radioactivity-measuring methods can be very different, an attempt has been made in 7q5.2 and 5.5 to describe them according to a common scheme. First the principle used (i.e. the physical effect measured and its mode of measurement) is described, with, if possible, an analytical description of the measurement (including geometry) and the radiations and nuclides that can advantageously be measured by that method. All methods are essentially determined by the detectors used and the experimental procedures applied. Therefore the detectors, source preparations, counting procedures and instrumentation used are then briefly described. and in most cases, the evaluation Finally, of the results corrections that must be applied and the attainable accuracy. 5.2.
RELATIVE LOW- AND MEDIUM-GEOMETRY SPECTROMETRY
5.2.1.
DEFINED
SOLID-ANGLE
is
COUNTING.
discussed,
including
INCLUDING
Introduction
5.2.1.1.
Princioles
Many radioactivity measurements are performed by low- or medium-geometry solid-angle counting, the simplest radioactivity measuring method. This method is characterized by the solid angle subtended at the source by the detector or by a diaphragm in front of it (Fig, 3--7). Only the radiation emitted from the source into this "effective" solid angle, n,,,, can be counted, neglecting scattering. The ratio of the whole solid angle (4n sr) to the effective solid angle, which can be very close to 1 (Fig. 5-l), is usually named the geometry factor, G (Eq. 3-6). The measured count rate must be multiplied by G and by the number of particles emitted per decay, in order to obtain the source activity, provided that the radiations are isotropic The geometry factor can be calculated for every source-detector geometry, but this can sometimes be tedious. Therefore, in practice, attempts are frequently made to approximate to the simplest case, namely a point source radiating isotropically a part of which radiation is incident normally upon a flat-surfaced detector masked by a circular diaphragm of diameter 22, at a distance a from the source (Fig. 3-7). In this case the geometry factor G is derived from the following simple formula G = 4n/n,,,
= 4n/[2n(l = 2/{1
so
that
- cos B,,,)]
zJ(a2 - 9))
,
G = 4z2/aZ
This expression (Fig. 5-1) can often be used as a first approximation geometrical situations and for the comparison of two geometries.
(5-3) in more
complex
838
Radioactivity
10
0
Fig. 5-l
measurements:
Geometry
factors,
30
20
G
principles
=
40
4a/Reff
and practice
50
for circular
diaphragms
with diameters 5 and an axial point source. 5.2.1.2.
Terminolopy
The terminology for defined solid-angle counting methods is not used uniformly. Because the geometry is such a very important parameter of a detector it, the geometry, is very often coupled with the descriptive name of the detector. It also indicates the nature of the geometrical factor that must be used in the computation of the efficiency of the detector system. In usually
this context, detectors with a termed b-geometry detectors.
solid angle of only a few percent of 4x sr are The term medium geometry is reserved for solid
angles from a few percent of 4n sr up to a few percent less than 2a sr. A method using a detector that subtends a solid angle of a few percent above or below 2?r sr to the source And methods using detectors subtending solid angles to the source are known as 2~ methods. percent less than 4n sr are designated as 4~ methods; and methods using of only a few solid angles lying a few percent above or below 2n sr and a few percent below 4a sr are Methods using very precisely measured diaphragms usually called m-geometry methods. placed in front of the detector to define the solid angle of detection subtended to the defined-solid-anele methods. It source are usually known as low-, or medium-geometry should also be emphasized that the term defined solid-angle counting includes the use of such as solid-state, that are used in a fixed source-to-detector geometry, all detectors, as in y-ray spectrometry. 5.2.1.3.
Relative
(indirect)
and direct
("absolute")
measurements
Two different types of solid-angle counting method have proved to be especially advantageous and are frequently used with remarkable success. They depend crucially on the radiations to be measured and on the detectors applied. For strongly absorbable and weakly scattered radiations (alpha particles, ions, x rays with energies below about 50 keV, and, electrons) direct counting can be performed with very high accuracy, less satisfactorily, especially if detectors that are 100% efficient for the measured radiation are available. On the other hand, for relatively weakly absorbable and more strongly scattered radiations relative measurements (with reference to otherwise well(7 rays and, less so, neutrons) especially if energy-sensitive detectors of offer great advantages, calibrated sources) The energy ranges considered here are, as usual, those covered high resolution are used. by radiations from radionuclides (from eV, but, mostly, a few keV up to about 3 MeV). The two methods are very different in several respects. For direct counting the crucial problem is to obtain the most accurate possible estimate of the corrections, but the accuracy of relative measurements depends on the similarity of the unknown and the standard source. Direct measurements are mostly made on nuclides with one characteristic radiation and small while relative measurements are mostly performed on nuclides with measurable backgrounds, considerable background caused by them. Therefore, several radiations and, consequently, relative solid-angle counting and direct defined-solid-angle counting are treated in two different sections (775.2 and 5.3).
Radioactivity measurements: principles and practice
5.2.1.4. Descrintion of solid-anele counting In direct ("absolute") measurements, generally of one radiation, all pulses per unit time, M, above an adequately chosen discrimination level are counted during any suitable period of time and can be used to calculate the source activity in terms of the computed solid angle and the photopeak (i.e full-energy-peak) efficiency, s,(E), of the detector. In the case of relative measurements, in which sources of radionuclides, with one or more 7 rays, are to be assayed against a calibrated source of the same radionuclide, only the counts contained in full-energy peaks of individual radiations are used for the comparison. Then, if the laboratory standard (subscript st) and the unknown source are equivalent in every respect, including source preparation (but not necesarily in half life, which is neglected in the following), Eq. 3-6 can be reduced to N = N,,W
B)/(M,,R,,
- B)
= Cm - B)/c,W =
(5-4)
M/<;(E)
where N is the number of decays occurring in the source during the chosen counting time, T, N is the number of counts in time T, R is the relative correction for dead-time losses and pile-up, B is the background count in time T, and r,(E) is the photopeak efficiency for 7 rays of energy E; c;; is sometimes used to denote the photopeak efficiency including deadtime, pile-up and background corrections, but this is, in general, not recommended. Equation 5-4 shows clearly the advantage of the relative method. The efficiency, e,(E), can be measured with suitable well-characterized calibrated sources for different energies, and an efficiency-calibration curve can be established. From the calibration curve the efficiency at any energy can be read and the activity of the source emitting the radiation selected for the measurement can be computed by use of the simple equation 5-4. The establishment of an efficiency curve is therefore the central problem of every relative counting method (75.2.3). It is also necessary to obtain accurate values for M, R and B, and this question is discussed in the following section. However, when the standard and the unknown source are not quite equal, matters become much more complicated. In such circumstances, corrections for all or part of the factors of Eq. 3-6 must be applied to Eq. 5-4, and this can lead to large uncertainties. 5.2.1.5. Peak. total and intrinsic efficiencies The full-energy-peak, or photopeak, efficiency cp is always defined as the probability of observing one count in the photopeak per particle, or per photon, emitted by the source. In principle, it is not necessary to know the efficiency provided that the measuring conditions for both the standard and the unknown source are very closely the same. Thus, for example, only the numbers of pulses above the energy corresponding to the peak maximum might be taken into consideration. But in order to make some of the corrections, especially that for coincidence summing in the case of photons, the whole peak count rate due to the photoelectric effect must be known. Therefore, all practical definitions of the photopeak efficiency should include as many pulses in the photopeak as possible. Several other definitions of efficiency, besides that of the very important photopeak efficiency, are used in defined solid-angle counting. The total efficiency, et, generally includes all pulses with energies above background, often obtained by extrapolation of the differential pulse-height distribution to zero energy. The total efficiency is used chiefly in activity measurements made with cylindrical NaI(Tl)-scintillation detectors and, with less accuracy, for the coincidence-summing corrections to measurements made with germanium detectors. The definition can be somewhat different for different purposes, e.g. x-ray It is, therefore, always of great importance to say pulses could be included or not. exactly how a total efficiency is defined; also the term "intrinsic efficiency," which is used in different ways (see, e.g., Knoll, 1979). 5.2.2. Practical nrocedures and instrumental details 5.2.2.1. Countinp svstems Most systems used for low- or medium-geometry counting consist of an appropriately designed unit comprising a source holder and detector, and electronic pulse-processing components connected to the detector. In many cases, the source-detector unit consists of an enclosure that can be evacuated (or flushed with helium) in order to count strongly absorbed radiation, such as a particles, and it can, in general, be shielded to enable the counting of 7 rays (see also 83.4.3.). Many different source holders and source-detector geometries are in use. Most systems can accommodate sources on thin plastic or metal foils. The gamma-ray counting systems are also usually suitable for sealed sources in many forms, such as ampoules and bottles, either within reentrant cavities in the detectors, or at different distances from the detector, or in some cases with the source surrounding the detector that is located in a reentrant cavity within a container known as a Marinelli beaker (Debertin, 1980). The systems used for metrological FIR1
39/8-I
work of high precision are often quite elaborate,
839
Radioactivity
840
measurements:
principles
and practice
but those for normal routine work in the laboratory are usually much simpler, but are often provided with automatic sample changers and automatically operated pulse-processing and The systems used in the field are kept as simple as possible recording electronic systems. But it is important in every case, not and are, therefore, not usually of great accuracy. The photopeak efficiency can vary even, to change any system components after calibration. for example, with the level of the liquid nitrogen in the cryostat of a Ge detector (Jedlovszky et al., 1983). Examples of defined-solid-angle counting systems are shown in Figs. 5-2 and 5-3 for gamma-ray counting, and in Fig. 5-4 for alpha-particle counting.
Simple, versatile x- and Y-ray spectrometer Fig. 5-2 measurements with a 3" x 3" NaI(T1) detector.
Typical arrangement of a Ge(Li) Fig. 5-3 for relative Y-ray measurements.
5.2.2.2.
or cooled
for relative
Si(Li)
detector
Detectors
Many different types of detector can be used for relative defined-solid-angle counting, but NaI(T1) and Ge detectors are nearly exclusively employed for ~-ray spectrometry. Other detectors, for special applications or for other radiations, are Si(Li) and SiSB (silicon surface barrier) detectors, ZnS(Ag) and other inorganic scintillation detectors, To day, Ge detectors plastic and other organic scintillators (see 74.6 et seq.). are mostly used for r-ray spectrometry, and there are already so many types and sizes on the market that, for any given purpose, a judicious selection is necessary; and manufacturers catalogues can be usefully consulted. Coaxial Ge detectors (truly coaxial with a central hole along the entire length of the right-circular cylindrical crystal, and one-end drifted coaxial) are the preferred types for gamma-ray spectrometry at energies above about 100 keV; but for lower energies (below about 300 keV) planar and high-purity (HPGe) detectors, and especially windowless detectors are most advantageous. High-purity germanium detectors and they can also be used for lower do not deteriorate if raised to room temperature, energies. If the size of a NaI(T1) detector is not critical for the experiment, a 76-mm x This size is a 76-mm right-circular-cylindrical crystal should be given preference. widely accepted standard with which many measurements, and for which many calculations, have been made (Heath, 1964; NCRP, 1985).
Radioactivity
measurements:
principles
and practice
841
Typical low-geometry alpha-particle counter with exchangeFig. 5-4 able components. Detectors are chosen for those of their properties that are important for the measurement. The detector material, volume (or at least approximate volume), geometrical form, and the encapsulation material and geometry are trivial parameters, which must be known. The most important characteristic properties are, however, the resolution and efficiency which must be measured. The resolution (R) of a detector for a certain radiation and for a well-defined geometry is given by the full width at half the maximum of the photopeak of this radiation, either in terms of the energy (keV), or relatively, in percent of the energy corresponding to the peak maximum. The resolution is strongly energy-dependent, and, to a first approximation, is proportional to E-'/z. Typical resolutions for good "standard" ?&cm x J&cm n x 3”) Na(T1) crystals are 50 keV (or 7.5% of the peak energy) for the 662-keV peak in :t decay of 13'Cs; and 80 keV (or 6.0% of the peak energy) for the 1333.keV peak in the decay of "Co. The corresponding data for a 50.cm3 Ge detector are 1.4 keV (or 0.2%) at 662 keV, and 2 keV (or 0.15%) at 1333 keV (current best value about 1.7 keV). Directly connected with the resolution is the peak-to-Compton ratio (P/C ratio), the ratio between the peak maximum and the mean of the counts in the Compton region (1040 to 1100 keV for the 1333-keV peak). but, normally, values The best Ge detectors reach a P/C ratio of 200, between 30 and 60 are available; the corresponding NaI(T1) values are 10 and around 5. The efficiency of a detector depends on its nature and geometry and on the energy of The efficiency is defined in different ways (75.2.1.5.). the radiation to be measured. the most important definition is that of the For the characterization of a detector For NaI(T1) detectors the photopeak efficiency is almost always photopeak efficiency, cp. distance of 10 cm. indicated for the 662.keV peak using a 13'Cs source at a source-detector It can be compared with the photopeak efficiency (0.0125) of a good 3" x 3" NaI(T1) crystal. For Ge detectors the reference conditions are not so clearly defined, but are generally referred to the 1333.keV peak using a 6oCo source at a source-detector distance efficiencies of a Ge of 25 cm and a crystal volume of 50 or 100 cm3. The relative detector, c2, are stated in percent of that of a 76. x 76.cm (3. x 3-inch) NaI(T1) crystal For large Ge detectors cy can exceed at 1333.keV for a source-detector distance of 25 cm. 10%. Typical values of efficiencies are given in Figs. 5-5 and 5-6, and in Table 5-l. The stated values can only be an indication of orders of magnitude, but are very useful for the planning of experiments. Table
5-l.
Typical efficiencies for NaI(T1) and Ge at 1333 keV
Efficiency Et (0) cp (0) tp (10) ep (25) $/Et (10)
3" x 3" NaI(T1) 0.35 0.12 0.0065 0.0012 0.3
50-cm3 Ge 0.1 0.01 0.0005 0.0001 0.1
for the
Radioactivity measurements: principles and practice
842
should The characteristic properties of detectors (such as cp, et, cr, R, P/C, FWHM) not only be measured before use, but must also be continuously tested, because detectors The necessary measurements are discussed are often not stable over long periods of time. in 75.2.4.6.
Typical photo-peak efficiencies, ep for some frequent lY Fig. 5-s used detectors and source distances, d (numerical data taken from Crouthamel, 1960; Heath, 1964; Helmer, 1982; Moens and Hoste, 1983: Morel et al., 1983).
Intrinsic photo-peak efficiency of some common x-ray detectors Fig. 5-6 (numerical data taken from McMaster et al., 1969; Israel et al., 1971; Gallagher et al., 1974; Banham and Jones, 1983). 5.2.2.3. Electronics The counting
electronics (see chapter 6) connected to a detector of a defined-solid-angle system can vary from very simple and manually-controlled instruments to very The minimum completely automatic systems, controlled by high-capacity computers. COlllphX, electronic equipment necessary is a low-noise preamplifier (which is, in the case of a solid-state detector, usually cooled in the detector cryostat), a stable linear amplifier, To this an integral discriminator, a scaler, and the power and high-voltage supplies. minimum there might be added a multichannel pulse-height analyzer (MCA) with live timing, or a small on-line computer for data processing, spectral display and printer read-out of Very useful, and necessary additions for good accuracy, are a pulse rate vs. energy. precision pulser, that can be connected to the preamplifier, and a biased amplifier, which can expand any part of the pulse-height spectrum above a chosen level. The adjustment of the amplifier for optimum resolution, and to minimize corrections, is a crucial experimental problem, especially because it depends also on the spectrum and The main adjustment is that of the time constants of intensity of the measured radiation. all the amplifiers, but also pole-zero cancellation, base-line restoration, pile-up rejection, stabilization of amplification, and d.c. level must, if existing, be properly chosen (see 16.4). Usually time constants around 1 ps are chosen for the fast solid-state detectors, but much larger one.s can be used advantageously under certain conditions, especially if the highest resolution is not needed (Bouchard and Vatin, 1977; Gehrke,
Radioactivity measurements: principles and practice
843
1982). Pulsed optical-feedback preamplifiers (POFP's) should be used with caution (Funck, 1983), especially if the pulser method is used for dead-time correction (see (5.2.4.2). Very sophisticated electronics may even provide computer control of the time constants. As so many parameters have frequently to be adjusted, it would be most advantageous if a relatively simple second electronic channel could be used in parallel to the main channel, in order to check the crucial adjustments and to monitor the stability of the whole system. The most expensive part of the electronic instrumentation is the multichannel analyzer If it is not necessary to know the spectrum of the measured or a comparable computer. radiation, a detector with a simple integral discriminator (the threshold of which must be And a very simple well chosen and defined) is sufficient for relative measurements. spectrometer system using a 127 x 127-mm right-circular NaI(T1) detector (e.g. Fig. 5-2), with energy-calibrated integral discrimination, is an extremely useful instrument for relative defined-solid-angle counting that should be available in every laboratory. But as l-ray abundances are generally evaluated from -/-ray photopeak areas in -j-ray spectra,xA's The minimum number of MCA are standard instruments for such relative measurements. on the range of energies to be measured and the required channels needed, depends accuracy. For accuracies around 1 percent, at least 5 to 6 channels are needed to cover the full width at half maximum (FWHM) of the recorded photopeaks. This would require, for a usual FWHM of about 2 keV (at 1333 keV), an energy increment of approximately 0.35 keV/channei. Therefore, if an energy range of 2.5 MeV has to be covered, with an accuracy For an accuracy of about 5%, only about 1000 of l%, about 8000 channels would be needed. But even 100-channel analyzers could be very useful for many channels would be needed. Although such analyzers are not now tasks, especially if used with a biased amplifier. commercially available very inexpensively from they could probably be constructed integrated-circuit components that can be obtained commercially. Multichannel analyzers offer, in general, many advantages. Very advanced systems, especially those connected to larger computers, provide direct energy- and peak-area computations, and radionuclide identification. Even some of the simpler systems now offer "live timing" in addition to the usual clock timing. Live timing means, in general, that the time for which the MCA is not blocked to incoming pulses is recorded. Live timers thus yield, directly, the required count rate. Unfortunately, many live timers are not very accurate, especially at higher count rates and should, therefore, be carefully tested. If peak areas are being measured without a live-timing MCA then a correction is necessary for both dead-time losses and pile-up. Pile-up happens if a pulse overlaps randomly with another, or in coincidence with another from the same event, then amplitudes will add to give a summed- energy pulse (see 10-111-E in Knoll, 1979). Corrections for both dead-time loss and pile-up can best be made by using the pulser method described in or checked by using 75.2.4.2. Sometimes these two corrections can be better evaluated, the MCA live timers and calculating the pile-up. 5.2.2.4. Countine orocedures Relative defined-solid-angle measurements can be made with most instruments under different geometrical conditions, especially with different source-detector distances. Frequently, sources of different activities can also be used; such sources can be readily In this way optimum counting conditions can be chosen, such as a prepared from solutions. source distance of 10 cm, or more, to keep summing corrections low, and count rates below 1000 s-1, in order to reduce dead-time loss and pile-up correction, without having to count for too long a time. The unknown source to be measured, which is always made as similar as possible to the standard sources used for the calibration, must be very cautiously positioned in the measuring chamber. The neglect of this requirement is a frequent cause of error, especially The length of the counting period is chosen to give a total of at low source distances. counts commensurate with the required uncertainty, remembering that the relative estimated standard deviation equals N-l". It is advantageous to subdivide the total counting time, T into 4 to 10 equal periods in order to check the stability of the equipment of the equipment and the statistical behaviour of the results. The latter are mostly evaluated by measuring peak areas (774.11.5.2 and 5.2.2.5). Just the counting above a well-chosen integral-discriminator threshold with quite simple instrumentation can yield very valuable results (Vaninbroukx and Grosse,1966). By using the peak-area-counting method the unknown activity of a source can be obtained as follows: (i) the total counts under a chosen peak are measured and then corrected for all systematic biases (q5.2.4), and (ii) by the efficiency, c, derived from a calibration curve or a direct calibration with a standard of the same nuclide (a5.2.3.3), the activity of the unknown source is computed using the following equation: A
=
N/T
=
(MR
-
B)UC,/oT
= (M - B)IICj/('T) ; = (M - B)lIC,f/(cN,).
6 = Cst 3
(5-5) (5-6)
Radioactivity measurements: principles and practice
a44
The correction factors, Cj (IIC,= RIIC,),are those discussed explicitely with equation (Eq. 3-6), B is the number of background counts (all pulses below the peak), and the last term (Eq. 5-6) applies if the pulser method (75.2.4) is used for the correction of dead-time loss and pile-up (f = pulser frequency, N, = counts in the pulser peak). Also other procedures are common and important for accurate measurements, several test procedures. The latter are discussed in some detail in 75.2.4.5.
especially
5.2.2.5. Peak-area evaluation The evaluation of the total number of counts within the area of the photopeak, due to a given radiation, constitutes a serious practical problem in all relative definedsolid-angle gamma-ray measurements (see 74.11.5). This difficulty arises because photopeaks from semiconductor, and other detectors are asymmetric, with an additional component at the low-energy side of the assumed normal distribution. Furthermore, the backgrounds below the peaks show a step down, towards higher energies, below about the peak maximum (McNelles and Campbell, 1975). Therefore, the evaluation procedure is always rather complex. It can be performed manually by a simple addition method and can be partially or fully computerized using curve fitting by a least-squares method. For the manual evaluation (e.g. Debertin, 1980), the peak energy is first determined and the FWHM is calculated either from a Gauss function fitted to the higher-energy side of the peak or estimated from experience. Then the "peak region" is defined, and counts above background summed in that region. The best choice of the peak region seems to be given by E, + 5s (Jedlovszky et al., 1983), where Em is the energy corresponding to the peak maximum, and s is the estimated standard deviation (FWHM = 2.355s). But Em f 3s has also been recommended by Debertin (1980), and asymmetric definitions can also be applied. Then the background in the peak region must be determined. The simplest way to do this is to assume a linear background between the count rates in the channels (or the mean of a group of channels) just below and above the limits of the peak region (Debertin, 1980). For greater accuracy a step-like background (with a step height of about 1.5 percent of the peak maximum), possibly combined with a linear background (Jedlovszky et al., 1983) can be The sum of the numbers of pulses in the peak region minus the number of subtracted. background pulses yields the required number of counts. This simple procedure is Its accuracy is, in general, satisfactory for most cases and can be easily computerized. comparable with that of the best computer evaluations, but its applicability is limited, and it cannot be applied to measurements of double or multiple peaks or to very weak ones. Many different procedures and programs for a fully or partially computerized peak-area evaluation are reported in the literature (Kokta, 1973; Yoshizawa et al., 1980; Prussin. 1982; Houtermans et al., 1983; Helmer and McCullagh, 1983; Jedlovszky er al., 1983). 5.2.3.
Calibrations
5.2.3.1. Introduction Defined-solid-angle counting systems can be used for two purposes, (i) the identification of radionuclides by identifying the energies of their emitted radiations, and (ii) For the the measurement of the abundances of radiations or the activities of sources. first, in which a knowledge of the solid angle is not required, the system must be calibrated for energy-us-channel number (75.2.3.2.). For the second, the efficiency of the detection system (75.2.1.5) must be measured, for which the necessary procedure is described in (75.2.3.3 to 5.2.3.6. This must be done in both cases by the use of adequate reference sources because calculations are often not accurate enough, especially for Ge detectors because their dimensions (and edge effects) are not sufficiently well known. Nevertheless, calculations of total efficiencies of NaI(T1) detectors (e.g. Grosjean and Bossaert, 1965) and Ge detectors, and of photo-peak efficiencies of NaI(T1) detectors (Birattari and Salomone, 1980) and of Ge detectors (Moens and Haste, 1983; Nakamura and Suzuki, 1983) can be very useful. They allow one to check the experimental values, help to establish calibration curves, and can directly be used for interpolation and extrapolation, e.g. to higher energies, not available with long-lived radionuclides. The efficiency calibration of solid-angle counting systems can be performed by different techniques, namely by the use of one single calibrated source of the nuclide to be measured, or by means of a series of calibrated sources, preferably with each emitting 0lle radiation only, (75.2.3.3), of one standard prepared from a suitable mixture of or one calibrated multigamma-ray source of a single suitable radionuclides (75.2.3.4) of an All these measurements aim at the establishment radionuclide (75.2.3.5). efficiency-calibration curve with the highest possible accuracy (75.2.3.6). The most important, often violated, condition for precise relative counting is the near or complete equivalence of the unknown source and the calibrated sources and of the measuring conditions. The actual differences (such as dimensions and absorption) can be corrected for satisfactorily (75.2.4), but the differences between the shapes of r-ray and x-ray Despite these differences, calibrated x-ray peaks are more easily overlooked. sources can also be used for the measurement of r-ray efficiencies, or vice versa, if suitable corrections are applied. These can amount up to about 10% for radionuclides of
Radioactivity
measurements:
principles
a45
and practice
high-2 values and are always negligible for low-2 values (Schulte et al., 1980; Debertin the peak shapes of annihilation radiations and normal 7 Similarly, and Pessara, 1981). rays differ considerably from each other, which can easily be seen by comparing a spectrum Also the shapes of escape peaks and r-ray peaks of %r with that of an annihilation peak. from excited states, following nuclear reactions, are slightly different from the shapes of radioactive r-ray peaks. The relative efficiencies of solid-angle measuring systems are usually obtained using But for higher energies, above about 1.5 MeV, suitable photopeaks from calibrated sources. the calibration can be better made using doubleor, less and small Ge detectors, advantageously and less important, single-escape peaks (Fig. 5-7). Such a calibration is made in the same manner as that for the photopeak.
1 ?;‘A:
0.003
! ll!lllN 0.02 0.05
0.1
!
a2
‘?E
3.;13.;Na!lTC?j
~LLULLM 1517 2 25 3 3.5 4 4.5
Typical escape-peak-to-photopeak efficiency ratios for x-ray Fig. 5-7 and double ( cDE) annihilation-radiation escape ( C& and single (( escape for some Ge(Li) and @ aI(T1) detectors YS energy of incident radiation. Photon efficiency calibrations in the x-ray region (below about 100 keV) suffer from The first is the which are not present at higher energies. additional effects,
two excitation of fluorescence x rays in the material surrounding the detector, especially the The second effect is the partial penetration of radiations diaphragm in front of it. through the edges of the collimating diaphragm in front of the detector, resulting in an The use of diaphragms of different absorption-edge-like feature of the calibration curve. materials (such as Pb, Ti, Sn, and Fe) and of different thicknesses allows one to estimate the amount of these effects. There is also the K edge of Ge at 11.1 keV (Pessara, 1983). 5.2.3.2.
Energv
calibration
output-pulse with linear components give Energy-sensitive detectors electronic to the energy, E, absorbed in the detector so that V = heights, V, that are proportional If the output pulses are recorded in a multichannel analyser in aE, where a is a constant. which the relation between the pulse height and channel number, k, is also linear, then V = bk, for constant b, and E = bk/a.
(5-7)
In principle, two calibration points (preferably at the two ends of the energy range The evaluation of such measurements can, used) suffice to define the linear relationship. of 0.5 keV and under normal conditions, easily be done manually with a maximum uncertainty fractional channels being taken into account. Because the deviations from 0.5 channel, is linearity are also generally lower than 0.5 keV, such a two-point energy calibration of radionuclides or single sufficient for most purposes, especially for the identification peaks (Debertin, 1980). For energy calibrations of y-ray spectrometers, higher accuracies may be needed and In these cases a calibration checks of linearity over the whole energy range are useful. This can be done with several individual sources (e.g. for many energies is necessary. those listed in (5.2.3.3. or - much more easily - with a single source of mixed single-nuclide radionuclides (e.g. those discussed in 75.2.3.5) or with a multi-Ramma-ray
Radioactivity measurements: principles and practice
846
source, wo ) l=Eu, etc. (also see 75.2.3.4 and Fig. 5-8). e.g. For the highest accuracies, the position of the peak maximum (in channels) is, in general, calculated by fitting Gauss functions to the experimentally observed peaks. The deviation from linearity of the energy-vs-channel calibration curve is usually expressed as the difference, between a well-known peak energy, E, and its energy, Es, derived by linear regression. This difference E - ER, is, in general, a small fraction of 1 keV, and the uncertainty of this difference, and that of the whole calibration. can be less than about 15 keV, and, in special cases, much less.
Fig. 5-8
Typical
Y-ray spectrum of a mixed-radionuclide source
57Co 13gCe, 5lCr, 8%r, l37Cs, 8%. 65Zn) and of a multi-y-ray sour& (56~0) taken with a large Ge detector. The energies of the radiations most frequently used for these energy calibrations are Debertin, Yoshizawa et al., 1980; known with extreme accuracy (see Thus, for example, the energy of the standard 1980; and Table 10 of NCRP 58, 1985X). transition in the decay of ig8Au is 411.8044 keV f 0.0001 keV. Therefore the uncertainties in the energies of these standards can mostly be neglected. can be disturbed by peak shifts due to physical effects, Energy measurements This alone can especially by low-angle scattering and self-absorption (also see a5.3.4). source-detector measurements in different discrepancies between cause significant Corrections must be applied for these shifts, especially when higher accuracy geometries. is needed. 5.2.3.3.
Full-enerev-ueak
efficiency calibrations using sinele radionuclides
To measure the activity of a source of a single radionuclide, the simplest and, often, most accurate method is to make a comparitive y-ray, or x-ray measurement with a well characterized standard of the same radionuclide under the same geometrical conditions of source and detector. The activity of the unknown source is then obtained from the simple relation A = A,,N/N,t = &M/M,,
v
(5-8)
where A and Ast are the activities of the unknown source and the standard, and N and NSt and M and MSt are, respectively, the corrected and directly measured count rates recorded If the activities of two sources are by the detector system for each of the two sources. nearly equal, the approximation of Eq. 5-8 will often give the activity of the unknown with sufficient accuracy. But corrections, such as indicated in Eq. 3-6, for ever-present small differences between the two sources or the measuring conditions must almost always be made. The use of several radionuclides each emitting only one, or, but less desirably, two y rays is also the most accurate method of establishing a calibration curve for a The preference for one 1 ray is because scattered Compton photon-detector system. radiation from the more energetic of two cascade y rays increase the uncertainty in the
Radioactivity
measurements:
peak-area evaluation of the lower-energy coincidence summing between the two y rays
principles
7 ray, and is avoided.
a47
and practice
the
possible
need
to
correct
for
Today many multi-gamma-ray sources are available from national standardizing laboratThose with half lives longer than one month are ories and also from commercial suppliers. Some shorter-lived ones may be useful for special calibrations, such listed in Table 2-4. Some pure x-ray emitters, such as 37Ar, as, for example, s'Ga, "Br, l'O'"Hf,and "lT1. =Fe, 93mNb and 131Cs, may also be useful, but are difficult to standardize (see,however, 75.3). The double r-ray sources are also useful for indirect efficiency measurements. If the efficiency for one of the photopeak energies is already known, by a calibration using another radionuclide, then that for the other photopeak energy can be derived from photopeak measurments of both 7 rays. This method is of special interest in its application to measuring the intensity of neutron-capture 7 rays in the energy range between 2 and 10 MeV (see, for example, McCallum and Coote, 1975). 5.2.3.4.
Full-energy-oeak
efficiencv
calibration
using
multi-gamma-ray
emitters
Calibrations can be performed very rapidly if, instead of using many individual sources, just a single source (or, even two or three sources), that emits many Y rays of different energies is available. Such multi-gamma-ray sources can be prepared from a solution of a single radionuclide having a suitable decay scheme, namely one that emits many 7 rays that are evenly distributed over the required energy range. If such a radionuclide is not immediately available, then it may be possible to prepare a suitable source from a mixture of r-ray-emitting nuclides that cover the required range of energy. The simplest calibration is that with a single-nuclide multi-gamma-ray source, as all the 7 rays are decaying with the same half life. But it also suffers from considerable uncertainty because many 7 rays of different energy are in coincidence which, therefore, causes coincidence summing, the correction for which is difficult (75.2.4.3). This effect can, if neglected, lead to considerable errors in the efficiency, which might exceed 50% for unfavorable geometries. Therefore such single-nuclide multi-gamma-ray sources should only be used at sourceto-detector distances greater than 10 cm, in order to keep this correction small and calculable. But if high accuracy is not required, or if only routine monitoring of the stability of a detector system is to be performed, the use of such sources is very advantageous. Even for high-accuracy calibrations, multi-gamma-ray sources, also in over as many I-ray combination with other sources, can be used for efficiency calibrations peaks as possible, or as needed. Helmer (1982), for example, uses 19 sources of 18 7ray-emitting nuclides (including 5 multi-gamma-ray sources) with 58 evaluated 7 rays, for the calibration of an HPGe-detector system over the energy range of 30 to 2,800 keV. The selection of the most suitable multi-gamma-ray source for a specific efficiency calibration is not always easy. Its photon radiations should cover the energy range of For that, all component uncertinterest, and also provide the highest possible accuracy. ainties (especially those associated with the -/-ray-emission probabilities) must be taken into consideration Debertin. 1980; Helmer, 1982). Most calibrations pertain to the energy range between 100 and 1,500 keV, in which range "'Eu is, at present, the most suitable standard. It emits intense y rays with rather evenly-spaced energies between 122 and 1,400 keV, and also x rays of about 40 keV. The photon-emission probabilities are now rather well-known (Debertin, 1979; Meyer and Massey, 1983; NCRP, 1985). Some minor disadvan(such as a small disturbing peak at 409.2 keV, some double peaks, and probable tages contamination with ls4Eu) can be rather easily overcome (Debertin, 1980). 5.2.3.5.
Photoueak
calibrations
usine
mixtures
of radionuclides
The fast calibration by a simultaneous measurement at many peak energies can be performed without the intrusion of coincidence summing, if mixtures of y-ray-emitting nuclides, ideally with single r-ray emission, are used as the calibration source. The latter can be produced from a quantitative mixture of standard solutions of the individual deposition of drops of the individual standard solutions on to nuclides, or by quantitative a source mount, or its removable parts (e.g. a "sector source" such as described by Genka and Ishikawa, 1983). The radionuclides comprising the mixed source can be chosen to meet the purpose of the experiment, especially the energy range neededand the probable duration of use. The activities A, of the different nuclides should be so chosen that their corresponding peak heights will remain nearly equal for the duration of their use. Mixtures of single-gamma-ray and multi-gamma-ray nuclides can often be used advantageously, if appropriate corrections are applied. Typical mixed-radionuclide l-ray emission-rate standards are composed of 57Co, s°Co, s5Sr, "Y, 'OQCd, l'?Sn, l"Cs, or 13'Ce (Coursey et al., 1982), or, for longer use, lz5Sb, 154E~ or '55Eu (NBS SRM 4275b, solid, and 4276b,
a48
Radioactivity
solution),
or '&Mn, "Co,
measurements:
principles
652n, 60Co, lz3Ba, lz7Cs, or
lszEu
and practice
(Genka and Ishikawa,
1983)
A disadvantage of mixed-nuclide sources is the need to make a different decay correction for every measurement (different for each radionuclide component) which may introduce an additional uncertainty. Difficulties can also result from the evaluation of peaks of very similar energies, e.g. as with a 65Zn-15ZEu mixture, and annihilation radiation with the 514.009-keV transition in the decay of 85Sr. If the annihilationradiation peak is used for the calibration, or correction, at the energy of the 85Sr peak, the difference of spectral account (Debertin, 1980). 5.2.3.6.
Establishing
shapes
of annihilation
a calibration
and normal
7 radiation
must be taken
into
curve
The simplest way to construct an efficiency curve is the manual method using visual interpretation and some weighting according to the overall uncertainties of the individual results(e.g. Debertin, 1980, Helmer, 1982). An efficiency curve established in this manner suffices for most applications. The calibration curve can be better derived by computer analysis, for which an analytical function, relating efficiency and energy with adjustable constants, has to be assumed. Several functions, most frequently polynomials, have been proposed, as for example the following by McNelles and Campbell (1973) and by Meyer and Massey (1983)
In r(E) =
or the following
by McCallum
; ai(lnE)i l=O
and Coote
In r(E) =
,
(5-9)
(1975)
; b,(ln l/E)' i=O
(5-10)
In these expressions there are about five adjustable constants, a, or b, for the energy interval from about 100 keV to 10 MeV, or subdivisions of it. Other functions that are often suggested for the c~-vs.-E relation are semi-empirical equations with up to 10 adjustable constants for the energy range from 10 to 10,000 keV (e.g. Hajnal and Klusek, 1974). The constants of these relations are computed by least squares. The description of the efficiency-energy relation by an equation with five to ten constants is not very practical. It is, therefore,usually avoided by the subdivision of function can be the whole energy region into suitable sections, wherein the efficiency described by an equation with only a very few constants. The best subdivision depends on the actual measuring conditions and the purpose of the experiment. In general, energy ranges of about 1 to 60 keV, 30 to 120 keV, 100 to 400 keV, 200 to 2,500 keV, and 2 to 10 MeV are most appropriate (Debertin, 1980, Helmer, 1982) but others are also used successfully, e.g. 80 to 1000 keV, and 0.7 to 10 MeV (Meyer and Massey, 1983). In practically the peak efficmost important energy region, from about 200 to 2,000 keV, the experimental in a double-logarithmic presentation. iencies always vary nearly linearly with energy, Thus, one has for this energy region log cp =c+blogE,
or
Ep(E)
=
(5-11)
a Eb
(5-12)
The two adjustable constants a and b , which are usually calculated for the energy E, vary with the different conditions. This is especially so for a, but b always remains close to minus one. Frequently, second-order example, that due to McCallum
polynomials, with three and Coote (1975), namely
In C,(E) = a + b(log E-‘)
+
constants
are
used,
such
as,
for
(5-13)
c(log E-l)'.
The other energy regions can be treated in the same way. The energy region from about 5 to 60 keV is different from the others, in so far that detectors can be 100% efficient in that range. The detection efficiency then depends only on the geometry factor which is In this case the method calculable, under favourable conditions, with high accuracy. The additional problems met at these becomes a direct ("absolute") one (see also y5.3). It could be added that the Pb K-edge low energies have already been discussed in a5.2.3.1. jump in the calibration curve due to diaphragm penetration can amount to a few percent (Debertin, 1979). Also, the energy region above about 2.5 MeV and up to about 10 MeV can possibly be treated differently, because the efficiency-energy relation seems to be more closely linear on a semilog plot than on a log-log plot (Meyer and Massey, 1983). In order
to check
the accuracy
of the constructed
calibration
curve
and to facilitate
Radioactivity
measurements:
principles
and practice
relative efficiencies ep/tpO, can be interpolations and, less frequently, extrapolations, Here presented in a semilog plot, e.g. with a linear ordinate ranging from 0.95 to 1.05. cp,,is the photopeak efficiency calculated from an equation, the coefficients of which were with a = 0.5, b = 1, and E in keV). The adjusted by least squares (e.g. cpO = aKh, in general, reduced representation of the efficiency curve shows, only a few percent may be read from the curve can be done with deviations from unity, so that efficiencies (see also 75.2.4.5). sufficiently good accuracy 5.2.4. Corrections. 5.2.4.1.
accuracy
and system
monitoring
General
The overall uncertainty of any relative solid-angle measurement depends, according to associated with the measured number of counts, with Eq. 5-5, on the separate uncertainties the efficiency for the energy considered, and with the corrections that have to be applied. The uncertainty in the number of counts stems from their statistical nature and from uncertainty in the value obtained for the peak area. Both can be kept to below about 0.1% Thus, by careful attention to the quality of experimentation (Jedlovszky, et al., 1983). the overall uncertainty of the measurement of an unknown activity will usually be determined by the often considerably higher uncertainties associated with the detection efficiency, and with the corrections that must be made. The uncertainty in the detection efficiency is, in general, predicated on those of the various corrections and on the basic uncertainty of the calibration standard itself. If the unknown source being measured is directly compared with a very similar standard, in shape and substance and in the same geometry, the measurement approaches one that is strictly ralative, and some if not all corrections may cancel, and the final result may not even require that the detection efficiency be known. But this situation in which the uncertainty is minimal can not always be expected to occur, and, for general use, a detection-efficiency curve for the system must be established. In general use, pile-up corrections from corrections due too can be kept below unfavorable practical 5.2.4.2.
Dead-time
the most important uncertainties arise from dead-time losses and (75.2.4.2), from the coincidence-summing correction (75.2.4.3.) and to absorption and scattering effects (75.2.4.4). These uncertainties about 0.5%, if favourable measuring conditions can be chosen. But in cases, they can reach many percent.
losses
and pile-w
corrections
If only simple electronic counting channels are used, consisting of, say, an amplifier, integral discriminator, and scaler, corrections for dead-time losses can be made satisfactorily Because, according to the classical principles. are generally used even rather high in this simple case, dead times of a few microseconds While "normal" pile-up does not occur in such systems, the count rates can be handled. only possible disturbing pile-up arises from random summation of pulses smaller than the discrimination threshold (inclusive of noise) to form sum pulses exceeding this threshold. be avoided by proper choice of the measuring conditions. A very useful But this can discussion of dead-time and pile-up effects, by J.G.V. Taylor, is to be found in 72.7 of And comprehensive bibliographies on both subjects, edited by J.W. Mtiller and NCRP (1985). J.J. Gostely, respectively, have been published in BIPM (1981a and 1981b). For systems using multichannel analyzers (MCA's) and peak-area evaluation (or window discrimination) the dead times introduced by the analog-to-digital converters (ADC's) are, Pile-up (random and dead-time correction becomes necessary. in general, much higher, summing) also occurs and causes a transfer of pulses from the peak area under consideration especially severe for highThe pile-up is, of course, to a region above the peak. resolution detectors. For example, Helmer (1982) finds, for a typical Ge system, a pile-up At 6000 s-l, the correction amounts to correction proportional to the total count rate. photons. about 3% for 22.keV photons, and about 2% for 356.keV and higher-energy The simplest and yet fairly accurate method for measuring dead-time and pile-up Pulses from a precision pulser with losses is the pulser method (see NCRP, 1985, 72.7). precisely known low frequency, f, usually of 50 Hz, are fed, in this method, into the preamplifier together with the detector pulses. The position of the pulser peak in the accumulated spectrum is so chosen that the pulser peak neither interferes with the other If the shapes of the pulser and detector peaks nor does the background interfere with it. pulses are quite similar, the ratio of the number of pulses fed in by the pulser in time T, fT, to the number of pulses recorded in the pulser peak, N,, is taken as an approximate correction for dead-time and pile-up losses to every peak in the same spectrum. This for several reasons (Debertin and Schatzig, 1977), namely: correction is only approximate, (i) the shapes of the pulser and detector pulses are not exactly the same and are often influenced differently by the amplifiers and other electronic components; (ii) because of this difference in the shapes of the a pulser peak and a y-ray peak, they are differently in the peak-area evaluations: and (iii) distorted by pile-up, and this causes discrepancies the pulser pulses are periodic, not random, and the effects caused by this difference is Nevertheless, because the overall correction is generally not taken into consideration. not greater than a few percent, the approximate correction by the pulser method suffices in further most cases (Houtermans et al., 1983). But it cannot be used, without additional
a49
Radioactivity measurements: principles and practice
850
corrections,
feedback
if the source (Funck, 1983).
is rapidly
decaying,
or
if the preamplifiers
have
optical
Many other methods have been proposed for the correction of dead-time and pile-up losses (Houtermans et al., 1983). A very simple method is to measure the correction experimentally, using calibrated sources of different activities over a suitable range of activity (Macvani, 1984). Another simple method of wide applicability is to eliminate dead-time loss with a live-timer and to calculate the pile-up loss. With more complex electronic components, the live-time method can be extended to include correction (Andai av,dJedlovszky, 1983; GP1 and Bibok, 1983: Kennedy, 1984).
the
pile-up
In conclusion, automatic computer-based methods have been proposed, that can even be applied to mixtures of radionuclides with different, and also short, half lives (Westphal, 1979; Kennedy, 1984). 5.2.4.3. Coincidence-summine
correction
If a radionuclide emits two or more photons simultaneously, the probability of coincident pulses being detected and summed in the detector system is much greater than that for the pile-up of pulses from randomly emitted photons. The correction that must be made for summing losses from the peak-area evaluation is not count-rate dependent, but is a function of the photon-detection efficiency, which includes the solid angle subtended by the detector to the source. The summing losses depend essentially, therefore, on the distance between the source and the detector, and they can be very high (100% or more) for short source-detector distances and for detectors of large area. The uncertainty associated with the correction is also high. It is therefore very clear that conditions leading to such large values for the summing correction must be avoided. Therefore sourcedetector distances in excess of 10 to 15 cm are commonly used for calibrations when good precision is required. The calculation of coincidence-summing corrections is, in principle, very simple. If, for example, a radionuclide emits two photons in coincidence, each with 100% probability of emission as in the decay of 6oCo, then the summing-coincidence correction for the first photon, S(7'), is given by S(7)) = Ep(7')/[$(7')
- $(7’)+7n)l
9
(5-14)
where 7'l is the second coincident photon, and cP and Ed are the photopeak efficiency and the total efficiency, repectively. This correction is positive for single radiations, but negative for the overcross radiations in cascade decays. The principle of the calculation used above can be readily extended to more than two coincident radiations, but the resulting equations become more and more complex (Debertin and Schtitzig, 1979; Morel et al., 1983; Schima and Hoppes, 1983). Nearly all of the calculations reported pertain to point sources and do not take angular correlations into account. The theoretical estimates of the coincidence-summing corrections can easily be tested by experiment, especially by measuring a mixed source of a single 7 emitter and a double 7 emitter at different sourceto-detector distances. 5.2.4.4. Attenuation and scatterinp. corrections If the source to be measured and the standards used are not nearly equal, corrections must mostly be applied for the self-absorption in the source and the attenuation in any source cover or supporting material and in any absorber between the source and the detector. The self-absorption and attenuation corrections can, in general, be calculated with good approximation, especially if the source-detector distance is so large, compared with the source dimensions, that all radiations from the source to the detector can be regarded as perpendicular to the detector surface. An example that is often quoted is the correction for the 7-ray self-absorption in a flat surface of thickness f. In this case, one has that the number dn of 7 rays leaving the source in unit time from a layer of thickness dx at a depth x, is dn = %Aapdx
e-Px
,
here A, LIand p are, respectively, the area, specific activity and density of the source, and p is the linear attenuation coefficient for the radiation emitted. Integration yields
R
=
=
I dn = (Aap/2~)(1 - e-fit), I x=0 n t=m(l - em@).
(5-15)
Many other examples can be found in books on shielding. The attenuation correction is strongly energy dependent and can reach very high values at low energies. For example, a O.l-mm thick alumminium absorber between the source and the detector reduces the intensity of a 10.keV 7 radiation by about 30% (0.4% at 100 keV
Radioactivity measurements:
principles
and
practice
851
Even normal air-pressure variations can influence Low-energy and 0.2% at 500 keV). measurements which are, therefore, performed using vacuum chambers (Bambynek et al., 1966). Scattering is, in a wide energy range, the dominant interaction process of 7 rays. It not only Leads to an attenuation of the radiations, but contributes also to the spectra measured. At low energies, for example, backscattering at the detector can contribute considerably to loss of pulses from the peak. Scattering can be reduced by proper construction of the measuring chamber with as little material as possible near the source and the detector, or between them. As the amount of scattering is rather difficult to calculate, its effect is usually included in the efficiency (Eq. 3-6). This means that the conditions for scattering must be kept constant during the calibration and measurement of an unknown source. With regard to backscattering from the surrounding structure, a useful "rule of thumb" is that the source-detector configuration should be about 2 m from the room floor and ceiling and from the walls. 5.2.4.5. Overall accuracy The overall uncertainty of a defined-solid-angle activity measurement is calculated from the component uncertainties using the error propagation law, always at a level of one estimated standard deviation, unless otherwise stated ((3.4.1.2). In the case of a direct comparison of nearly equal sources, the contributing uncertainties are those associated of the activity of the standard and with the two peak-area with the measurement computations. In favourable cases, the former can be known to 0.1 or O.Z%, and the area This means that direct comparisons measurement can be made with about the same accuracy. of nearly equal sources can be performed with overall uncertainties of several tenths of a percent, down to about +0.3% for very favourable conditions. If an activity measurement is based on a previously established efficiency curve, the overall uncertainty is a combination of the curve uncertainty with that of the source measurement. As the efficiency curve too relies on a number of source measurements (standard sources, in this case), the component uncertainties are due to the corrections Helmer needed and are, therefore, similar for both, the known and the unknown sources. (1982) lists these component uncertainties for the measurement, with a typical Ge system, He also calculates overall total uncertainties for each of 58 different -/-ray peaks. peaks, ranging from 0.25 to 3.9%. With some smoothing of the curve, Helmer estimates the uncertainty of his efficiency curve to about 2% in the energy range from 30 to 85 keV, 1% Debertin for 85 to 120 keV, 0.75% for 120 to 420 keV, and 0.5% for 420 to 1,420 keV. (1979, 1980) states similar overall uncertainties of 0.7 to 2.0% for the energy region from 13 to 250 keV, 0.5 to 0.8% for 250 to 1,900 keV, and 1.5% for 1,900 to 2,800 keV. These Using figures can be regarded as conservative and typical data for modern Ge systems. these figures and the uncertainty of peak measurements (0.3 to 4%, according to Helmer) the overall uncertainty of a measurement of an unknown activity can thus be estimated to be about 0.6%, under most favourable conditions, and up to about 4%, in unfavourable cases. 5.2.4.6. System monitoring It is the most important feature of a relative measuring procedure, that the calibration is only valid for a well-defined particular state of the measuring system Every change of any component or condition can cause serious (including the sources). errors and uncertainties. Therefore, a continuous and careful check of the stability of the measuring equipment, especially of the detector, is indispensable for high accuracy work. Such monitoring following:
should be
frequently
undertaken
(e.g. weekly)
with
respect
to the
.
Energy calibration
. l
to the peak shape (FWHM, FWTM and, possibly, peak-to-Compton ratio), with a test pulse (of Gaussian shape), and of a source pulse;
l
for the photopeak efficiency at two or three different energies (one below 100 keV);
.
to the main corrections (dead-time and pile-up loss, and coincidence summing);
.
and to the overall repeatability (including source positioning).
(peak position);
Two kinds of sources are especially useful for these tests: well-known "Co standards (e.g. thin, reactor-irradiated cobalt foils in thin capsules) and "'ELI standards. It must be expected that present Ge detectors will change their efficiency up to several percent within a few years. 5.3. DIRECT LOW- AND MEDIUM-GEOMETRY
DEFINED SOLID-ANGLE COUNTING
5.3.1. Introduction Direct ("absolute") low- and medium-geometry defined-solid-angle counting involves the accurate measurement of the solid angle subtended at the source, of unknown activity, by a
a52
Radioactivity measurements: principles and practice
well-defined diaphragm, the aperture of which is completely covered by a radiation detector located behind it. (Spernol and Lerch, 1965; Bambynek, 1967; Blanchis, 1982) Only radiations passing through this diaphragm and interacting with the detector are Multiplication of the measured count rate by a geometry factor counted (Fig. 3-7). (75.2.1.1), yields (under ideal conditions) the source activity. The accuracy of an activity measurement is limited by the accuracies of the individual terms and factors in the analytical expression of the result (Eq.3-6). Some of the necessary conditions for the attainment of high accuracy are more or less "trivial", others influence the accuracy critically. The highest accuracy, in low and medium geometries, can only be achieved for strongly absorbed and weakly scattered radiations; namely those that neither penetrate the diaphragm nor are scattered out of, or into, the effective solid angle. Such properties are especially typical of a particles with energies below about 10 MeV, and less with x and 7 rays with energies below about 80 keV and, least of all, of electrons having energies below a few MeV. Some of the necessary conditions referred to above are: The electronic counting channel should be able to measure relatively high count rates of at least 104 s-1, in order to keep the statistical uncertainty and the measuring times The electronic components should be stable and also provide for within suitable limits. the possibility of applying accurate corrections for effects of limited resolution, dead times, and so forth. The background should be sufficiently well known and the effects of interfering radiations (from impurities, contamination, daughter products, nuclear reactions and higher-order processes)should be kept as low as possible and subtracted. Corrections derived from the decay scheme (branching ratios, etc.) and allowance for decay can nearly always be applied with sufficient accuracy. In addition to self-absorption and backscattering which are discussed inTy5.3.4 and 5.3.5, the sources themselves pose several basic problems, which can be understood easily but overcome only partially and with considerable technical difficulty. Extended sources should be sufficiently homogeneous; this can be checked by scanning with small apertures. Finally, supports and sources should be sufficiently conducting in order to avoid build-up A good example of the preparation and definition of of electrostatic surface charges. high-quality sources is the evaporation of homogeneous uranium layers on to platinum-plated quartz discs that have been mirror-polished (Moret et al., 1970; Miischenborn, 1971). Certain effects critically limit the overall accuracy and can cause errors of several These effects deal with the percent, if they are not properly taken into consideration. detector-response function or efficiency (75.3.2.4), with the effective solid angle (ll5.3.3), and with scattering and absorption occuring between the origin of the measured radiation in the source and its interaction with the detector (175.3.4 and 5.3.5). The direct ("absolute") low-geometry solid-angle method for the calibration of aparticle emitting sources allows one today to reach, under favourable conditions, accuracies of about 0.02% (Blanchis, 1982). 5.3.2. Instruments, detectors and practical urocedures 5.3.2.1. Countins! systems and electronics are very similar to The counting systems used for direct ("absolute") measurements those used for indirect (relative) measurements (see 75.2.2.1 and Fig.5.4as examples). The electronic systems should include a multichannel analyzer (MCA), at least for the inspection of the spectra. But, for accurate counting higher count rates, MCA's are often not Therefore, in general, a fast counting channel with a stable and wellenough. fast defined dead time should be used in parallel with the MCA (also see 75.2.2.3). 5.3.2.2. Source-detector chamber The source-detector chamber must be constructed with the greatest care, so as to minimize the difficulties in correcting for scattering and absorption effects. The effects of small-angle scattering (see 75.3.4.3), should be avoided by, for example, not using 2x The source holder should be of a rather rigid construction, which is also geometry. essential for an accurate measurement of its dimensions, and for the accurate positioning of the sources. Large-angle scattering (75.3.4.4), on the other hand, is lowest for low-Z values of the scattering material. Therefore, low-Z material, such as aluminium, should be The advantage lies not only in the lower-scattering used for the chamber walls. probability, but also in the fact that the residual energies of the scattered particles are also rather low (Fig. 3-8). Thus, backscattering of particles on to the detector surface leads to pulses corresponding closely to their initial energy without introducing any In addition, the energies of particles scattered from the walls are sufficiently errors. Large-angle lower than their initial energy that they can be discriminated against. scattering on the chamber walls might be important but will, of course, be lower with a
Radioactivity
Larger chamber
measurements:
principles
and practice
853
diameter.
Another critical problem is the choice of the shape and material of the diaphragms. Several shapes can be used (see Blanchis, 1982), but the body of the diaphragm must always and to avoid be at least several-millimeters thick, in order to ensure high stability The innermost edge, which deformation when the parts of the chamber are screwed together. but defines the effective solid angle, must be as thin as possible to avoid scattering, thick enough to exclude penetration and facilitate accurate machining. A few tenths of a millimeter are usually adequate, because the aperture diameter at such a thickness can be measured with the necessary precision of 0.05 mm, or better. Another important point is that the chamber should be constructed in such a way that its dimensions, which define the effective solid angle, can easily be measured with the An essential condition for that is the attainment of evenness and accuracy needed. plane-parallelism of all parts of the chamber. 5.3.2.3.
Detectors
solid-state detectors are most suitable. If large If high resolution is required, areas are needed, thin plastic detectors are best suited. If electrons should be excluded detectors of ZnS(Ag) coated on to thin plastic discs are most completely from counting, For the detection of although they are, in general, not 100% effective. convenient, below about 10 keV, and x rays, below about 3 keV, windowless low-energy electrons, For high-accuracy work fast organic scintillation counters are, in counters must be used. general, indispensable. 5.3.2.4.
Detector-resoonse
function
and efficiency
The response of the detector to the incident radiation is most completely described by that, under the probability any given the detector-response function R(E,E'), i.e. experimental condition, a radiation incident upon the detector with an energy E’ appears in This function is such that the relation the detector-output or spectrum at an energy E. between the incident radiation spectrum N'(E') and the recorded output spectrum N(E) is given by
N(E) = ti(E,E<)
N’(E’)dE’.
(5-16)
0
The complete knowledge of the response function would imply a complete knowledge of the continuous functions N'(E)and R(E,E’) for every value of E' < Emax, and for all relevant but a set of curves for a measuring conditions. That is, of course, not practicable, series of well-chosen parameters E' could be very useful. detector (e.g. thin The usual spectral reponse function of an energy-sentitive plastic) to incident radiation of energy E,, consists of a peak that is very nearly "Gaussian" around, very approximately, E,, plus a lower-energy tail that decreases with decreasing energy. However, towards very low energies a large increase occurs, due to background and secondary radiations, consisting mainly of conversion electrons and x rays. The low-energy tail is due to inhomogeneity of the detector, backscattering at the detector and its surface, window absorption, reduced charge collection (e.g. x-ray escape and field irregularities at the borders), recombination due to impurities, dust on the source or the detector, source effects, and energy loss by scattering. All these effects, except the last one, pertain to radiations emitted at their origin into the effective solid angle. These "right" radiations must be taken into account for the determination of the count rate. The radiations scattered back by the surroundings are "wrong" (i.e. not having been originally emitted into the effective solid angle), and must therefore be discriminated The choice of the discrimination level is therefore rather important. against. It can spectrum, that is reasonably be chosen at the minimum, or "valley" of the experimental located, in general, at about 2 to 3 MeV; and it is therefore, of course, an advantage if the peak-to-valley ratio is large (optimally much greater than 1O3). A comparison of the response function with the actual spectra, taken under varied experimental conditions, may then be used to estimate the influence of other disturbing effects (also see 775.3.4 and 5.3.5). The detector-response function can be obtained, to a good approximation, by using source of monoenergetic Q particles. Sources of 239Pu, 24lAm, and 244Cm electrodeposited
a
onto thin foils are, amongst others, suited for such measurements. If the source-detector chambers are properly constructed and the geometrical conditions well chosen, the measured spectra follow very nearly the response functions. The spectra obtaLned suggest that the detector efficiency is above 99.98%. 5.3.2.5.
Measurine
and testina
Drocedures
The practical procedures are, in the case those applied in indirect measurements (qf5.2.2.4 accuracy.
of direct measurements, very similar to and 5.2.4), but with more emphasis on the
a54
Radioactivity
measurements:
principles
and practice
Also the te.st procedures are similar in relative and "absolute" defined solid-angle In the latter case the tests of the reproducibility of measurements (including counting. source positioning and source preparation), of the response function (especially of the peak-to-valley ratio) and of the background (including interfering radiations) become the most important ones. Suitable test sources are prepared with long-lived a particle emitters having a small amount of secondary low-energy radiations, e.g. 239Pu or 244Cu. In a particularly interesting test source, as its this respect a z41Am source provides accurately measured coincidence activity can also be counting and by by liquid-scintillation counting. 5.3.3. Geometry-factor
measurement
The geometry factor, G = 4r/neff, is the most important term in direct low- or medium-geometry defined-solid-angle counting, because it normally takes on high values (from 10 to more than 104). It is evaluated using an analytical equation or a mathematical using the measured geometrical dimensions. In both cases the geometric data procedure, define the accuracy of the geometry factor. By far the most frequently used geometry is the on-axis point-source configuration, or close approximations to it. This geometry is the only one, that can be described by a closed analytical function (see Eq.5-3). The other important geometrical configuration is the off-axis point-source geometry, by using which solid angles subtended at extended sources can be calculated. As the exact expression for the off-axis point-source geometry cannot be integral represented many approximate solutions have been proposed in the literature and several analytically, computer programs were developed for that purpose. Let z be the source-to-diaphragm Then for off-axis distance, 2a the aperture diameter, and p the distance from the axis. smaller than the radius of the aperture (p < a), Eq.5.17gives distances of point SOUlYCS?S by far the best convergence for most practical applications (see Jaffey, 1954):
l/G =r 0.5(1
- :) D
3a2pG ___
8D5
15azp4z + ~ 32D'
[zZ
(3/4) aZ)
35aZp% _-
[24
(5/2)a2z2 + (5/8)a4] +
(5-17)
64D=
where D = (a' + z')~". Only for p = a and z/a < 0.5 is a two-term approximation less approximations for extended on-axis sources and accurate than 0.01%. Jaffey also indicates calculates their uncertainties due to those in the z, a or p values. An approximation for the general case (off-axis extended source) is given by Curtis et and Rogers (1962) tabulate, for example, 230,000 6-digit al. (1955). Masket inverse-geometry factors (l/G) with an accuracy of 10-e to 2x10m6, for z/a values from 100 to 0.3 and p/a values of between 1 and zero. Their table allows easy interpolations for most practical cases. The distance between the surface of the source and the plane of the diaphragm can be The simplest method is that of measuringthe thicknesses of the measured in different ways. length-measuring device, such as a individual parts of the chamber using a suitable Even if the sections of the chamber are very properly designed and machined, cathetometer. there will be a residual uncertainty in the source-diaphragm distance of a few hundredths together. A of a millimeter because of deformations that occur when the parts are screwed and source problems consists in using simple way to avoid intricate length measurements twin chambers and two identical detectors on the same axis and "looking" at a source placed Then only the distance between the two diaphragm edges halfway between them (Fig. 3-7b). of the source-diaphragm distance must be known with high accuracy, while the uncertainty may be larger by about two orders of magnitude. The diameter of the aperture should be measured in different directions (e.g. using measuring microscope) and a mean calculated (also see Morgan and Tolmon, 1966). The
combined
uncertainty
of
the
geometry
factor
is
derived
from
the
a
component
For more detailed investigations, more refined expressions uncertainties and Eq. 5-3. should be used, e.g. those derived by Jaffey (1954). As the relative uncertainties for all measured dimensions are about the same, the choice of larger dimensions is preferable. Source-detector distances of 10 to 50 cm and diaphragm diameters of 3 to 10 cm seem to be most suitable, if large detectors can be used. 5.3.4.
Scatterine
5.3.4.1.
General
effects
Radioactivity
measurements:
principles
and practice
855
The interaction of the radiations from the source with matter in the source, between and then by absorption in the detector can lead to counting the source and detector, minus errors. The radiation emitted originally into the ineffective solid angle (4s sr n,,,) can be scattered into the detector, while the radiation emitted into the effective detection (Fig. 3-7~). solid angle can be scattered out of it and escape The interaction of radiation with matter, although a collective effect, may be subdivided and treated as individual interactions between the particles involved, depending on their nature and energies. Considering only Q particles with energies below 10 MeV, the production of bremsstrahlung can be neglected, because of the high mass of the a particles and the low energy transfer to electrons. So that the dominating effect, at these energies, is due to electrostatic Coulomb interactions between the o particles and the electrons and nuclei of the matter traversed. These interactions can be divided into elastic and inelastic scattering. In elastic scattering only kinetic energy is transferred to the scattering centres, and the direction of motion of the incident particle is changed. In inelastic scattering, however, most of the transferred energy is spent in excitation and ionization processes. As, in the scattering of an incident a particle by an atomic electron, the transferred energy is more than three orders of magnitude greater than that transferred in scattering by the nucleus, only predominately inelastic scattering needs to be considered in accounting for the energy On the other hand, only the elastic scattering of e particles by losses of cx particles. nuclei needs to be considered for most angular effects. 5.3.4.2.
Rutherford
scatterins
and enerev
transfer
The Coulomb scattering of a particles by nuclei is governed by Rutherford's equation This equation, derived by Rutherford for the differential cross section (Siegbahn, 1965). Its in 1911, remains fundamentally the same even from newer and more refined derivations. This most characteristic property is a sin?(0/2) dependence on the scattering angle 0. relationship expresses such a strong dependence of the scattering probability on' the scattering angle, that multiple small-angle scattering and single large-angle scattering can be treated as two different effects ((g5.3.4.3 and 5.3.4.4). Another basic relation is still needed for the understanding of scattering effects in a-particle counting, namely that for the energy transfer to scattering centres by the The incident radiation as derived from the conservation laws of energy and momentum. results for the residual energy, Ei, after scattering into the differential solid angle, by a particle of mass M, at 2ssinBdB, of a particle of mass M, and initial energy E,, rest, are shown in Fig. 3-8. The most interesting result is the strong dependence of the residual a-particle energy, at a certain scattering angle, on the mass of the scattering centres. A study of this effect may lead to a reduction of this disturbance encountered in a-particle counting. (see 75.3.2.2) 5.3.4.3.
Small-arwle
scattering
Small-angle scattering can, in principle, only have an effect in defined-solid-angle counting of a particles, if it takes place very near to the border of the effective solid angle. Furthermore,it can only cause errors, if the density and, or, the nuclear charge of the particles on the two sides of this border differ considerably. Otherwise, the scattering into, or out of, this thin border layer compensate each other to a high degree, A difference of materials on the two sides of the border of the effective solid angle is nearly completely absent in low or medium-geometry solid-angle counting, but appears at the whole surface of the source in 2s counting. This may imply corrections and, or, errors of several percent (see end of this section). Measurements at very different solid angles and under very different geometrical conditions, with diaphragms having deep inner edges, with baffles changing the ratio of inward and outward scattering, show that, except for very small solid angles (G >lO,OOO), small-angle scattering changes the count rate by less than 0.01% (Blanchis, 1984). This value can also be estimated from 2s measurements. Hutchinson er al. (1976) and Lucas and Hutchinson (1976) derive the following equation for the ratio of 2s measurements, N,,, to the actual activity, N,, of thick sources: N&N, where
Z
is
the
atomic
= 0.5(1 + 0.5~1O-~Z)(l
number
of
the
source-backing
- O.Bt/R)
(5-18)
,
material,
t is the
thickness
of
the
of the a particles in the source material. Equation 5-18 is an source and R is the range At greater thicknesses the scattering effects approximation valid only for t/R < 0.15. (first parentheses) and absorption (second parentheses) can no longer be separated. 5.3.4.4.
Large-anale
scattering
Large-angle scattering can take place within the source, on the source support and holder, in the chamber gas and on the chamber walls, on the diaphragm and the baffles, on the detector window and in the detector itself and its surroundings. Its extent can be
Radioactivity
856
measurements:
principles
and practice
estimated using the Rutherford equation, and can also be measured with good accuracy. Because the scattering is proportional to the number of scattering centres the greatest effect may take place on the walls of the chamber. The calculations of the wall scattering (i.e. with a wide, not-too-long aluminium or steel show that, under normal conditions chamber), the correction due to this effect is considerably below 0.01% (Blanchis, 1984). pulses from large-angle But, if the chamber material has a low-Z value, any non-avoidable wall scattering can be discriminated against by proper choice of the energy threshold. Only if large source-to-diaphragm distances and narrow chambers are used, can scattering from the wall amount to as much as a few tenths of a percent to the count rate. If such the use of baffles (Fig. 3-7d) may improve the geometric configurations are unavoidable, measurements considerably. These baffles should be very thin and conducting, e.g. O.l-mm-thick steel or aluminium diaphragms. The scattering at the inner edge of the diaphragm is a special kind of wall scattering. It can be calculated in the same way as any other wall scattering and can easily be measured using diaphragms with different heights of the inner edge. For a steel diaphragm with a "normal" edge of 0.1 to 0.3 mm in height, and for reasonable geometries, the scattering effect on the count rate is much smaller than 0.01% 5.3.4.5.
Attainable
It has been due to scattering
accuracies
shown that, for a particles with energies can be kept below 0.01% by a proper choice
below 10 MeV, all corrections of the measuring conditions.
For other radiations such a high accuracy is out of reach. Beta particles that have energies below 2 to 3 MeV suffer much stronger multiple scattering and absorption than do o Even in low geometry their measurement is considerably disturbed by scattering, particles. Further, the continuous energy distribution of p particles especially backscattering. greatly complicates the situation, especially at low energies. So uncertainties of a few p radiation, must be expected in percent, and even considerably more for low-energy defined-solid-angle measurements of these radiations (Allen, 1965). Low-energy x rays are scattered according to the laws of the Compton effect which is analytically described by Similar calculations as for a particles can be performed using the Klein-Nishina formula. low1966). However, the final accuracy of x-ray and this formula (Bambynek, medium-geometry defined-solid-angle counting can not be reduced to less than a few tenths of a percent (Bambynek et al., 1966). 5.3.5. Absorption 5.3.5.1.
Enernv
effects loss and particle
absorotion
alpha-particle measurements can be completely The results of defined-solid-angle self-absorption in the source. It is absorption effects, especially falsified by reasonable to distinguish between two kinds of attenuation, namely energy loss and particle The first is the partial loss of the energy of a absorption (or attenuation, for 7 rays). the existence of which as an independent entity continues, the second is the particle, complete disappearance of a particle. If the remaining energy of a particle having suffered is still higher than the discrimination threshold, it will be counted and an energy loss Particle absorption, on the other hand, always causes a counting no error is introduced. For the calculation of the latter, the energy loss, for which a correction must be made. Penetration of after all absorption losses, must be known. spectrum of the particles, particles, through the edge of the diaphragm that defines the geometry, is a further effect is of the same order of For (I particles, the correction for penetration to be considered. of the measurement of its diameter. Therefore a crude magnitude as the uncertainty estimate of this correction is sufficient. 5.3.5.2.
Energy
loss. Bethe
theory.
range and ran=e-energy
relations
The dominant interaction which causes energy loss and finally particle absorption is inelastic scattering of the incident a particles by the electrons of the absorber atoms This process is rather complex as, for instance, LI particles undergo frequent (75.3.4.1). so that their mean residual charge decreases charge exchange with the atoms encountered, in an inelastic collision with The mean energy transferred, considerably with energy. is only a few electron volts, so that about lo5 collisions are needed, before electrons, theory does not Therefore, the energy-loss Bethe-Bloch the CI particle becomes absorbed. energy loss per unit describe the individual scattering process, but only the differential path length, dJ?/dx. Due
to the small
energy
transfer
percollision,
the real path
length
of a particles
is
nearly equal to their "range", i.e. the distance between the starting and end points of their paths, and the range variation, known as straggling. For the calculation of absorption effects, the relation between the mean range, R, and the energy, E, of the particles must be known. It can be calculated from the integral of the energy loss per unit path length,
R =
/E#‘,(dE,dx) 0
(5-19)
Radioactivity measurements: principles and practice
857
Bethe's theory indicates that the range is proportional to E: and (Z~,IY,Z,N,)-~, where E, is the energy, 2, the atomic number and M, the mass of the incident particle; and 2, the atomic number and N, the number of the absorbing particles per unit volume. More refined theories suggest an /?I* law for the range, a relation that had already been derived experimentally in 1910 by H. Geiger. More detailed theories lead to very complex expressions. For practical purposes several semi-empirical tables of energy losses, range and related data, with adjustments based on experimental data, are available, e.g. those by Northcliffe and Schilling (1970). The large differences between the values found in the various tables reflect the modest accuracy of these data. 5.3.5.3. Aloha-oarticle
loss due to source self-absorotion
Source self-absorption is the most important problem in a-particle counting, because it may be very large and can seldom be avoided. The model of van Schweidler (1913) (Fig. 5-9a) is very suitable for the calculation of particle absorption. It assumes a laterally infinite source, but with the same effective solid angle subtended at every point of the source (i.e. an "infinite point-source model"). As can be seen from this model, for 0,,, less than Bcmin (i.e. for an effective solid angle smaller than the critical minimum, that is equal to arccos (t-x/R,)), all particles emitted into this effective solid angle leave the source. Consequently, no net self-absorption loss can happen at all. Furthermore, for 0eff < @,*i, the spectrum of the emitted particles is relevant only at energies greater than E, = E, - E(t/cos R,,,). This can be more easily understood when looking at Fig. 5The term E(r) is the residual energy of a particle of original energy E, which has 9b. already travelled a distance r). So a discrimination threshold below E, can be chosen, which excludes all loss of particles by self-absorption. This is a fundamental asset of the low- and medium-geometry solid-angle method, except for 2s geometry, and for saturation-thick sources.
Fig. 5-9 "Extended point-source" model for the calculation of spectrum distortions due to selfabsorption in the source. a) Von Schweidler's cylindrical-coordinates model, b) spherical-coordinates model. If o,,, ' @C,,,, the absorption loss can be calculated using the model proposed by van Schweidler, who employed it only for 2n geometry, but it can easily be extended to solid angles smaller than 2asr. In such cases, using x1 = t - R,cos 8,,, (as cos 0, = (t - x1)/R, = cos 8,,,) and the activity per unit source thickness n0 = N,/t, one obtains
= (n,/2)
Xl dx[(r
_I-
- x)/R,
- ~0s
e,,,]
0
=
(N,R,/4t)(t/R, - cos @,ff)'
(5-20)
With the number of particles, N,, emitted originally into the effective solid angle,
Radioactivity
850
N,
one has,
for the relative
measurements:
n&(1 -
=
cos
absorption
8,,,)/2
yields
and
sources AN,/N,
for saturation-thick
,
(5-21)
8,,,)'/2t(l
- C0.s o,,,)
(5-22)
AN,/N, = t/2R, for 2s geometry AN,/N, = (l-co?. O&/2
for saturation-thick
and practice
loss,
AN,/N, = R,(t/R, - COS
This equation
principles
sources
(5-23)
= 0,,,/4r = l/G
,
(5-24)
(t 2 RO), and =
l/2
,
(5-25)
in 2s geometry.
The last result, Eq. 5-25, was probably first derived by von Schweidler. The simple result of Eq. 5-24, that has probably never been published, may be of some importance for the measurement of thick alpha-particle sources, such as fuel elements. 5.3.5.4.
Spectra
distorted
bv self-absorption
Figure 5-10 shows some spectra calculated for different geometrical conditions, using the model of Fig. 5-9b and following, to a certain extent, the derivation of Abrosimov and Kocharov (1962). It can be seen from Fig. 5-10 that E, is then very close to E, and the spectra are thus nearly undistorted by source self-absorption. On the other hand, effective solid angles with O,,, > Bcmin, saturation-thick sources, near-saturation-thick ones in every geometry, and all sources of any thickness in 2s geometry, give rise to strongly deformed spectra down to zero energy.
r
0
1
2
3
Source-selfabsorption-distorted Fig. 5-10 different geometries.
4
5
alpha-particle
spectrum
for
It is noteworthy that all quantitative and qualitative results derived here confirm completely those derived from von Schweidler's model (75.3.5.3) Also Haeberli et al. (1953) get compatible results, although they use a very simplified van Schweidler model with R = E (or a = b = 1 in R = & and E in MeV). If the experimental conditions are well-chosen, only the source self-absorption and the detector-response function affect the particle-energy spectrum at the detector output significantly. By folding of the self-absorption-distorted spectrum with the essentially "Gaussian" response function one obtains a spectrum that can be used for the evaluation of the finite discrimination correction (Abrosimov and Kocharov, 1962). In practice, however, conditions are chosen so that the low-energy tail of the final spectrum is so low that the particle loss by discrimination can be neglected.
Radioactivity measurements: principles and practice
859
5.3.5.5. Penetration of foils, and transmission throueh diaphraFm edees The penetration of foils by a particles can be understood and calculated in the same For a point source of activity no located just way as the self-absorption (75.3.5.3). below the centre of the absorber foil of thickness t, and again for 8,,, < B,,i,, there is no counting loss, and for 8,,, > Bcmin,one obtains the following counting loss
AN = N,(2*/4*)
=
Beit sinfl d0 = (N,/~)(cos~, - case,,,) I9 CUli" (5-26)
(N,/2)(t/R, - cos 19&
For N, particles emitted into the effective solid angle, the relative counting loss is, according to Eq. 5-21, AN/N, = (t/R, - cosO,,,)/(l -
cost',,,)
(5-27)
This yields, for 8,,, = 2a, the often used expression N=
N,
- AN = (N,/2)(1 - t/R,) .
(5-28)
The residual energy spectra after penetration can also be calculated using the model of Fig. 5-9b and an assumption for the range-energy relation. The main result is interesting in that even for a rather strong reduction of the initial energy by a relatively-thick absorber, the broadening of the original a-particle-energy distribution is relatively low, for small effective solid angles. This allows one to use, for these conditions, relatively thick cover foils that separate the source and detector parts of the central chamber This is important for without introduction of additional corrections and uncertainties. measurements of nuclides with gaseous daughter products. The assignment of a value to the effective solid angle (q5.3.3) rests on the This is never quite assumption that all particles hitting the diaphragm are absorbed. Some particles are scattered (!J5.3.4), others penetrate the edge of the diaphragm true. ThLs latter transmission effect is defining the effective geometry, losing some energy. Such a small effect can be very small for D particles, because their range is short. calculated, with sufficient accuracy, in the same way as the penetration of 9011s The situation is similar for low-energy x and Y radiations, but the (Blanchis, 1982). discontinuous behavior of the cross section of the absorber material must be taken into For x and 1 radiations with energies above about 15 keV, and for neutrons, consideration. the transmission correction may dominate and may limit the attainable accuracy (Bambynek, 1967; Lee, 1982). 5.3.6. Overall accuracy. other radiations and examples of auolication 5.3.6.1. Overall accuracy The low- and medium-geometry defined-solid-angle method is discussed here in detail Firstly, it is an example of a very thoroughly investigated for four related reasons. Secondly, the discussion shows that a good understanding of the basic physical method. processes is of decisive importance in placing this method amongst those by means of which the highest accuracy can presently be reached, under favourable conditions, namely 0.01 to This is only possible because some basic technical conditions can be met, such as 0.02%. the availability of high-resolution detectors, fast and stable electronics, and because critical corrections for scattering and absorption can be kept small and well determined. thoughtful measures Thirdly, the method is a good example of the benefit to be gained by aimed at improving the accuracy of metrological methods (75.3.6.3). And, lastly, it is a rather simple method that can be applied using relatively simple instrumentation. 5.3.6.2. Other radiations In this context only fission products are of some importance in radionuclide metrology, but of not more than limited interest to those who are engaged in the establishment of regional radioactivity-standardization laboratories. (Also see 75.3.4.5.) 5.3.6.3. Examples of apolication With the improvement of the accuracy of this method from 1% to 0.02% for 01 particles and from 10% to 1% for low-energy x and 1 rays, during the last two decades, many useful practical applications have been promoted or made possible. High-accuracy a-particle counting made it possible to measure the half lives of uranium and transuranium nuclides with an accuracy of about 0.1% (e.g. Vaninbroukx et al., 1976). These, in conjunction with a-particle activity measurements, permit the evaluation, with comparable accuracies, of the amounts of such nuclides present in different materials. This is a basic condition for reasonable safeguards work and is important for the definition of materials in the nuclear-power industry. It also improves the measurement of
Radioactivity
860
neutron fluxes using branching ratios.
fission
measurements:
foils
and
is ideal
principles
and practice
for measurements
of a-particle-to-fission
The application of the defined solid-angle method to high-accuracy x-ray counting also led to the improvement of the accuracy of fluorescence yields by an order of magnitude (e.g. Bambynek et al., 1972) with corresponding improvements in the many x-ray measuring techniques applied to-day (Knoll and Rogers, 1982), Finally, it may be mentioned once again that an improvement in any individual method contributes to the improvement of the whole system of radionuclide metrology, because of the strong interconnections between the different methods. 5.4. 4Il METHODS 5.4.1.
Iiitroduction
5.4.1.1.
Principles
As geometry factors of defined solid-angle counting are usually much larger than one, their uncertainty often determines the overall uncertainty of an activity measurement made it can be advantageous to use methods which allow one to Therefore, by that method. measure all radiations emitted into the whole solid angle, 47r sr. This is not only the largest possible solid angle, but also the one that is known with the highest accuracy. There are therefore many practical configurations for 4a, or near 4n, counting. The 4a geometry can be a great asset in 4~~7, or 4ap-7 coincidence counting, although In this respect, the counting of "wrong" radiations (such as 7 rays in in a different way. or b bremsstrahlung in the 7 counter) can cause serious errors if the the ,8 counter, This correction for coincident "right" radiations are not detected with high efficiency. solid angle are radiations vanishes only if the efficiency and effective "wrong" This respectively 100% and 4n sr, and if, in addition, there is no source self-absorption. has been achieved to high degree of accuracy, and low uncertainty, by the method of 4np-7 counting using efficiency extrapolation to 100% p-channel efficiency. 5.4.1.2.
Possible
source-detector
arraneements
and aDDliCable
radiations
4?r configurations are currently used: A relatively small (usually Many different in the centre of a detector (especially 4a gas-ionization solid) source can be placed the activity to be measured can be homogeneously mixed counters, as treated in 75.4.2); (liquid-scintillating, 75.4.3, or Ferenkov counting); with, or dispersed in, a solution "internal" gas counting (75.4.4); "internal" solid counting (e.g. a NaI(T1) crystal "doped" with ZZNa); a source (or radiation beam)can be introduced into the centre of a detectorvia a reentrant tube (well or "pin-well" detectors, 775.4.5 and 5.4.6); and a thin source can be sandwiched between two or more thin solid-state detectors ("phoswich" counting). But for high accuracy it is necessary that the 4n Many types of detector can be used. This eliminates or reduces detector should strongly absorb the radiation to be measured. and sourcemost errors (especially those due to scattering), except source self-absorption mostly nuclides emitting which must be kept small. Consequently, mount absorption, such as pure p emitters, are suited to 4?r Imeasuring absorbable radiations, strongly 4?r measuring methods lead mostly to large For weakly absorbable radiations, methods. detectors (e.g. hadron calorimeters). 5.4.1.3.
Corrections
In 4?r counting methods residual corrections determine the final accuracy, and, as in But here, especially in other methods, they can be identified with the help of Eq. 3-6. the case of the classical 4n method with foil-mounted sources in a gas-ionization counter, must be made can be measured separately the dominating effects for which corrections (Smith, 1954; Mann and Seliger, 1958; Pate,1960). These dominating effects are foil absorption and backscattering and backscatter from one They can be evaluated by half of the counter into the other, from the gas and tlhe walls. counting the pulses originating from the top and bottom halves of a 4a counter (so oriented), separately and in parallel, and also the coincidences under different conditions In this case one can write that the measured count rate, of source backing or sandwiching. is given by mt, in the top half of the counter is, to a certain approximation, m, = (n,/2)F,[l + Br + B,(l - &)'(I
-
rf)‘l
I
(5-29)
of all corrections other than for where n0 is the source activity, F, is a combination backscatter by the foil, 8, is the backscatter or absorption, pt is the fractional backscatter from the bottom half counter into the upper one, and p'f is the fractional foil Similar relations can be derived for the bottom half of the counter and for absorption. It is clear from Eq. 5-29 that the evaluation of the coincidences between the two halves. its terms is only possible by making additional experiments with changed parameters and the And it should be remembered that deviations from the assumed model use of extrapolations. But will alter the energy spectra and will complicate the evaluation of the measurements.
Radioactivity
investigations measurements. 5.4.1.4.
of
Attainable
this
kind
help
accuracies
with
measurements:
to
improve
principles
the
and practice
understanding
and
861
accuracy
ot
such
examules
The accuracies of 4a gas-ionization methods depend strongly on the measuring conditions and the nature of the emitted radiations, whereas liquid-scintillation counting of a particles of about 5 MeV in energy can be carried out with uncertainties as low as a few hundredths of a percent. Biological 14C samples can be assayed using 4?r counters filled with gas and operating in the proportional region, but with accuracies usually not much better than within several percent. Nevertheless, such modest accuracy in assays of low-energy p-ray emitters is often sufficient. Therefore, 4n counters using gas-ionization detection in the proportional region are still frequently the instruments of choice, because they are simple and inexpensive. 5.4.2.
4n urouortional
and Geieer-Miiller nas counting
Defined-solid-angle counting at low solid angles has been used for six decades since the days of E. Rutherford, H. Geiger and E. Marsden. The second half of the 1940's saw the introduction, by many authors, of the 4rfl counter for the assay of @-particle, and later u-particle, sources. Pate (1960), in an extensive review, has referred to the different experimenters and authors of that period. Also at about the same time, Mann and Parkinson (1949) and Engelkemeir and Libby (1950) used the internal ("4n") Geiger-Miiller gas counter for measuring 14C activities in samples of CO,. An elementary 4aa or 47r,6counter consists of a source mounted on very thin plastic film (coated with a thin conducting film), completely surrounded in 4?r steradians by two proportional or Geiger-Miiller gas counters in various configurations (see Figs. 5-11, 5-12 and 5-13). More recently the 4a geometry has been applied to LI-, p- and r-ray low-level-activity metrology using liquid scintillation and solid-state detectors, as, for example, NaI(Tl)-shielded CaFz(Eu) sandwich detectors for a particles (Mayhugh et al., 1978); liquid-scintillation techniques for a- and p-particle, and electron-capture sources; and reentrant pin-well NaI(T1) crystals, and two large 4rr (203 mm (8 inch) in diameter) NaI(T1) shallow-well crystals arranged in 4rr geometry for the assay of photon emitters (J.M.R. Hutchinson et al., HN, 1973, p. 187).
Fig. 5-11 Cut-away representation proportional counter.
Fig. 5-12 Cross counter.
section
of a cylindrical
of a spherical
4a
gas-flow
4~
gas-flow
proportional
Radioactivity
862
measurements:
principles
and practice
Cut-away view of a pillbox-type 4a gas-flow proportional Fig. 5-13 counter. The success of the 4aa and 4r@ proportional or Geiger-Miiller counters depends primarily on avoiding losses of a or @ particles in the source and source mount and this involves the preparation of exceedingly thin conducting films on which the sources can be deposited in the form of drops and then spread out to form extended thin layers by means of wetting or seeding agents, the latter providing nucleation sites where large numbers of small source crystals are produced on drying (also see 73.3.3). Carrier should be kept to a minimum and should preferably consist of hydrogen ions provided by the addition of small amounts of acid. Carriers alone of the same salt may produce "clumping" with "islands" of source material separated by areas devoid of deposit, as shown by Seliger and Schwebel (1954) for KI by electron-shadow micrography. The basic source mount can be a very thin plastic film normally of VYNS (a polyvinylchloride-polyvinyl-acetate polymer) prepared by floating an organic solution of the plastic on water from which it can be lifted after evaporation of the solvent. The film then has a thin film of gold (or gold-palladium) evaporated upon it to render it conducting (to complete the cathode surface) and its surface density can be of the order of 1 pg cmez but should not be greater than about 10 fig cm? for routine use. The efficiencies for 4ao and 4x8 counting can be measured using radionuclides decaying In an international by o- and p-particle emission followed by prompt -/-ray emission. comparison of measurements of 241Am sources (Rytz, 1964) 4aa sources were found to have an Using efficiency of about 99.6 percent implying a source self-absorption of 0.4 percent. the same coincidence-counting technique, Gunnink et al., (1959) and Merritt et al., (1959) For measured the source self-absorption of beta particles for several radionuclides. sources having a mean superficial density of 2 pg cmmz, the source self-absorption varied from one percent for 24Na p particles (Em,, = 1.39 MeV) to between 20 and 40 percent for the 88.5.keV p-particle transition in the decay of 13"Cs. Other techniques include electrospraying of deposition on specially prepared ion-exchange-resin p. 353; and 73.3.3).
sources (Merritt er al., pads (Lowenthal and Wyllie,
1959) and HN, 1973,
Gas-proportional counters of 4~ geometry that can be operated at elevated pressures in order to increase the detection efficiency by decreasing the P-particle range in the counter, for the purpose of carrying out coincidence counting using the method of efficiency extrapolation developed by A.P. Baerg and his colleagues (see Baerg, HN, 1973, These counters can be operated at p. 143; Legrand et al., HN, 1973, p. 101; NCRP, 1985). 70 and 75 atm. (7.6 MPa), respectively, and can be used to obtain x-ray spectra following electron capture of nuclides with rather high atomic number. A 30.cm-diameter cylindrical 4a gas-flow proportional counter operated at atmospheric pressure has been used by Troughton (1977) to obtain the K and L+M x-ray spectrum following internal conversion in losmAgin the decay of l%d. A very extensive literature exists on both 471 gas counting and on the preparation suitable sources for 4n counting. Many useful references to this literature are given the Herceg Novi Summer School Proceedings (Herceg Novi, 1973) and in NCRP (1985). 5.4.3.
Liauid-scintillation
5.4.3.1. The
of in
counting
General preparation
of
sources
for
use
in
liquid-scintillation
counting
(LSC)
has
been
Radioactivity
measurements:
principles
and practice
863
process has been discussed described in q3.3.4.3 of this report, and the scintillation This section will outline the experimental procedures developed in the briefly in 74.6.2. It is, apart from often negligible applications of the method to radionuclide metrology. wall losses and escape from the upper surface of the scintillator solution, a method in which the effective solid angle is equal to 4~ steradians. The liquid scintillator comprises an organic scintillator such as anthracene dissolved The radionuclide to be assayed is introduced into the in a suitable aromatic solvent. [3H]-toluene or such as a labelled organic compound, scintillator either (i) as (ii) as an aqueous solution such as [%-water, using a second solvent [%-n-hexadecane, emulsion, (iv) as a finely divided solid (iii) as a liquid-liquid such as ethanol, or (v) as a precipitate or a filtrate on a solid support suspended in a gel scintillator, The counting sample is usually contained in a such as filter or anion-exchange papers. screw-cap counting vial 27 mm in diameter and some 60 mm in height, viewed by cylindrical, phototubes (in various modes of non-coincidence, or one, two or three electron-multiplier and the whole assembly is mounted in a refrigerated in double or triple coincidence), A double-coincidence system is especially useful for the reduction of phototube enclosure. The sample backgound "noise" as such "noise" pulses occur only randomly in coincidence. Further details should be rigorously purged of oxygen which is a strong quenching agent. "The Application of Liquid-Scintillation are given in Monograph BIPM-3 (1980), entitled In addition to six review articles this monograph Counting to Radionuclide Metrology". of which attention could well be given to the book by contains just over 300 references, and Spernol (1965), Birks (1964), and articles by Horrocks and Studier (1964), Vaninbroukx sample preparation Gibson and Gale (1968), Houtermans (1973), Peng (1977, that describes Another NCRP (1985) and Coursey et al. (1986). and contains some 250 references), and short treatise by Dyer (1980) has much practical advice and over 100 excellent references. Precautions must be taken against chemiluminescence and delayed phosphorescence, the latter resulting from sample or even vial-cap (Dyer 1980) exposure to ultra-violet light. Garfinkel et al. (1965) have even observed that vials closed with white plastic screw caps gave up to 44% higher count rates than the same vials closed with black plastic screw caps. 5.4.3.2.
Basic
urincioles
Liquid-scintillation counting can be applied to the assay of o-particle and Gibson has pointed out (BIPM, 1980) p-particle emitters, and of some electron capturers. that the energy deposited in a scintillator by a 5-keV electron if converted to light with But 95 to 99 percent of the energy is a wavelength of 425 nm would produce 1,700 quanta. so that in a typical scintillator it could give dissipated as heat in the scintillator, Of these, according to Birks (1964), some 40 percent will be rise to as few as 17 photons. lost by ionization quenching, so that a 5-keV electron may ultimately giverise to only as But these few as three photoelectrons incident upon the first dynode of the phototube. three photoelectrons are the mean of an assumed Poisson distribution of photoelectrons There is thus a finite generated at the photocathode and striking the first dynode. probability that no electron will be incident on the first dynode; a probability that is This is called the given, for a mean of three electrons, by em3 which is equal to 0.05. The assumption of the Poisson distribution has been tested and zero-detection probability. strongly confirmed by Houtermans (1973) who calcualted the frequency spectrum at the output of the phototube for the arrival of single electrons (so-called monos), and two, three or One more electrons for the 5.9-keV x rays and Auger electrons frm the decay of 55Fe. electron incident upon the first dynode of the phototube may give rise to an output pulse at the anode of between lo6 and 10' electrons. Likewise if other photons striking the cathode of the phototube give rise to 0, 1, 2, 3, or more photoelectrons at the first dynode, then there will also be a probability of in general, this effect is zero detection at the second dynode, and so on. But, negligible. The x rays and Auger electrons of 55Fe are just about at the threshold of detection for most LSC systems. Moreover, the resolution of the system is so poor that the threshold On the other hand, this poor resolution enables linear extrapolation is not well defined. of discriminator data to be carried out for B-particle emitters with high maximum energies, above about 150 keV (Vaninbroukx and Spernol, 1965). The effect of zero-detection probability is only serious with low-energy ,+particle emitters such as 'H and I‘C, for which the extrapolation to zero energy is no longer monotonous. This problem was largely solved by Horrocks and Studier (1964), Bryant ef al. (1967) These authors fitted curves based on the Fermi probability and Gibson and Gale (1968). distribution of p decay to the experimental data above the region of zero-detection probability, which arises simply as an artefact of the phototube. This method was further developed by Grau Malonda and Garcia-Toraiio (1982), and used by Ishikawa (1984) and Coursey in terms, usually, et al. (1986). The method is, however, a relative method of calibration in effect the tritium calibration covers the low-energy part of tritiated-water standards; It is thus, strictly, a of the spectrum where the detection probability can be zero. method of efficiency calibration, rather than of efficiency tracing, the latter term having been already preempted by Campion et al. (1960) for a method whereby a +‘?.y-emitting nuclide was used to standardize a pure @-ray emitter by coincidence counting (75.2.2.4). Grau
Radioactivity
864
measurements:
principles
and practice
Malonda and Garcia-ToraAo (1982) have presented the theory double-phototube system, and it has been described and the theory (1985) and Coursey et al. (1986).
of their method slightly extended
for a in NCRP
This method of relative calibration also involves the figure of merit of the The scintillator-phototube system and the empirical quenching parameter of Birks (1964). figure of merit has been defined by Gibson and Gale (1968) as the number of electrons at the first stage of the phototube divided by the energy deposited in the scintillator; by Birks (1975) as the pulse amplitude at the phototube anode divided by the energy deposited in the scintillator; and by Grau Malonda and Garcia-Toraiio as the energy deposited by a particle inthe scintillator (corrected for ionization quenching and wall effects) divided by the average number of photoelectrons incident upon the first dynode of the phototube. The ionization quenching is usually computed using an empirical equation due to Birks (1964), but it can also be measured by several methods, of which those using an extended y-ray source to produce Compton electrons in the liquid scintillator or the wall are now most frequently used (NCRP, 1985). 5.4.3.3.
Relative
calibrations
bv liquid-scintillation
counting
As mentioned in the preceding section a very useful relative method of LSC calibration can be achieved in terms of the Fermi probability distribution of p decay, the quenching the escape of primary particles from the upper parameter Q(E), a term W(E) representing surface of the liquid scintillator or to the walls with insufficient unquenched ionization to be recorded, and the figure of merit of the LSC system, as 0 keV_', the average number of photoelectrons striking the first dynode of any one given phototube divided by the energy, E, of a detected particle. Generally the method employs an LSC system in which the scintillations from the vial are presented to the two phototubes operated in coincidence to Only a brief description of the method reduce phototube noise and spurious pulses. follows, and the interested reader should consult NCRP (1985) and Coursey et al. (1986) more detailed information and further references. If a particle of energy E deposits all its energy in the scintillator then the number of electrons incident on the first dynode would on an average be #Q(E)W(E) if there were no zero probability of detection. But for an average number of qEQ(E)W(E) electrons the Poisson the first dynode of the phototube distribution gives a incident upon probability) equal to exp(-oEQ(E)W(E)), and probability of none (i.e. the zero-detection But for two the efficiency of a system with one phototube would be 1-exp(-qEQ(E)W(E)). background-reducing coincidence mode the efficiency is equal to phototubes in the and using the Fermi probability In the case of @-ray spectra, [l-exp(qEQ(E)W(E),12. P(Z,E)dE, the efficiency for the system in this coincidence mode, ec, for pdistribution particle energies between 0 and Em,,,, is
JE$?,E)[l
exp(l
- ~EQ(E)W(E)]]'
dE
-0
e,
(5-30)
=
EBmax
s P(Z,E)m 0
In the Grau Malonda and Garcia-ToraAo approach two radionuclides, one of known the activity, are introduced into identical liquid scintillators with equal quenching, figure of merit 7 of the system may be evaluated from the radionuclide of known activity Fermi probability and used to calibrate that of unknown activity, using the appropriate function for each radionuclide. In practice a small correction for quenching measured by Using an NBS [sHj-water standard, the Horrocks (1976) H-number method can also be made. r4C samples with an overall uncertainty (random plus Coursey et al. (1986) calibrated non-random) equivalent to one estimated standard deviation of 0.2 percent. Gibson and Gale use calculated values for the exponent in Eq. 5-30 (See Ch. IV by It therefore more strictly belongs J.A.B. Gibson in BIPM, 1980, or Gibson and Gale, 1968). to the next paragraph, but is a theoretical analogue of the more recently developed Grau But it is interesting to note, as pointed out Malonda and Garcia-Toraiio relative method. system and using typical values for 0, Q(E) and in NCRP (1985), that for a single-phototube qEQ(E)W(E))] is essentially equal to W(E) given by Gibson and Gale (1968), [l exp(1 The reason for this is that, while the unity between E = 20 keV and E = 3.5 MeV. efficiencies Q(E) and W(E) increase m and decrease from unity, respectively, with increasing energy E, the decrease in W(E) is more than compensated by the increase in E up to about 3.5 MeV (see Fig. IV-6 in Ch. IV by J.A.B. Gibson in BIPM, 1980). 5.4.3.4.
Direct
5.4.3.4.1.
calibration
bv liauid-scintillation
counting
Extrapolation
the For P-particle emitters with maximum energies greater than about 150 keV, losses due perturbation due to the "mono" spectrum (H. Houtermans, HN, 1973, p. 121) and to zero-detection probabilities at low energies become completely insignificant compared with the total number of b particles summed over the energy spectrum.
Radioactivity
measurements:
principles
and practice
865
Because the linear energy transfer (LET) of a particles is so much greater than that a liquid the ionization density in the "wake" of an a particle traversing of electrons, Thus the possibilty for scintillator is about 10 or 20 times greater than for electrons. recombination is much greater in the a-particle track than in the track of an electron, and In fact a therefore ionization quenching (a term coined by Birks, 1964) is also greater. 5-MeV a particle will deposit a net amount of unauenched energy in the scintillator that is equal to that deposited by a fl particle of about only 500 keV. Thus both a-particle emitters and energetic o-particle emitters can be very well Vaninbroukx calibrated by extrapolation of a discrimination curve to zero pulse height. and Spernol (1965) obtained calibration values for the activities of samples of 241Am and several high maximum-energy flemitters that agreed with values obtained by independent methods to better than kO.5 percent. 5.4.3.4.2.
Double-
and triple-coincidence
counting
methods
(1970) have developed a system of non-linear equations for a Kolarov et al. two-phototube LSC system giving the figure of merit and efficiency of detection for each for both in the summing mode and for the two in coincidence. When phototube separately, [%-water standard they applied to the measurement of a National Bureau of Standards obtained a result that was about 4-percent different from the certified value (R. Vatin, Ch. V in*IPM, 1980).
Pochwalski et al. (1981) introduced another phototube to give a symmetrical threephototube LSC system and measured the activity of the p-particle emitter in the liquid ratio known as the TDCR scintillator by measuring the triple-to-double coincidence cg are the respective counting efficiencies of all three phototubes in method. If ZT and coincidence and all three phototubes arranged in double coincidence, then eT = N,/N, and coincidence ratio K is given by Eo = N,/N,z whence the triple-to-double N,
ET
NO
'D
K=-=-_.
(5-31)
eT and They then changed the optical efficiency using a coiled spring and so varied As K increases with increasing efficiencies, cT, eD and K all approach EDI and also K. These authors fitted fourth-power unity and N, and N, approach to the disintegration rate. polynomials to the values of cT and cD to enable them to extrapolate to K = 1.
Broda
Extensions of both the theory and applications et al. (1988) and Pochwalski (1988).
of
the
TDCR
method
are
discussed
by
Wu et al. (1987), have described an interesting method for the direct standardization of 14C, in the form of ['%-n-hexadecane in solution in toluene together with the Their phototubes. scintillator PBD, in a vial viewed by two matched electron-multiplier circuitry was such that count rates N' and N" from each phototube could be recorded and (The phototubes here were used in the also the coincident count rates, N,, between them. mode to which Eq. 5-30 true coincidence-counting mode and not in the noise-reduction channel allowed integral pulseSingle-channel analyzers in each phototube applies.) with an appropriately fitted polynomial, to amplitude discrimination and extrapolation, and missed ionizing events in the "through" electronic noise zero pulse amplitude, Coincidence counting enabled the actual average rate of numbers of photons scintillant. emitted from the vial to be measured; a method first applied to measure the alertness (efficiency) of two observers by H. Geiger and A. Werner in 1924 (as illustrated in Fig. & The rate of numbers of photons exiting from the vial was also 6 in Mann et al., 1980). obtained using two optical-diaphragm discriminators with extrapolation to zero reciprocal This phototube anode current, I, that was equivalent to an infinitely wide-open aperture. use of a diaphragm as an optical discriminator is closely analogous to the use of a coiled spring to alter the detection efficiency in the TDCR method, described above But it is not completely clear that any further optical-discrimination correction for zero-detection probability needs to be made to the result obtained by coincidence counting In fact Fig. 3 of the Wu et al. paper for the activity of 14C, as measured by Wu et al. seems to confirm this in that a plot of N'N"/N,N, against X,/I shows N'N"/N,N, essentially This may be associated with the fact, equal to unity for values of I,/I between 1 and 6. term in Eq. 5-30 mentioned above, that between about 20 keV and 3.5 MeV the exponential Therefore, as indicated in the first sentence of differs but little from unity. 75.4.3.4.1, perturbations and counting losses due to zero detection become insignificant Thus the assay of 14C for B-particle emitters with maximum energies above about 150 keV. is a borderline case, and it would be of interest to apply the method of Wu et al to 'H for which the relative effect of zero-detection losses would be so much greater. 5.4.3.4.3.
Coincidence
counting
counter is very As with many other detectors of 4a geometry, the liquid-scintillation Frequently the well suited for use as the j3 detector in P-7 coincidence counting. The flat face of the scintillator source is contained in a cell of hemispherical geometry. re-entrant-well cell sits on the cathode end of the phototube, with a 4-cm or 5-cm-diameter
Radioactivity
866
measurements:
principles
and practice
An intercomparison of measurements of the activity NaI(T1) detector placed over the cell. of a 1%~ solution between four international laboratories using the method of 4*B(LS)-7 coincidence counting by efficiency variation is reported in BIPM (1980). The extreme limits to the range of 13 reported results was only 0.6 percent. 5.4.3.5.
Other
methods
"Dual-label" assays, especially of samples containing mixtures of 'H frequently made in laboratories making LX measurements in connection with applications in the life sciences. The method is described in NCRP (1985) the method used to make the necessary quench corrections. Other pairs of that may be assayed by this method are 3H and "S, 3H and 3zP, and l'+Cand 36C1.
and 14C, are radioactivity together with radionuclides
5.4.4. Many radionuclides such as 3H, r"C (as CO,), 37Ar and samples of other radioactive noble gases have been calibrated by the method of internal gas counting using a suitable proportional-counting gas such as methane containing a small but measured amount of the gas to be calibrated. This is a 4?r method that avoids the problem of source self-absorption. It was probably first described in 1947 by Miller and by Brown and Miller, using internal gas counters in the Geiger-Miiller region. Later, similar measurements were carried out by Engelkemeir and Libby (1950) using single counters that were cylindrical in form with an axial wire anode. As the length of the counter was usually much greater than the radius of its cylindrical cathode, there was a uniform electrical field strength between @ihe anode wire and the cylindrical cathode wall over much of its length. But at each end of the counter the electrical field would be distorted and end-effect corrections had to be made (see Fig. 5-14 and Spernol, 1967). For cylindrical counters of small diameter there might also be a significant correction needed because of the loss of radiation to the walls without creating one ion pair in the counting gas.
Schematic representation of the electric field strength Fig. 5-14 along the anode wire of a proportional counter for internal-gas counting (after Garfinkel et al., HN, 1973). A somewhat simpler method, but which eliminated the need to calculate end corrections was used in 1949 by Mann and Parkinson (also see S.B.Garfinkel et al., HN, 1973). This method was based on the use of two (and later, three) cylindrical gas counters of different as possible. lengths, but, in every respect other than length, constructed as indentically The anode-wire supports were precisely machined end plates so that (as illustrated schematically in Fig. 5-14) the difference in count rates between the two counters should give a count rate for an ideal counter with uniform electric field and needing no correction for the distortion of electric field at the anode-wire supports at each end of the counter. It was important, however, that the shorter counter should not be so short that the electric field should never attain a uniform value along the length (in the middle) of the counter. At the National Bureau of Standards two sets of three such compensated internal gas One set has cylindrical cathodes of copper counters have been in use for some 30 years. and the other set has smaller but similar cathodes of stainless steel. Any residual wall effect was eliminated by operating the counters at different to zero pressures, plotting count rate against the reciprocal pressure, and extrapolating In many cases such extrapolations the reciprocal pressure (i.e. to infinate pressure). possibly because ,9 showed no change in count rate as a function of inverse pressure, particles incident upon the wall induce the emission of secondary electrons that then reach Such an effect has been observed by De Roost et al. (1969) in the form of the anode. equally spaced afterpulses in a 4nfl proportional counter, the time interval between pulses corresponding to the time of transit between cathode and anode. Other configurations of internal gas counter have been designed by Spernol and Denecke (1964) and Olsson et al. (1962). The former consisted of a single cylindrical counter with specially designed guard electrodes to preserve the uniformity of the electrical field; the latter consisted of a single cylindrical counter with one end so constructed that it could NBS tritiated water standards be moved back and forth to alter the counter length. calibrated by the former (Spernol and Denecke) counters agreed with the NBS value to 0.2 In many ways the Olsson et al. design, although more percent (Mann and Spernol, 1964). complicated than the simple NBS design, should have an advantage in that their counter both configurations. Here in the long and short position has exactly the same end-support
Radioactivity
measurements:
principles
and practice
867
again, however, the NBS and Uppsala results for the half life of "C (Godwin, 1962) were in very close agreement. Internal gas counting systems must be equipped with suitable gas-handling and equipment pulse-shaping (for pressure, volume and temperature) and quantifying The NBS internal gas counters are provided with a cryogenic preamplifiers and amplifiers. filling and mixing system, and the count-rate data from the six counters are collected simultaneously on a minicomputer that can be operated, if required, as a multichannel analyzer (S.B. Garfinkel, et al., HN, 1973, p. 59). An ingenious method of position-sensitive internal gas-proportional counting in tubular counters with resistive axial anode wires or metal-coated glass fibres has been developed by Mori and colleagues, in order to eliminate the counter end corrections electronically. A paper (Mori et al., 1987) given at an ICRM seminar on Techniques in Radionulide Metrology held in Rome in 1987 describes the method and cites previous references, while a later twenty-year review of radioactivity measurements made at the 1987) gives a short but very Nagoya University Department of Engineering (Watanabe et al., comprehendible description of the method. Very briefly, the counter described by Mori et al. (1987) consists of a 95.cm-long and 20.pm-diameter nickel-chromium anode wire, with an electrical resistance of 2.09 kn, stretched along the axis of a 4-cm-diameter cylindrical stainless-steel cathode. Each end of the wire went through a lumped resistance and charge-sensitive amplifier to a "position processor". If, for convenience of presentation, we think of the cathode as being horizontal with a left (L) and right (R) end, then for a charge Q collected from an ionizing event occurring at a distance x from the left end of the anode wire of length y, the ratio of the charge outputs from each end of the anode wire is given by the simple expression QL/(QL + QR) = x/r. The authors estimate an overall uncertainty of fl.l% in their measurement of the activity of a sample of [r4C]-methane, but anticipate a lower uncertainty by making more precise measurements of the effective volume and by using a "partially resistive anode wire". 5.4.5. Direct activitv measurements with reentrant-well crystals 5.4.5.1. Introduction In 1963, Brinkman and Aten. described how a single NaI(T1) crystal could be used, in conjunction with a multichannel analyzer, to measure the activity of a radioactive source that decayed with no direct transitions to the ground state of the daughter nucleus, but that emitted two cascade photons in coincidence. This method of sum-peak coincidence counting can also be practiced with two shallow-well-type NaI(T1) crystals placed face-to-face in 4s-sr geometry, or in essentially Oa-sr geometry, within the reentrant cavity of a so-called well-type NaI(T1) crystal (see J.M.R. Hutchinson et al., HN, 1973, p, More recently "pin-well"-NaI(T1) crystals have been fabricated that have wells 187). measuring between 2 and 8 mm in diameter from which the geometrical escape window from the open end of the reentrant well is only of the order of one or two percent. Hutchinson and Mullen (1983) report experiments with an all-the-way-through "well" in which the geometrical escape factor is 1.296% of 4s. 5.4.5.2. Available types. applications and calibration A well-type photon detector is a right-circular cylindrical single crystal with a coaxial reentrant cylindrical hole (well) cut to a depth of about 0.5 to 0.6 times the height of the cylinder. It may also be cut, with greater accuracy, all the way through (see 75.4.5.1). The source to be measured is placed in the bottom of the well (or half-way through the bottomless well) so that the detector "views" the radiation from the source at the largest possible solid angle, of nearly 4rr sr. The detector material is most frequently thallium-activated sodium iodide, NaI(Tl), but cesium iodide, CsI(Tl), bismuth germanate. Bi,Ge,Olz (now, generally referred to as BGO), and cadmium tungstate, CdWO,, are also used (see y4.6.1 and p. 33 of NCRP, 1985). It should be noted that 99 percent of 200.keV photons are absorbed on traversing 34 mm of NaI(T1). For CsI(T1) and BGO the corresponding values are 23 mm and 9 mm, respectively. These figures help to choose the required crystal dimensions. Semiconducting crystals (Ge(Li)or HPGe) can also be used to construct well-type detectors (also see 7 5.4.5.5). Such detectors are very useful instruments for relative and direct ("absolute") measurements of activity or of photon-emission probabilities, because the detection efficiency is in general not too strongly dependent on source position or on photon energy. The measurements with large well-type detectors are much less time consuming than 4?r(PC)--, coincidence measurements and are often of comparable, if not superior, accuracy: the latter being the case for certain nuclides with complex -/-ray spectra. If a well-type
scintillation detector is to be used to calibrate a source of unknown
868
Radioactivity
measurements:
principles
and practice
activity, its detection efficiency for the radionuclide in question must be determined, either from calculation or by measurement. The calculation of the total efficiency is if accurate dimensions of the crystal and its housing are known and accurate possible attenuation coefficients are available (Mannhart and Vonach, 1976). Several corrections such as for scattering in the material surrounding the detector or in the lining of the well, for bremsstrahlung and source positioning have to be evaluated. Mannhart and Vonach (1978) have further reported a method for an experimental determination of total efficiency by measuring count rates using suitable single-T-ray sources the activities of which do not need to be known accurately. For these measurements the sources are placed either at the bottom of the well or in an exactly reproducible position outside, on the detector axis and some 10 cm away. By using an iterative procedure, they obtained efficiencies with uncertainties of 0.3% or less. For sources emitting coincident y rays, the uncertainties of the calculated efficiencies were even considerably lower. The important fact that efficiency calculations for radionuclides with complex r-ray spectra are often more accurate than those for single r-ray emitters can be understood from the following simple considerations. If two y rays in cascade are detected with efficiencies e, and ez, respectively, the probability of non-detection is l-e that is equal to (1-el)(l-ez). If the decay scheme comprises n independent branches with partial abundances, h,, and k, coincident transitions from each branch i, the total efficiency becomes e =
; h,[l - I?(1 - ei,)] i=l j=l
,
(5-32)
where eij is the efficiency of the jth coincident 7 ray from the ith branch. The inefficiencies, 1 - e,,, are already quite small and their products even much smaller. Therefore, in the case of complex decay, the calculation of the total efficiency can be highly accurate, even if the parameters of the decay scheme are not accurately known. For practical applications Eq. 5-32 may have to be completed in order to take into account the effects of bremsstrahlung, conversion electrons, characteristic x rays and of discrimination thresholds (see Winkle?? and Pavlik, 1983). Among the radionuclides for which Pavlik and Winkler (1983) could measure the activities with uncertainties between 0.1% and 0.7% the following multi---ray emitters should be noted: 56Co, '5Se, 82Br, 'lomAg, lzsSb, 13'Ba, 134Cs, 15'Eu, l"Ta, and "'Ir; and also some single---ray emitters such as ?Zr, 54Mn, "Sr and 13'Cs. Instead of using total efficiencies, the measurement of activities by photopeak analysis is sometimes preferred. But an experimental measurement of the photopeak efficiency is of limited accuracy because of uncertainties in the evaluation of peak areas, geometrical dimensions and of multiple scattering processes, and of attenuation coefficients (Fig.41 of NCRP, 1985). 5.4.5.3.
Detectors
and counter
construction
The crystals used for 4vr(NaI-Tl)7 measurements have typically a diameter and a thickness of 127 mm (5 inches) and are mounted as an integral unit on top of a suitable electron-multiplier phototube. More details on the systems used in five laboratories are presented in a review article by Ballaux (1983). Dimensions can be made to order and measured by the manufacturer to within 0.05 mm or better. The outer surface and the inside of the well must be covered with light-reflecting layers (e.g. Al,O, or TiO,). The reentrant well is usually lined with aluminium to protect the crystal surface and also to reflect emitted light. As an example, the NaI(T1) detector described by Mannhart and Vonach (1976) was placed inside a lead shield of 5-cm wall thickness and lined with graded layers of Cd, Cu and Al, in order to prevent x rays generated in each previous layer of Pb, Cd and Cu from reaching The background count rate thus obtained was about 33 5-l for a threshold the detector. energy of 22 keV. Legrand et al. (1975) employed a somewhat smaller NaI(T1) crystal (102 x 127 mm) with a 50.mm-deep well of 12.mm diameter. The inside of the well was covered with Al,O, paint (0.5-mm thick) and lined with 1 mm of Be. We may also mention the NBS sun-peak method that utilizes two 203 x 102.mm crystals that can be operated in the summing, coincidence and anticoincidence modes Hutchinson et al., HN, 1973, p. 187). 5.4.5.4.
Practical
urocedures.
The total -,-ray efficiency of a well-type crystal depends different behaviour: From about 60 keV better than 0.5%. and a accurate,
source Dreoaration
NaI(T1) (J.M.R.
and counting
(the ratio of the numbers of detected to emitted photons) There are three regions of rather on the photon energy.
to 200 keV, the efficiency is close to 100% and can be calculated to For energies above 200 keV the calculations are considerably less calibration by means of single-y-ray standard sources may be
Radioactivity
measurements:
principles
and practice
869
preferable. An uncertainty of between 0.5 and 2.0% may then be reached in the region below 1.25 MeV. At the latter value the efficiency is in general between 60 and 70%. In the region below 60 keV the efficiencies vary rapidly with energy. Moreover, there are not many reliable calibration energies in that region and efficiency uncertainties range from 5 to 15%. The influence of the material surrounding the scintillation crystal and of the source dimensions must also be measured if full advantage of this method is to be taken. If the crystal dimensions are not known accurately enough, an alternative method for measuring the detector efficiency and its energy dependence can be applied, as described by Mannhart and Vonach (1978). This method requires the measurements of count rates from the same uncalibrated sources inside and outside the well. By using either single-r-ray sources or sources emitting two coincident -y rays, an efficiency curve covering the energy interval from 480 keV to 1.84 MeV has been evaluated by these authors. The preparation of sources for 4?r7 counting does not involve the same regarding thickness of source and backing, as do sources for particle counting.
criteria, Very thin
sources and backings are needed only for nuclides emitting a large proportion of low-energy In most other cases the procedure consists of dispensing a weighed drop of the photons. After evaporation of radioactive solution on to a plastic foil (mylar, cellulose, etc.). the solvent, which may be accelerated by infrared heating, the source is covered by a similar foil and welded on to the first, thus forming a sandwich. It is possible to use liquid sources in thin-walled polyethylene tubes, or even very 1984), provided that adequate corrections are calculated. thick solid sources (Winkler, Marinelli beakers that contain bulk sources and surround a NaI(T1) crystal detector are very useful for the assay of environmental samples (see p. 270, NCRP, 1985). But the sources are, in An outstanding advantage of 4x7 counting is its simplicity. general, much weaker than for particle counting because pulse pile-up must be avoided and Count rates are generally not higher relatively long dead times (10 MS) have to be used. than about 5000 5-l , depending on the background count rate. The discrimination level should be kept as low as possible (10 to 25 keV), depending on the energy level of the background and electronic noise. The latter may correspond to less than 8 keV. 5.4.5.5.
Corrections,
evaluation.
accuracv
and testing
As a well-type detector can be used in a great variety of situations as to the source and the instrumental details, it is necessary to configuration), (type of nuclide, calculate or measure, in each case, a number of correction factors in order to make the Because the results of efficiency calculations are best use of its measuring capabilities. valid only for the naked crystal and for point-like sources, the influence of the material surrounding the detector and that of the light-reflection layers and linings inside the well must be taken into account by separate measurements or calculations. The same is true for corrections due to source position, geometry and thickness. Special radiation effects bremsstrahlung) as well as the influence of a finite (B rays, 7-7 angular correlations, discrimination threshold must also be taken into account. The Lining of the well diminishes the efficiency of a well-type crystal detector. But in the vicinity of the iodine absorption edge (32 keV) the absorption does not vary exponentially with photon energy. In that energy region the interactions are mostly by photoelectric effect in the innermost layers of the crystal well, from where more than 20% of the iodine x rays escape and are lost. Therefore, the choice of the discrimination threshold should represent a compromise between the effects of absorption of primary x rays and the escape of iodine x rays. Low-energy 7 or x rays may create some difficulties because of the presence of a finite discrimination threshold, which is always required to prevent interference from electronic noise. This is especially so if a considerable part of a peak lies below the threshold. This effect may be enhanced by low and unstable detector resolution. A low threshold may therefore be advantageous. On the other hand, it is possible to suppress the detection of the low-energy part of the spectrum by using an absorber (1 mm of perspex causes a reduction by a factor of 100 or more) and to take this into account by calculation. The corrections for the effects of extended and, or, thick samples are generally measured experimentally, but can also be calculated. It should be noted that, above 200 keV, thick samples feign a higher efficiency because Compton-scattered radiation in the source shifts the energy to values for which the efficiency is greater. From a practical standpoint, the central question is: how accurately can activities be measured? Several authors have measured sources of very well- known activity, such as those measured in international comparisons ((2.2.3), with their own well-type detectors, The differences were generally in the range of 0.1 to 1 percent (see Ballaux, 1983). As comparisons are more difficult to perform with thick and large-volume samples, there is not much information available on such measurements.
Radioactivity
870
5.4.5.6.
Applications.
examules
measurements:
and suecial
principles
and practice
systems
The use of 4sy measurements by large well-type detectors is a welcome alternative to 47r(PC)-7 coincidence counting, especially with nuclides decaying by electron capture and subsequent multiple-~-ray emission. In those cases the counting efficiency and hence the The simplicity and rapidity of 4lrr measurements predispose accuracy are particularly high. one to use this method for routine radioactivity assays of short-lived nuclides, such as used in medicine (?? ="'Tc, l'lIn, lZ31) 16gYband "lT1, which are being increasingly Vatin, 1983). The possibility of measuring thick sources of bulk samples with high accuracy offers sections of numerous advantages in measuring activation cross neutron-induced the A further interesting application has been reported for the measurement of reactions. counting. solution samples of g9Tc by bremsstrahlung A different concept of a 4x7 counter has been developed by Denecke (1984), in the form of a 4nCsI(Tl)-sandwich spectrometer. It consists of two crystals, each of 50.8-1~1 cavities of lo-mm diameter, machined in diameter and 25.4.mm thickness, with hemisepherical The sources are placed in the cavity centre of the the center front of each crystal. joined crystals. Thin hemispherical absorber shells of polyethylene were hot-pressed to fit in the cavities, in order to absorb particles but not photons. For this configuration, the photon-detection efficiency between 10 and 200 keV is practically 100% and highly accurate photon- emission rates can be measured. A still different type of solid 4x7 counter is the well-type Ge(Li) detector described by De Bruin et al. (1979). These authors used a cylindrical Ge(Li) crystal of 45.mm diameter and 62.mm height with a 46.mm deep well of 16-m width. Good energy resolution and relatively high detection efficiency, almost independent of sample dimensions are, by larger summation effects. however, counterbalanced The latter lead to sample-dependent distortions of the high-energy y-ray spectrum which had to be avoided by the use of absorbers of high-l. material. 5.4.6.
4r ionization
5.4.6.1.
chambers
General
The basic facts about the ionization of gases have been described briefly in 74.4.1. Radionuclide metrology makes ample use of T-ray and P-ray ionization chambers operated more The main features of such activity measurements and or less in the saturation region. In the present section we their application to quality control are explained in 74.5.1. can therefore confine ourselves mainly to a discussion of practical aspects, i.e. of the Errors, corrections and equipment used and of the method of measuring ionization currents. will also be explanations concern calibration procedures considered. The r-ray but the measurements of p rays and other electrons are not fundamentally measurements, different, except for the much higher absorption. 5.4.6.2.
Ionization
chambers,
sources
and suworts
Among the numberless possibilities to arrange a pair of electrodes in a volume of gas, chambers are by far the most important ones. the parallel-plate and cylindrical For electrodes are best suited and will be radioactivity measurements coaxial cylindrical The source to be measured is introduced into a coaxial reentrant considered exclusively. The material and the shape of the electrodes have considerable tube, at ground potential. influence on the chamber response to ionizing radiations. The ideal ionization chamber would be one with a response varying linearly with the The former can be approximated in a of photon energy. source activity, and independently wide range of activity, whereas the latter is impossible. function may be Some calculations in order to improve the shape of the response successful, but the construction of a good ionization chamber will widely rest upon former Besides the geometrical dimensions, the nature and and trial and error. experience, electrode pressure of the gas filling, and the material and thickness of the collecting will influence the ionization current. With air at ambient (atmospheric) pressure, the chanber walls can be made very thin, but the sensitivity is low and depends considerably on Therefore, most chambers for activity measurement are filled with a pressure and humidity. dry, inert gas at a high pressure (1 to 2 MPa; 10 to 20 atm) and sealed, in order to keep Argon is preferred in many cases; nitrogen may give a better the mass of the gas constant. The higher sensitivity of pressurized linearity but a 2 to 3 times lower sensitivity. chambers must of course be purchased at the price of relatively thick walls of the chamber and the reentrant tube. The electrode arrangement of the chamber in use at the BIPM is shown in Fig. 5-15. The wall material is stainless steel, the electrodes are made of aluminium, and the chamber The insulators are of ceramic material, the sensitive is filled with nitrogen at 2 MPa. volume is 5.2 dm3.
Radioactivity measurements: principles and practice
H-V
Sectional view (schematic) of a pressurized, well-type Fig. 5-15 ionization chamber (after Rytz, 1983). The design and construction of a pressurized well-type ionization chamber is too delicate an undertaking, even for experienced metrologists, to give satisfactory results. Therefore, it is advisable to purchase one of the trustworthy products on the market (see Fig. 74, NCRP, 1985). If liquid samples are to be measured, these must be contained, as aqueous solutions, in flame-sealed standard ampoules of glass. If merely relative results are sought, e.g. for checking dilution factors, other vessels may be used provided two or more identical ones Solid samples of identical configuration can also be compared with each are available. other. Contamination of the chamber well must be strictly avoided. The ampoules for liquid samples must be considered as part of the ionization chamber, because they are involved in each single measurement in exactly the same way. However, as each time a different ampoule must be used, it is important to have available a large Thus, for the SIR as an number of completely equivalent and interchangeable ampoules. example, several thousands of ampoules are available that have been manufactured from the same glass melt, in order to assure the uniformity of the material (p. 220, NCRP, 1985). Moreover, the possible variations of the dimensions of 30 randomly chosen specimens have been checked with great care and expressed relatively in terms of apparent activity variations (see Rytz, 1983). The samples and the reference sources have their appropriate supports made of light chamber well. The material, e.g. perspex, and are introduced sequentially into the correct position in which the sources should be placed for measurement can be located by surveying the reentrant tube with a point source and observing the ionization current as The correct position is the point source is displaced laterally or axially in the tube. Further, it is important to check the defined by a minimum and a maximum, respectively. repeatability of the measurements when a reference source is measured many times and taken out of the chamber and of the support, each time. The preferred radionuclide for use as a reference source is ZZ6Ra because of its long Such sources must be manufactured by specially equipped and well-known half life. suppliers, and the radium salt must be densely packed in double-walled, arc-welded envelopes of Pt-Ir alloy, so as to be perfectly sealed. It is desirable to have available a set of sources covering the whole range of the high-precision measurements envisaged. The ratios of these sources must then be checked periodically, in order to verify their airtightness. The airtightness of the ionization chamber must also be tested by periodic measurements of the ionization current, each time with the same source and the same capacitor (see q5.4.6.3). 5.4.6.3. Ionization-current measurements Many
different
circuits
for highly precise measurements
of weak currents have been
Radioactivity
a72
measurements:
principles
and practice
described in the literature (H.-M. Weiss, HN, 1973, p. 291; K. Zstinszky, HN, 1973, p. 299; Blanchis, 1985). The Townsend balance with continuous or stepwise compensation (see Figs. 5-16 and 6-24) is often used in combination with preset voltage, charge or current. Other circuits measure the time average of the voltage drop across a high resistance (Walz and In all cases a highly sensitive Weiss, 1970), or they employ feedback-current integration. charge measurement is needed, often a vibrating-reed instrument for voltage or but it is no longer electrometer (e.g. Gary, of the Applied Physics Corporation, manufactured) or a digital voltmeter (e.g. Keithley, see 76.8.2.1) sometimes with feedback (76.8.2.2). The electric quantities measured (voltage, capacity, resistance) do not have to be known accurately. All that is needed is a highly stable current-measuring system and Santry et al. (1987b)have described the automatic-control and datareference source. of the National Research Council of processing equipment installed at the laboratories It comprises a Keithley Model 617 Programmable Electrometer and an IBM XT Personal Canada. and enables the activities of y-ray-emitting radionuclides to measured with Computer, reproducibilities of 0.05%.
Block diagram of a semi-automatic circuit for ionizationFig. 5-16 Townsend balance with stepwise compensation current measurements.
(after Rytz, 1983). In the operation of most ionization chambers the collecting electrode is kept close to ground potential. The high d.c. voltage to be applied to the high-voltage electrode is often taken from dry batteries, but these are, nowadays, being replaced, more and more, by Negative or positive potentials of low-noise electronic power supplies. highly-stabilized, several hundred volts, up to about 2000 V are usually applied. The capacitance of such ionization chambers is of the order of 50 pF, and that of the For most measurements it is cable to the collecting electrode may be of the same order. Some of the capacitor in parallel with the chamber. necessary to add an external commercially available products are more suitable and a careful selection as to temperature and leakage is important. The capacitance also varies considerably with dependence to arrange a set of such For high-precision work, it is therefore advantageous humidity. capacitors in an airtight box provided with high-quality insulators and containing a drying becomes very stable and After several weeks, the capacitance agent (e.g. silica gel). nearly insensitive to small temperature changes. Deformations of the cables may give rise to spurious charges and must be avoided. Rapid changes of the voltage applied to cables, capacitors or insulators may induce delayed variations that can be avoided by providing waiting periods of about 20 s after such changes (e.g. after the opening of the short circuit). 5.4.6.4.
Activity
measurements
The principal virtues of using well-type ionization chambers for the measurement of Although activity are the simplicity of operation and the high precision of the results. such measurements are necessarily indirect, i.e. related to standard sources via a stable in metrological work can hardly be overestimated. their importance reference source, of the high possible precision can only be taken if a number of However, full advantage The main facts concerning the precautions are observed and certain tests applied. measurement of an unknown source by means of a standard (and hence a calibration factor, K) have been explained in l/4.5.1. 5.4.6.5.
Efficiency
and efficiency
curves
is defined as the activity of a The equivalent activity, A, (see ~4.5.1.1.2), radionuclide sample that gives the same response as the long-lived reference source at time is t,; the reference times of all five "'Ra reference sources used in the SIR programme a relative efficiency of the ionization The reciprocal of A, represents 1976-01-01.
Radioactivity
chamber. A, chamber and measured by relation
principles
873
and practice
is thus a characteristic quantity for each radionuclide, in a given ionization the same geometrical environment, It can be that is independent of time. means of a previously, and directly, standardized source, according to the
A, = A[R + f(R - l)/(&, where
measurements:
-
f)l
exp(-&(t,
- Ql
exp[&(t,
- to)1
,
(5-33)
A is the certified activity of the national-laboratory standard source at a stated reference time t,; R = I,,/I, is the ratio of the responses to the BIPM "'Ra reference and nationallaboratory standard; f is the background-plus-leakage current; x S( X,, are the decay constants of the submitted radionuclide standard and of 226Ra,respectively; and tm is the mean, or otherwise stated, time of the BIPM measurements.
The background current, f, should be measured for about 60 minutes, both before and after measuring a source. In general, it does not vary much, especially if the chamber is mounted within a shield of lead bricks, about 5-cm thick. The plot of an x-y recorder gives, in addition, a valuable check of the performance of the measuring system. The quantity A, is identical to the "relative KR factor" Ks in Eq. 4.1 and can be used to establish an efficiency curve, either directly (see, e.g. Weiss, 1973) or in a more elaborate manner, as described for the SIR programme (Rytz, 1983). Such curves are very useful for interpolations and the evaluation of impurity corrections. A typical efficiency curve for a commercial radionuclide ("dose") calibrator is shown in Fig. 96 of NCRP (1985). 5.4.6.6.
Corrections
Corrections for r-ray-emitting impurities, present as impurities in a source to be measured, can easily be calculated if the amount of the impurity can be established. These corrections can be considerable for impurities emitting high-energy photons in a source: that emits only low-energy photons, as, for example, a "Co impurity in a 57Co source. Corrections may also be needed for bremsstrahlung, if the sample emits high-energy p rays and if the measurement involves the use of the y-ray efficiency curve. Beta-ray ray-bremsstrahlung efficiencies for some p-ray emitters have been measured at BIPM, and an efficiency curve determined. Corrections can easily be evaluated, and are small except in extreme cases, such as for '44(Ce+Pr). As saturation may not be achieved in the whole sensitive volume of the ionization chamber, recombination may occur and a correction for non-linear response may be necessary. Tests should be carried out using sources of different activities of the same radionuclide and for different l-ray energies. 5.4.6.7.
Uncertainties
As is well known, the precision of the measurements with a well-type ionization chamber is often higher than that of most direct methods. But this should not incline one from making a detailed analysis of the various uncertainty components, taking into account that they may depend on the photon energy. The components to be considered are l l l l l
uncertainty of the non-linearity correction, instability of the current-measuring system, statistics of ion collection, variations in ampoule dimensions, repeatability (standard deviation) of the mean
ionization-current
ratio
The influence of the ampoule walls is about twice as large at 60 keV (241Am) as it is at 1.25 MeV (?Zo). i.e. the sum For SIR measurements, the combined relative uncertainty, in quadrature of all these components at a level of one estimated standard deviation, is about 0.1% for *"IAm and 0.05% for 60Co. 5.5.
COINCIDENCE
COUNTING
5.5.1. General The measurement of activity by the method of coincidence counting involves the recording of individual emission rates of two simultaneous radiations from the same nuclear transition, in each of two separate detector channels, together with the rate of coincidence, in time, between them, provided that the second radiation does not arise from an interaction of the first radiation outside the decaying atom. Thus the coincidence method can be used to measure the activity of an amount of a radionuclide that decays by emitting a beta particle followed by a prompt gamma ray from the daughter nucleus. It cannot be used without serious complications in cases where two radiations associated with the decay consist, for example, of a beta particle and external bremsstrahlung, such as in the decay of 32P, Clearly, if the efficiency of each of the two detector channels was
Radioactivity
874
lOO%, then the coincidence
count
measurements:
principles
rate should be equal
and practice
to that in each channel
is one of the most powerful in the repertoire of The coincidence-counting method radionuclide metrology. H. Geiger and A. Werner first described its use, in 1924, to monitor the efficiencies of two observers recording the number of scintillations caused by alpha particles striking a given area of a ZnS(Ag) screen subtending a known solid angle to The principle of this experiment is illustrated in Fig. an alpha-particle-emitting source. of two detectors if but it is equally applicable to finding the efficiencies 5-17, different radiations emitted from a radioactive source. ""llt,me +
Observer
A (CAN,)
ObserverB
Cotncidences
or
N,=
(&,N,l
(E,EBN,)
Na.Na
number
of coincidences
-6X5 3 =10
The principle of activity measurement by coincidence counting. Fig. 5-17 As was done in the early days, each observer used a low-power telescope and recorded the occurence of a flash on the ZnS(Ag) screen by pressing a key that caused a needle to move across a strip of smoked paper. 5.5.2. Applications
to activitv
measurement
The application of the coincidence-counting method to the measurement of activity can perhaps be best illustrated by considering a specific example, namely that of the calibration of sources of a simple beta-gamma emitter such as 6oCo. This radionuclide decays by emission of a beta particle to the 2.5-MeV excited state of 60Ni whence it decays with a half life of the order of a picosecond, with the emission of two gamma rays in cascade to the ground state of 60Ni. In terms of such a short half life the emissions of the beta and gamma rays are essentially simultaneous. These radiations are then detected and counted by means of a p-7 coincidence-counting system, similar to the basic system shown in Fig. 5-18, that detects and records beta- and gamma-ray count rates and also the rate of coincidences between them. of the source, and Ng, N, and N, be the beta-channel, Let N, be the activity gamma-channel and coincidence count rates, respectively. Then ep, equal to Np/Nos and c., of the two detectors for their respective equal to N,/N,, will represent the efficiencies radiations. As was emphasized by P. J. Campion in 1959, it should be noted that these efficiencies include all effects that lead to count rates, in the respective beta and gamma channels, except those due to dead-time losses. In addition the respective count rates must
a75
Radioactivity measurements: principles and practice
Block diagram of the basic components of a typical 4n@-Y Fig. 5-18 coincidence-counting arrangement (after NCRP, 1985). have been corrected by subtracting the background count rates, and N, must be corrected for accidental coincidences arising from the fact that the coincidence gate is open for a finite time often of the order of one to ten microseconds, the latter, for example, being required in the case of a delayed gamma-ray emitter such as that of 1-ps half life in the 514-keV level in "Rb in the decay of "Sr. In terms of the beta-channel and gamma-channel efficiencies we can write down the coincidence equations, corresponding to those given in Fig. 5-17, for a simple beta-gamma emitter, namely: No
=
N,sa
p
N, = N, > ,
and
N,
=
N,c,+,
whence
N,
=
N$J,/N,
(5-34)
In addition, if a series of coincidence measurements is made over a period of time that is not short compared with the half life of the radionuclide being assayed, then the data may have to be normalized to a chosen fixed point in time. Such a normalization is usually referred to as a "decay correction" but it may seem somewhat inappropriate to refer to a law of nature such as the radioactive-decay law as a correction. A decay, or half-life, correction should actually refer to the updating of nuclear-decay data that must be made from time to time in the light of newly made evaluations. By no means do all radionuclides have decay schemes as simple as that of "Co which can be assayed using low-efficiency beta- particle detectors, with sufficiently high But the decay schemes of numerous beta-gamma emitters accuracy to meet many requirements. in common use are much more complex and involve further radiations such as conversion In such cases the use of a high-efficiency 4n electrons, x rays and Auger electrons. counter in the beta channel combined with the method of efficiency extrapolation to 100% beta- counting efficiency is mandatory (y5.5.3). But as A. P. Baerg points out in 73.2 of NCRP (1985) "there are cases in which low-efficiency beta-particle detectors may be advantageously used". He gives one such example provided by the assay of "'1 that decays by 100% beta-particle emission (Egmax= 153 keV) to the 39.58.keV excited state of lZgXe. This then decays promptly with the emission of 7.5% 39.58-keV gamma rays, plus conversion and Auger electrons, and some 70% of xenon x rays with energies between 29.5 and 33.6 keV. But these x rays can be used, together with the gamma rays, to signal the 39.58.keV xenon An lzsI source was standardized at the National transition in the gamma-ray channel. Bureau of Standards using a thin (0.25-mm thick) plastic-scintillator phototube assembly to detect the beta particles, and a thin (1.6.mm thick) NaI(Tl)-crystal phototube assembly to detect the photons. (Spernol et al., 1976). The thin plastic was very insensitive to photon interactions and any that could have interacted were excluded by pulse-height discrimination; and sufficient absorber was placed between the source and the detector to The NaI(T1) crystal was provided with a 0.13-mm-thick remove conversion electrons. beryllium window that, together with the air between it and the source, was sufficient to absorb all of the beta particles. Under these experimental conditions, the activity of the "'1 source could be measured by recording the count rates in the individual detector channels and the coincidence scaler, and substituting these into equation 5-34 to obtain N, (Mann and Hutchinson, 1976). Liquid-scintillation (LS) detectors have also been widely used in the beta channel, and are comparable with 4n,9 proportional counters with respect to their high detection An intercomparison between four national laboratories was organized by a efficiencies.
a76
Radioactivity measurements: principles and practice
BIPM working group in 1977 to compare results of 134Cs measurements obtained using the method of 4~p(LS)-r with efficiency extrapolation. The results, together with three in which 4a proportional or pressure proportional counters were used in the beta channel, are given, together with experimental details, in chapter VII of BIPM (1980). All of the sixteen reported results lie within a range of kO.5 percent. 5.5.2.1. Gamma-eamma coincidence counting This method involves the use of two photon-detector systems, and is not recommended as a method of choice except in special circumstances, It is discussed in some detail in NCRP is given, (1985), where the coincidence equation that is applicable to the assay of %o together with an indication of the difficulties involved and references to pertinent publications. The difficulties include: Effects due to possible angular correlation between two gamma rays; possible extra coincidences due to the Compton scattering of either gamma ray or photon from one detector into the other, and a need to know the relative effiencies of the two detectors to photons of different energy. Consequently, this method may be neither the least trouble-free nor the most accurate. It has, however, been rather fully discussed by Hayward et al. (1955) and Taylor (1967) in the respective applications to the standardization of "Co, and of lz51 and lQ:Hg. 5.5.2.2. Coincidence-countins
corrections
The principal corrections are for background, the loss of counts due to the dead time in each of the two single-radiation channels, and for accidental coincidences in the coincidence channel. For non-extending dead times r1 in channel "1" and r2 in channel "2", the corrected count rates are, respectively, N1/(l - N1rl) and N,/(l - N2~z), i.e. the number of counts recorded in a given "clocked" second of counting time divided by the actual live-time fraction of that second. Thus, if N counts per clocked second are recorded, the coincidence mixer will have been "dead" for a fraction NT and "live" for a fraction@ - Nr]of the clocked time. The dead-time corrections must, of course, be made before subtraction of the background count rates. In practice 'I and ~~ are usually equal. It is more difficult to calculate the dead-time correction for lost coincidences in the coincidence channel, because this depends on the single-channel dead times and the dead time and resolving time in the coincidence channel. It is also difficult to calculate the correction in the coincidence channel for "accidental" coincidences (i.e. unrelated coincidences occurring by chance between radiations from different decays). Many approximate formulae have been derived during the last two decades, mostly as single expressions for the activity, to take account of these corrections (e.g. Campion, 1959; Bryant, 1963; and Baerg,1973). Campion's and Bryant's formulae have been used frequently, although Bryant's formula is only valid for equal efficiencies in both channels (Smith, 1978). Today, the exact corrections derived by Cox and Isham (1977), or the extended or modified formulae of others (Smith, 1978, 1987; Funck, 1980) are mostly applied. A further improvement of the coincidence method may be obtained by the so-called computer discrimination as developed by Smith and Stewart (1975). In this technique, p-particle count raters are measured simultaneously, over a continuous range of p efficiencies, in coincidence with y pulses, using appropriate electronic equipment. Smith (1987) has extended this method to include simultaneous discrimination in both the 0 and 7 channels and has given explicit solutions based on the Cox-Isham formalism. These developments all pertain to non-extending dead times and, in general, to coincidence systems only. But developments in electronics now make possible the design of more sophisticated systems which have certain advantages, especially in lower uncertainties The in the corrections at high count rates, and other corrections may become necessary. use of extending dead times has also become common after its revival by Miiller (1973). The main features of some modern systems are: common dead times in all channels (J.E. De Carlos and C.E. Grenades, HN, 1973, p. 209; Bouchard and Vatin, 1977); live timing (Baerg er al., 1976; Chauvenet et al., 1987; Miyahara et al., 1987); use of very short pulses (Bouchard and Vatin, 1977; Gehrke and Johnson, 1982); use of extending dead times (Baerg et al., 1976; Bouchard and Vatin, 1977; Santry et al., 1987); variable (preset) dead and resolving times (Gostely and Noverraz, 1975); extrapolation techniques (75.5.2.3); anti-coincidence counting (75.5.3); and selective sampling (75.5.3.2). In addition to the above sources of error there is a further possible source that was pointed out by Gandy (1961), due to differences in the arrival times of channel "1" and Channel "2" pulses at the open gate of the coincidence mixer and to fluctuations in that difference. This effect, known as "jitter" may arise from electronic instability, from differences in the pulse-rise times, or from different electron-collection times in the two detectors, one of which might, for example, be a solid-state detector and the other a gas proportional counter the collection time in the latter detector critically depending, because of the lower ion mobilities, on the location of the initial ionization in the gas. The Gandy effect may, however, be reduced by adjusting the delay shown in Fig. S-18 so that there is a zero mean delay between the two channels (Williams and Campion, 1965; Special electronic circuits have also been Munzenmayer and Baerg,1969; Funck, 1980).
Radioactivity
measurements:
principles
designed to balance the delays automatically (Scheller can also be made for time jitter (Funck, 1981).
and practice
and
Seyfried,
1985).
077
A correction
In applications of the coincidence-counting method to the assay of p-y emitters using detectors that subtend relatively small solid angles to the source, it is necessary to correct for any angular correlation between the radiations emitted. But such a correction, SS well as other decay-scheme-dependent corrections, becomes unnecessary when either detector subtends an angle of 4s steradians to the source. This and its high efficiency, make the 4ap detector the instrument of choice in the standardization by coincidence counting of 8-7 emitters. Further refined corrections to provide greater accuracy for dead-time resolving-time effects in the coincidence channel, at high count rates or for long times, are briefly discussed and referenced in NCRP (1985). 5.5.2.3.
Coincidence
countine
with
efficiencv
and dead
extrauolation
The basic principle of the method of coincidence counting is that channels "1" and "2" shall respectively record radiations "1" and "2" only, and the coincidence scaler shall record the coincidences in time between the two radiations. But this is only feasible in the case of radionuclides that decay in a simple manner, as in the case of "Co where the simple Eqs. 5-34 apply. The decay of % is more complex, but the recording of the two separate radiations can be kept to the two separate channels by an appropriate choice and use of the two detectors. But the decay schemes of most beta-particle emitters are far more complex and frequently involve the prompt emission, from the daughter atom, of gamma rays, conversion electrons, x rays and Auger electrons. All of these can be detected by the beta detector, and, all but the gamma rays, can be detected with high efficiency if that detector is, as is no" often the case, a 47rp pressurized gas-proportional counter. This situation can, however, be turned to advantage by the method of efficiency extrapolation. If a is the internal conversion coefficient, and if cc0 and ep7 are the efficiencies for the detection in the 4sj3 counter of, respectively, conversion electrons and gamma rays, then Eqs. 5-34 can be rewritten as =EcB + C87 No
=
N,
=
l+a
NC = "here Lo is the probability ray being Compton-scattered
No Lea + (1 - sp)(
N, e,/(l N, [~p’,/(l
+ a)
)I
I
,
+ a) + (1 - rp)c,l
,
(5-35)
of observing spurious coincidences due, for example, to a gamma from one detector to the other, and being detected in both.
By inspection of Eqs. 5-35 it is seen that, for a S?rflcounter of high efficiency, the term (1 - ea) is small and tends to zero as eB tends to unity so that NJN, is still a very good approximation to co, and N, tends to Nfl,/N,. In practice the approximate values obtained for Na at values of co between, say, 0.7 and 0.95 are plotted against NJN, and then extrapolated to N,/N, equal to 1.00, or, alternatively, against to zero, to give, in both cases, the activity, N,, of the (1 - NC/N,), with extrapolation source. Initially the method of efficiency extrapolation utilized efficient 4r@ gas-flow proportional counters, operated at atmospheric pressure, and the beta-particle detection efficiency was changed by either dissolving the active source on its foil mount, adding carrier solution and redrying, or by adding very thin metal, or metallized, foils above and below the source. But more recently high-pressure 4np counters, operating at pressures up to 70 atmospheres (7 MPa), have been designed to enable the method of efficiency extrapolation to be effected simply by changing the discrimination level in the beta channel (Baerg et al. 1967; Baerg, p. 95, HN., 1973). As stated by these authors, the use of high-pressure counters is to prevent discrimination against higher-energy beta particles that may deposit only a small part of their energy in the detector's sensitive volume when operated at atmospheric pressure. In other words the efficiency extrapolation, of count rate against co or against (1 - ta) for low-energy events, must be monotonic. In practice this extrapolation can be made with a linear fit, or by means of a low-order polynomial. If several gamma rays of different energies, representative of beta branching in the parent nucleus, are emitted by the daughter nucleus, the efficiency extrapolation "as often carried out by selecting one suitable gamma ray and "gating" on to it. But the reliability of extrapolation procedures may be improved, where several beta branches are associated with promptly emitted gamma rays, by recording the count rates of two or more gamma rays at the same time ( Baerg, 1981; Smith, 1987). Appropriate equations have been developed to express N, as a linear function of the t"o or more NC/N7 ratios. These equations with decdils and references are given in NCRP (1985, 73.2.8.3).
a78
Radioactivity measurements: principles and practice
A further improvement of the coincidence method may be obtained by the so-called computer discrimination developed by Smith (1975). In this technique p-ray count rates in coincidence with -/-ray pulses, are measured over a continuous range of @ efficiencies using Smith (1987) has extended this method to include appropriate electronic equipment. simultaneous discrimination in both the B and 7 channels and has derived explicit solutions based on the Cox-Isham formalism. 5.5.2.4. Efficiencv tracing Coincidence counting has also been applied to the assay of pure beta emitters by compounding them with a beta-gamma emitter that has a simple decay scheme and a not-too-dissimilar beta-ray spectrum (Campion et al., 1960). Baerg et a1.(1964) made similar measurements by quantitatively mixing previously calibrated solutions of the pure beta emitter with the 8-7 tracer, instead of compounding the two radionuclides in the same molecule. Efficiency extrapolation to lOO-percent efficiency gives the total count rate of the mixture from which that of the tracer can be subtracted to give the activity concentration The report of a recent international comparison of of the traced radionuclide. 13'Cs-activity measurements using 134Cs as the tracer (Rytz, 1985) gives a full account of the formulae used. Electron-capture nuclides with moderate decay energies (e.g. 54Mn) have also been calibrated in this manner, the Auger-electron-x-ray shower, that is readily detected in the Further details and many references 4~8 counter, being treated as a single beta branch. can again be found in NCRP (1985). 5.5.3. Anticoincidence
counting
The method of anticoincidence counting, a complementary variant of coincidence But it has the vary great advantage of counting, was proposed by Bryant (1962). eliminating the need to correct for the Gandy effect, for accidental (random) coincidences, and for By, the spurious coincidences due to Compton scattering (see Eqs. 5-35). The only remaining corrections needed are those for dead-time losses and backgrounds. But one serious problem with the method is that the dead-time correction for the anticoincidence channel is difficult to derive. Bryant (1962) has, however, derived an approximate expression for the correction, which is also discussed in NCRP (1985). To understand the method it is convenient to consider again the case of simple 8-7 The principle of the method resides in also recording, in addition to coincident decay. gamma rays, gamma rays that are not associated with a recorded event in the beta-detector channel. This is accomplished by disabling the gamma channel for a sufficiently long time T before and after the beta particle has been detected. This is achieved by using the detected beta event to close a gate in the gamma channel for an extra time 2T and delaying all gamma signals by the time T. Thus only those gamma signals that precede or follow a recorded ,9 particle by more than T are accepted as anticoincident events. The value of T is chosen to exclude essentially all coincident gamma events, including those delayed by the Gandy effect. The total gamma-ray count rate is also recorded, and the difference between this total and the number per second of non-coincident gamma rays gives the rate of coincidences. The activity of the source can then be computed using the coincidence equation N, = N$,/N,. Another advantage, pointed out by Bryant (1962), is that the anticoincidence method, unlike its coincidence forebear, can be readily extended to measure the activities of radionuclides that decay to an isomeric state emitting delayed radiations, provided that the half life of the isomer is not too long. This can be achieved by increasing the extra time that the gamma-channel gate remains closed from 2T to 2T + r The time T + r is set equal to m half lives of the isomeric state, m being chosen so that the probability of recording an unwanted "coincidence", equal to 2-m, is as small as desired. Bryant describes the application of this method to measuring the activity of a s5Sr source using a 4x8 counter to detect the primary K x rays and Auger electrons from the 85Sr source, and a NaI(T1) crystal to detect the 0.514-MeV delayed gamma rays, with a half life of 0.9 ps, from "Rb. As Bryant (1962) further pointed out, the coincidence and anticoincidence measurements can also be carried out simultaneously and used to cross-check each other. The difficulty in deriving the dead-time correction in the gamma channel arises from the fact that there is already an inherent dead time, T,, that is generated following every anticoincident pulse, to which class of pulses the extra dead time 2T is not attached. The dead-time correction for the gamma channel must therefore incorporate both 2T, or 2T + r , and T,, that is generated. It is interesting to note that if Y is the anticoincidence corresponding to Eqs. 5-35 for the coincidence method is
count rate, the equation
Radioactivity measurements: principles and practice
Y =
=
N,
-
879
N,
N, (1 -
CT ca)
(5-36)
-
l+a' Two variants of the anticoincidence method have recently been great value, as they eliminate essentially all corrections due to They are the the live-timed anticoincidence-counting method of Baerg selective sampling method of Miiller (1981) that are described in the
developed that are of instrumental effects. et al. (1976) and the next sections.
But first it may be helpful to remember three principles of anticoincidence counting: (i) the final answer, namely the disintegration rate of the source is given by the are recorded in all channels by virtue coincidence equation N, = NC/N@'., (ii) count m of the set counting time or live-timer, even though it becomes habitual to refer to recording counts in each channel -- the insertion of artificial dead times in channels does not change the count rate exceDt that at very high counting rates a loss of a preponderance of very short-time sequential events may be lost thus disturbing the Poisson timedistribution; and (iii) the use of an extending dead time, of T + T /JS, in the beta or gamma channels means that m other pulse, either beta or gamma, can be recorded in the dead-time interval immediately preceeding that pulse. 5.5.3.1. Live-timed anticoincidence
counting
This method, that was proposed by Baerg et al. (1976), using extending dead times, eliminates essentially all remaining corrections for instrumental effects. (Also see, for Defining the anticoincidence count rate as Y, Baerg et al. example, Santry et a1.,1987a.) summarize the coincidence and anticoincidence equations, in forms suitable for efficiency extrapolation as follows: (a)
N, = F(N,/N,), tends to N, as
NC/N, + 1 ,
(b)
= N, + f(1 - NC/N,), tends to N,,as
(cl
= N, + f(Y/N,), tends to N, as Y + 0
(d)
= N, + g(Y), tends to
N, as
NC/N, + 1 ,
,
and
Y + 0
(5-37)
It enables the The circuit used by Baerg et al. (1976) is shown in Fig. 5-19. application of an extending dead time of the same duration T to both the beta and gamma By delaying the gamma pulse it is channels if an event is detected in either of them. assured that only beta and gamma events can be recorded that are totallv unassociated with any signal passing through the other channel. Referring to Fig. 5-19, any gamma-ray pulse will be delayed, by an amount of about 1 ps by the delay network, D,, to eliminate any Gandy-effect jitter. The beta- and gamma-channel signals are then routed through gates G, and G, to both their respective scalers and also to the delay network D, where they are The purpose of this delay is to enable first combined and then delayed by about 10 ns. either a beta or gamma pulse to be recorded before gates G, or G, are closed by activation of the extending dead-time circuit by the beta or gamma pulse.
Fig. 5-19 Baerg
Block diagram of a live-timed anticoincidence ci -uit (after 1976).
et al.,
This extending dead time must have a duration longer than any ,9-y jitter, and is usually not less than 2 P.S. At the same time the generated dead-time logic signal is applied through gates G, and G, to shut off the live timer for whatever the duration the extending dead time may last. The pulses recorded in the gamma-channel scaler are
Radioactivity
880
measurements:
principles
and practice
Therefore the antiscaler. uncorrelated with any events recorded by the beta-channel counts in the gamma-ray scaler coincidence count rate, Y, is given by the accumulated This briefly divided by the accumulated live time, the value of which is usually preset. The other and essentially describes the method of live-timed anticoincidence counting. gates shown in Fig. 5-19 are for second-order refinements that are described in Baerg et Much supplementary should be consulted for further details. al. (1976), which paper information may also be garnered from the sections in NCRP (1985, n3.2) that were written Baerg et al. also note that they extended to anticoincidence counting the by Dr Baerg. concept introduced by De Carlos and Granados (HN, 1973 p. 209) of pooling the beta- and These authors had also gamma-channel signals to generate a common, shared, dead time. pointed out its possible applicability to live timing in coincidence counting. of the activity of As a test of the method, Baerg et al (1976) compared measurements and anticoincidence counting. They three 60Co sources by both the methods of coincidence of beta detection by used the method of efficiency extrapolation varying the efficiency electronic discrimination, Their results are shown in Table 5-2, the uncertainties shown The results obtained by the two being standard deviations of type A (73.4.1.2) only. As the functions f and g go to methods also lie within a range of about 2 0.03 percent. zero when Y goes to zero, there is no need to know the count rate recorded by the gammaIt is, in general, only used to monitor the stability of that channel monitor (Fig. 5-19). channel. Table
5-2
and relative anticoincidence-counting results for different values of the extending dead time for 60~0 sources
Coincidence-
of different
activity
Extending dead time (w)
16,925 16,925 3,631 36,335 3,631 36,335 16,925 3,361 3,361
* Uncertainties Selective
et al.,
Coincidencecounting result (s-l)
3.5 5.4 5.4 13.4 13.4 53 53 134 265
5.5.3.2.
(from Baerg
in units
sampling
(5) (5) (1) (13) (1) (13) (5) (1) (1)
1976).
Relative anticoincidence-counting result
::
of the last digit(s)
0.99981 0.99977 0.99984 0.99967 1.00012 1.00015 0.99974 1.00030 0.99970
are shown
(46) (34) (39) (50) (42) (42) (32) (28) (24)
*
in parentheses
(SESAM)
This ingenious method, proposed by Miiller (1981) also selects non-beta-correlated signals in the gamma channel using the fact that, in a channel (here the p channel) with an extending dead time, T, no pulses can appear in a time interval T preceding the observed pulses (because, otherwise, the latter would have been lost) and therefore in this time interval pulses in the other, y, channel do not have a coincident partner ("anticoincident pulses"). The efficiency of @-ray detecti on can then be calculated from the ratio of the rates of coincident to anticoincident Y pLll*a*. The former arrive in time intervals of length T preceding 7 pulses, the latter in time intervals of more than T. This ratio will be essentially immune from the effect of radioactive decay, but the recorded beta count rate must be normalized for short half lives and both the beta and the gamma count rates must be corrected for background and dead-time losses. For high beta count rates the dead-time correction in that channel becomes more complicated, as does also the accumulation of the gamma-channel counting data. A simplified block circuit diagram is shown in Fig. 5-20. The extending (cumulative) dead time can, as suggested by Mtiller, be set at 25 @s and the gamma-channel delay at 60 On the detection of a beta particle the resulting pulse in the beta channel is used to ps. start a multichannel analyzer operating in the time mode to record the arrival times of pulses in the gamma channel with the introduced delay. For the first 35 p* it will record in its appropriate time-bins the times of arrival of all detected gamma rays, while in the second time interval of 25 ps it will record only those gamma-ray pulses that are uncorrelated with any beta-particle pulse. At the conclusion of the 25-p* extending dead time, the logic level of the dead-time gate will return to the "off" position, and the multichannel analyzer will turn off until the arrival of the next detected beta-particle pulse starts a new cycle of gamma-channel arrival-time storage. Thus the time-bins will continue filling up until an "arrival-time density spectrum" like that shown in Fig. 5-21 will be accumulated. The peak on the right represents the initiating beta pulse of coincident events, while the gamma-ray arrival times start 60 ps to the left because of the delay in the gamma-ray channel. After a sufficiently long counting time the registered counts in the two regions will fill up the respective time bins to average numbers of
881
Radioactivity measurements: principles and practice
Normalizing for the different receiving times in the G and g, in the two zones. two zones, in our example 35 and 25 ps, the count rates G and g are obtained. These, ignoring dead-time and background corrections, give
counts,
,
R, = g/G whence and
1 - R, = NC/N7
, (5-38)
N, = No/(1 - R,).
Schematic of the experimental arrangement used for the Fig. 5-20 selective-sampling method (after Mtiller, 1981). I number of registered gamma rays per channel
t
G
____
1
+T-(
I I .I I : ..........._. t ._^_...C._ ’ g
t
time (channel)
arrival of registered beta pulses
Selective sampling: measured frequency distribution of Y Fig. 5-21 pulses preceeding a registered ,9 pulse from a 60~0 source. The y pulses are recorded by repeated sampling, and their accumulation can be followed on the MCA screen. The time scale corresponds to 0.75 ps per channel (after Mfiller, 1981). Miiller (1981) remarks that most present-day multichannel analyzers are too slow, with channel-to-channel dead times of the order of 10 ps, to handle the count rate of a reasonably active source. He therefore used an electronic device called a "speed converter," with a resolution of some 50 ns per channel, that first stored the original sequence of arrival times and then transferred them to the multichannel analyzer at a lower speed (see BrBonce, 1976). This enables the transfer and storage of data in a time that is between 10 and 20 times slower than that required to record the pulses. For further information regarding the details and refinements of the method the Miiller's original paper (1981) should be consulted, together with a simplified version involving only time delays and gates (Miiller, 1985).
6.
ELECTRONIC INSTRUMENTS FOR RADIOACTIVITY MEASUREMENTS
6.1. INTRODUCTION In Chapter 4 various kinds of interaction between radiation and matter, as gas, liquid From such interactions there derive different methods of or solid, have been described. These detecting radiation, the principles underlying which have also been explained. interactions include gas ionization that finds application in the form of gas-ionization chambers, electrometers and electroscopes, and gas counters. Gas ionization also forms the basis for spark chambers and cloud chambers, that detect the tracks of ionizing particles, but which find their primary use in high-energy and particle physics rather than in the quantification of radioactivity. The rare, or noble, gases also act as scintillators when exposed to ionizing radiation, but detectors based on this principle are The interaction of radiation with liquids not common (see Knoll, 1979, for references). gives rise to the emission of photons that can be detected by the photocathodes of electron-multiplier phototubes, so that every radiation event in the liquid (above a certain threshold energy) can be detected individually by discrete pulses of electrons emitted by the last dynode of the phototube. ?erenkov radiation that arises from particles traversing a fluid with a velocity greater than that of light, can also be used for the detection of high-energy radiation, but is only rarely used to quantify it. Condensed rare gases can also be utilized as ionization chambers, but their use is still in the developmental stage. The potential use of liquefied xenon has, however, aroused considerable interest because of its high atomic number and of the fact that it should provide resolutions for gamma rays intermediate between those given by sodium iodide and germanium. (See Knoll, 1979, for some pertinent data and references.) In the case of solids, radiation interacts to produce ionization (electron-hole pairs), light and heat. Of these the first two properties are widely used for the detection and quantification of radiation (and, hence, radioactivity), but the last, as the basis of calorimetry finds use mainly in the assay of energetic alpha-particle or beta-particle emitters (e.g. 3zP, 63Ni, 226Ra+, and "special" nuclear materials). As will have been gathered from Chapter 4, the output of every detector in general used today is some kind of electrical signal. The simple electroscope, say quartz-fibre or gold-leaf, shows an electrostatic repulsion that decreases as the system is discharged by the radiation ionizing the surrounding gas. The ionization chamber gives rise to a steady current in the direct current mode, or a pulse of charge when it is operated in the pulse mode either as an ionization chamber or as a proportional or Geiger-Miiller counter. A scintillator emits prompt pulses of light, that are converted to pulses of electrical charge by means of a phototube. The phototube oc.tput may also in some cases be read as a direct current (see, e.g., 15.4.3.4.3). Semicondxtors when used as solid-state ionization detectors emit short pulses of negative and positive charge carriers (electrons and holes).
Typically the detection and quantification of radioactivity is accomplished by observing direct-current outputs, or counting pulse-output rates, of ionization devices. In either case the amounts of electricity to be measured are extremely small and are of the order of lo-' to lo-l5 A in the case of direct-current instruments and lo-" to lo-l5 C per detected event in the case of pulse detectors. The former used to be measured by means of electroscopes, string, quadrant, Lindemann-Ryersan, or vibrating-reed and Keithley electrometers, and the latter are usually measured by electrical-pulse techniques using integrated solid-state circuitry in the form of preamplifiers, amplifiers, multichannel analyzers, computers. and so forth. The many techniques used to acquire data about the properties of radiation emitted in the processes of nuclear and atomic decay, by recording the responses of various radiation detectors comprise the rapidly growing technology of nuclear electronic instrumentation - sometimes referred to as nucleonic instrumentation. The most widely used radiation detectors are the ionization chambers (and its radiopharmaceutically-oriented modification, the "dose" calibrator or radionuclide calibrator), the proportional counter, the sodium-iodide, thallium-activated, crystal, and the solidstate detectors. In North America the production of the high-purity germanium detector, HPGe, has almost entirely replaced that of the lithium-drifted germanium detector, Ge(Li), because the latter must be kept at cryogenic temperatures to inhibit the reversal of the drifting process, whereas the former can be maintained at ambient temperatures, and because the techniques of producing high-purity germanium crystals are now well established. We form of measure rators. ing and
thus see that not only do the most frequently used detectors give outputs in the short-duration low-amplitude pulses, but that pulse techniques can be used to the direct-current outputs of ionization chambers and radionuclide ("dose") calibIt is therefore important to gain some insight into the techniques of manipulatrecording small short pulses of electric charge.
Finally, it cannot be too strongly emphasized that, while this chapter attempts to outline the fundamental functions of electronic components. one no longer attempts to build
883
Radioactivity measurements: principles and practice
084
those components in the laboratory but, as often stated in earlier chapters, one now buys the component or function needed, or, at most, assembles it from integrated-circuit subcomponents. Thus any person who has been given the responsibility of selecting nucleonic equipment and, especially, solid-state detectors for a new regional radionuclide metrological laboratory would be well advised to consult the many excellent catalogues and brochures published by nuclear-instrument industry. Only in this way can one be sure of obtaining the most up-to-date equipment available in a rapidly developing art. 6.2.
PULSES
The average energy that must be expended in order to form one electron-ion pair in most gases is of the order of 30eV (ICRU, 1979a). Thus a 300-keV electron or a 3-MeV alpha-particle expending all their energy within an ionization chamber or a gas proportional counter will produce respectively lo4 or lo5 primary ion pairs. In the case of the proportional or Geiger-Miiller counter the number of ion pairs produced in this primary ionizing event will be further increased by the process of gas multiplication. An analogous process occurs in semiconductors, for which, however, the average energy expended to create an electron-hole pair is about 3 or 4 eV. Under the influence of an externally applied electric field to any "ionization" detector (gaseous or solid-state) the positive ions (gaseous) or holes (solid-state) move to the Electron and positive-ion drift velocities in most cathode and electrons to the anode. gases at typical pressures and applied voltages are respectively of the order of lo6 to 10' cm s-i (Bortner and Hurst, 1954) and lo2 to lo3 cm 5-l (Wilkinson, 1950). The respective collection times for electrons and positive ions are of the order of microseconds and milliseconds. In semiconducting crystals the electron and hole mobilities are not so disparate, and some can be found in which these mobilities are of the same order of magnitude. Thus Kittel (1971) quotes values for InAs of 77~10~ cm2V1.Y1 (electrons) and 1.25~10~ c&.~'s~~ (holes) at room temperature. Knoll (1979) also quotes mobilities for germanium at 300 K of 3.9X103 c&J-~s‘~ (electrons) and 1.9x103 cm'V_1s-r (holes); and at 77 K for germanium, 3.6~10~ cmzV-ls‘l (electrons) and 4.2~10 c&~~s~' (holes). (Also see Bertolini and Cache, 1968.) By way of example, for an applied electric field of 500 V cm-': A mobility of 77~10~ CII&.~~~~~would result in electron velocities of 38.5x106 cm s-1; and a mobility of 1.25~10~ ~rn*V~~s~' gives a hole velocity of 62.5~10~ cm 5-l. Corresponding collection times across a l-cm-thick semiconducting crystal would be 26.0 ns (electrons) and 1.6 /JS (holes). From these examples it can be seen that the output pulses from semiconducting crystals can be of very short duration. Considering both gas proportional counters and semiconducting detectors, it is clear that the electronic circuitry required to process and record numbers of detected events as a function of time must be able to handle output pulses that range from milliseconds to nanoseconds in duration. Ranges for current duration times in different types of detectors are: l
1 ns to 10 ns for scintillators semiconductors;
(liquid and plastic) and narrow depletion-depth
. 5 ns to 1.5 ps for pure or activated NaI and CsI scintillation detectors; . 0.01 ps to 5 ps for gas-filled detectors; Fairstein and Hahn (1965) emphasize that the instantaneous current in a detector is not proportional to the energy deposited in the detector; only the total charge or integral of the current with time are proportional. The pulse of charge generated in a proportional counter differs from the pulses generated in an ionization chamber or semiconducting crystal in that the anode of the counter is normally a fine wire that is used to produce in the adjacent gas a multiplication region of high electrical field, whereas ionization chambers and semiconductor detectors usually have parallel-plane or larger-diameter cylindrical electrodes. Taking into account the difference in the electronic and ionic mobilities in gases, the output pulses from a proportional counter or ionization chamber are somewhat more complex than those from semiconductor detectors. It is instructive to consider the sequence of events occurring in a proportional counter following the creation of a burst of ionization due to a primary ionizing event. purpose we will consider such a detector to which a suitable source of high For this voltage has been applied across the gas between the anode wire, or rod, and a cylindrical cathode. The electric field strength E, at a cylindrical surface in the gas, at a distance r from the axis of the counter, is given by V E=z
(6-l) L- In b/a
Radioactivity
measurements:
principles
and practice
885
where V is the applied voltage and b and a are respectively the cathode radius of the anode rod or wire. The value of E, therefore increases very value of r approaches that of a. As
soon
as
the
primary
ionizing
event
occurs
in
the
counter,
the
radius and the rapidly as the
electrons
formed
begin moving inward towards the anode and the positive ions outward to the cathode walls. Consequently an induced negative-voltage pulse begins to be generated in the anode by the The combined movements of the electrons towards it and of the positive ions away from it. electrons moving at velocities of the order of lo6 cm 5-l quickly reach the region of multiplication thus creating more ion pairs whose motions towards the anode and away from If there is a large residual resistance, R, it contribute further to the induced voltage. C, between the anode and cathode of the counter, then the negative pulse and capacitance, the product generated will be like that depicted in Fig. 4-4, for the case of RC large this figure The time scale of of R and C being the time constant of the simple circuit. both the movements of electrons that are is greatly distorted in that it illustrates accomplished in microseconds or less and the motions of positive ions that may take as long as several milliseconds to reach the cathode. the time taken for the primary The first interval of time, tI, shown represents electrons to reach the multiplication region which will be of 1 JLS duration, or less, if The next period of time, fZ the primary event occurs within 1 cm of the anode rod or wire. electrons generated in the multiplication region the time taken for the - Cl, represents The remaining growth of to reach the anode. This may be of the order of one nanosecond. the amplitude of the negative pulse is due to the much slower movement of the positive ions With mobilities of at least lo3 times less than those away from the multiplication region. of electrons this part of the pulse will take of the order of milliseconds to reach a in the unreal case of RC being infinite, the voltage on the anode, maximum. Thereafter, having reached a maximum asymptotically, would remain at that value. In real life, however, RC is not infinite and the pulse, having reached a maximum, will therefore slowly decay. In fact, in practice, the decay is hastened by incorporating C, into the circuit in the manner shown in Fig. 4-3. resistance, R, and capacitance, BY a careful choice of R and C, a pulse of adequate amplitude and of suitably short duration of This procedure for shortening the duration several microseconds can thereby be achieved. of the pulse is called "clipping". In the absence of clipping and at count rates in excess of a few hundred per second "pile-up" of the pulses from the detector will occur, giving rise to distorted pulses of increased amplitude, in the manner illustrated in Fig. 6-l. At higher rates of pile-up these increased amplitudes may exceed the dynamic ranges of subSuch clipping by means of an RC-decay circuit sequent amplifier stages and paralyze them. is known as RC differentiation, The rise time of such a pulse is defined as the time and the decay time is that required to go from 10 to 90 percent of the peak amplitude, required for the pulse to decay to l/e or 37 percent of the peak amplitude. The detectors described in Chapter 4 give output signals of from 10ml' to less than 10ml' coulomb per event. These pulses of charge give rise to small voltage pulses across The charge collected by the detector is the resistance R and capacitance C in Fig, 4-3. The amplitudes of the proportional to the radiation energy deposited in the detector. collected and the output voltage pulses are also approximately proportional to the charge radiation energy deposited. The purpose of all subsequent circuitry used to shape and amplify these pulses is to preserve such proportionality while giving them the power and characteristics compatible with the requirements of the analyzing systems, such as discriminators, counters, multichannel pulse-height analyzers, or computer-based programmable on-line analyzing systems.
@JLJLiS-
Pulse &apes from a typical radiation detector: a) at the Fig. 6-l 2mrJlifier input; b) after differentiation with a short time constant Note that the undershoot normally associated with the differRC. entiated pulses has been removed (after Mann ef al., 1980). 6.3. DIFFERENTIATING AND INTEGRATING NETWORKS The rise time of the negative pulse, in most detectors, ranges from 1 ns to the order of 5 /As, the latter being a rather large upper limit for most present-day detectors, The decay time of the pulse can range from nanoseconds, depending on the type of detector, to
a86 infinity
Radioactivity
depending
on the value
measurements:
of the decay
principles
constant,
RC,
and practice
of the external
circuit.
In Fig. 6-l the peaks of the pulses are depicted as a spike, or discontinuity. But it must be remembered that the time scale for the rise is of the order of nanoseconds whereas the decay takes of the order of a thousand times longer, i.e. microseconds or possibly, even, milliseconds. But whichever, the shape of the peak is still similar to those depicted in Figs. 4-4 and 6-1, and the differential quotient, dV/dt is a continuous function. Figure 6-2a represents a simple single RC-differentiation circuit in which the shape of the input voltage pulse, Vi, is again represented as a discontinuous function. The output voltage V, decays exponentially with the time constant R&, = 7, and falls to l/e (0.37) of its maximum value in time T. (The capacitance C, includes any residual capacitance, and may only comprise residual or parasitic capacitances.) This circuit is also used as a high-pass filter, derived from the fact that it attenuates low-frequency more than high-frequency signals (the impedance of a capacitance is inversely proportional to frequency). (For further details see Chiang, 1969.) Figure 6-2b shows a simple RC-integration circuit. The output of an uit is proportional to the integral of the input signal. The cirrcuit also time of the input pulse: The rise time of a pulse is defined as the time voltage to increase from 10% to 90% of Lts final value V,. This time is The integrating circuit is also used as a low-pass filter, because it frequency signals preferentially over low-frequency signals.
integrating circextends the rise required for the equal to 2.2 RC. attenuates high-
Fairstein and Hahn (1965-66) defined a differentiator as "a network in which the output signal approximates the mathematical derivative of the input signal," and an integrator as "a network in which the output signal approximates the mathematical integral of the input signal." The triangles shown in Figs. 6-2~ and 6-2d represent buffers (with unit gain) or amplifier-gain stages that provide electrical isolation between the different shaping circuits. The extra shaping circuit added to the output of the combined differentiationintegration network of Fig. 6-2~ to give the network shown in Fig. 6-2d simply serves to integrate the output pulse shown in Fig. 6-2~. The output pulse of the network shown in Fig. 6-?c is called a "unipolar pulse", and that from the network shown in Fig. 6-2d is called a "bipolar pulse". As there can be no net transfer of charge across the buffers, the areas of the positive and negative components of the bipolar output pulse be equal.
b) single RC shaping networks: a) single KC differentiation; Fig. 6-2 d) corn-KC integration; c) combined differentiation-integration; bined double differentiation-single integration. Vi = input Pulse, v,= output pulse, V,= maximum output pulse height (after Mann et al., 1980). Simple RC circuits do not give optimum pulse shapes either for reducing pile-up or for analyzing pulse amplitude. Modern circuits use complex, multipolar, active filters coupled with special d.c.-restoring circuits for improved performance. Thus while RC circuitry may be used in much of currently-operating nucleonic instrumentation, it is now being superceded by "Gaussian"or triangular-shaping circuitry or, in the case of scintillation detectors, by delay-line shaping. As noted in the preceding paragraph, the differentiation and integration of pulses can also be achieved by means of resistance-inductance (IX.) networks such as those shown in The time constant of the resistive-inductive circuit is equal to L/R, Figs. 6-3a and6-3b.
Radioactivity measurements: principles and practice
a87
where L is the inductance in henries and R is the resistance in ohms. As mentioned above in the case of RC circuits, the RL networks also do not give optimum pulse shapes for the reduction of pile-up or pulse-amplitude analysis.
Differentiation (a) or integration (b) of pulses by Fig. 6-3 resistance-inductance networks. Another network that is currently widely used to obtain a result similar to differentiation is that of the short-circuited delay line. A delay line in its most usual form consists of an inner conducting wire or rod running axially within an insulated outer concentric conductor. If the outer conductor is at ground potential and an electrical signal is impressed on the inner conductor of such a line that is of infinite length, the signal will travel along the inner conductor with a velocity that is inversely proportional to the square root of the dielectric constant of the material between the inner and outer conductors. If the dielectric is air, the propagation velocity of the signal will approximate that of the speed of light in a vacuum. The amplitude of the signal will, however, be attenuated because of energy losses, as it travels along the delay line. The ordinary coaxial cables that are used to connect various electronic components can also be used as delay lines. The higher dielectric constant of the insulation, used instead of air between the inner and outer conductors, gives rise to an increased delay, because of the lower velocity of propagation of the signal along the line. For an air-insulated delay line the signal is delayed by about 3.3 ns m-r. For most coaxial connecting cables the delay times will be approximately 5 ns m-l. (The characteristics of various coaxial cables and the velocities of signal propagation along them are given in Knoll, Table 16-l.) If a given length of a coaxial conductor is terminated by a short circuit at the end toward which the signal is travelling, the signal will be reflected with a 180" change in phase. It will then return to the input end of the line where the initial input signal and the delayed reflected signal, now of opposite polarity to give a shortene (clipped) pulse. The differentiating operation of a delay line is illustrated in Fig. 6-4 (a and b) for a step-function input pulse, in the ideal case where there is no attenuation in the delay line and the input resistance R, + R, is equal to the impedance Z,, of the delay line. In practice, there is attenuation and the amplitude of the reflected pulse would be less than that of the input signal. But modern good-quality d.c.-amplifiers are so designed that the base line remains at zero after the pulse has passed.
Delay-line differentiation: a) circuit with a single delay Fig. 6-4 line and a resistor, R b~~~~':~~~:e~~r~t:~~t~g~~~. equa1s the delay-line impedance; Double differentiation can also be carried out using two delay-line networks as illustrated in Fig. 6-5 with the resulting output pulse shown. For simplicity, the effect of RL decay has been omitted.
888
Radioactivity
Double
Fig. 6-5
works.
measurements:
differentiation
principles
and practice
by two ConseCUtiVe delay-line netRL decay on the Pulse shape
For simplicity the effect of
has been neglected. 6.4. AMPLIFIERS:
GENERAL
As has been indicated earlier, pulse-shaping circuits are essential for the purpose of reducing the tails of pulses generated in radiation detectors. Such radiation detectors may give pulses of charge with rise times of from nanoseconds to microseconds in duration, but with decay times of the order of milliseconds. Such slowly decaying tails limit the count rates that can be achieved to the order of one thousand per second if one wishes to preserve the proportionality between the measured amplitude of the pulse and the energy of the radiation detected. At higher count rates, unless the tails of pulses are clipped, the observed amplitudes will be larger because the recorded pulse is riding on the tail of a previous pulse. Such pile-up will cause distortion and, at higher count rates, may drive an amplifier into saturation. Pulse-integrating circuits also help to improve the signal-to-noise ratio in that, as "low-pass" networks, they also filter out higher frequencies. In order to operate scalers and other recording equipment it is often necessary to amplify, by many orders of magnitude, the voltage pulse derived from the small charge generzted in a detector. This is normally the function of a main amplifier with variable gain. But the main amplifier may be located some distance away from the detector, and the task of preserving the first feeble pulse from the detector is usually that of a small preamplifier that is located near to the detector, especially if it be a semiconductor. A preamplifier may be charge-sensitive, current-sensitive, or voltage-sensitive. The first of these three types is that which is appropriate to gaseous and semiconductor ionization-type detectors. If the charge generated in a detector were to be impressed upon a long cable having rather large capacitance, the voltage pulse that could be obtained from the initial charge would be insignificant. The charge-sensitive preamplifier should therefore be located as close as possible to the detector. Junction field-effect transistors (FET's) are used in the input stage of charge-sensitive pramplifiers, because they have have high input impedance and are significantly free from noise, especially when cooled to near liquid-nitrogen temperatures. Pulse-shaping is also necessary in order to optimize the signal-to-noise ratio and to provide the shape of pulse required by the pulse-height analyzer. Manufacturers will normally specify the input pulse-shape required by any given analyzer. The preamplifier should, in all cases, be placed as close to the detector as feasible. Preamplifiers should also be capable of driving the connecting cable to the main amplifier. This cable's impedance is commonly 50 ohms,and it must be terminated by its characteristic impedance at the input terminal of the main amplifier, either internally or externally, in order to eliminate reflections produced by mistermination. The charge generated in a gaseous or solid-state ionization detector is usually impressed across a resistance R and capacitance C, as shown in Fig. 4-3. The output-voltage-pulse amplitude is inversely proportional to the capacitance C, which, however, includes any stray, and possibly changing, capacitances associated with the detector. The stability of the output-voltage amplitude will therefore be very dependent on ambient factors such as temperature afid pressure. Such possible sources of instability have, however, been greatly reduced by using negative feedback preamplifiers, in which the value of the output-voltage amplitude depends principally on the value of a low-capacitance, stable feedback capacitor. The feedback-loop principle is also used in all types of operational amplifiers in order to improve their temperature stability, linearity, and rise-time characteristics. The output from the preamplifier is usually in the form of a tail pulse (Fig. 6-2a) that must therefore be reshaped at various stages in the main amplifier. 6.4.1.
Preamplifier
feedback
loop
The circuit of an a.c.-coupled charge-sensitive preamplifier is shown diagrammatically in Fig. 6-6. The feedback loop is shown through the capacitance C, and resistance R,. The test input is provided in order to introduce an external voltage tail pulse for testing the performance of the preamplifier or the entire electronic system, without the detector itself.
Radioactivity
measurements:
principles
889
and practice
Bias voltage
Q ’
CC(‘nF) -
-Low
noise
Driver
Voltage -
input stage
input
gain
low
c,
with
impedance output
high and
-
Impedance
4
93n
Series twminator resistance to match g3-ohm coaxial cable
(1pF)
II
CT{=1
pF)
R (son)
Block Fig. 6-6 preamplifier
diagram of a typical low-noise (after Ayers, 1973).
charge-.sensitive
--L ~x--t~R~~~-:;
Fig. 6-7 loop.
et al.,
&sic preamplifier-circuit diagram with negative-feedback A test pulse may be applied through R ,CT (after Mann 1980).
For the the basic
purpose of understanding the operation of the feedback circuit diagram, shown in Fig. 6-7, of the block diagram
loop, we will in Fig. 6-6.
consider In this
simplified basic diagram the three separate blocks are represented by a single triangle. Such symbols have already been used in Figs. 6-2 and 6-5 for an isolation stage or buffer. But they only represent the various functions performed by different electronic components be that normally commercially, and may selected from manufacturers' are available catalogues. to the preamplifier (triangle) are shown, the upper one In Fig. 6-7 two inputs The former noninverting (NI), and the lower one, which is here grounded, inverting (I). transmits the input signal through the preamplifier without inversion (without change in phase), and the latter input terminal gives an inverted output signal, as their names The "-A" in the b o d y of the triangle means that a negative input pulse exits as a imply. The capacitance C, and resistance R, positive output pulse with amplification equal to A. across the input and output of the preamplifier complete the negative feedback loop. A preamplifier with negative feedback operates in such a way as to reduce the input signal. In this mode of operation, which is also termed "closed loop", a fraction, f, of the negative output voltage is fed back and subtracted from the positive input signal (or positive output from negative input). The fraction f is determined by the feedback element. Suppose that the detector produces a total charge Qi, then this will give rise, in the open-loop mode, to an input voltage Vl to the preamplifier that is equal to QJC,, where C, is the "open-loop" capacitance, which is the sum of the detector capacitance and any stray capacitances, i.e. V, = -QJCF
(6-2)
preamplifier Therefore, with negative feedback, the voltage gain of a charge-sensitive becomes virtually independent of the gain of the preamplifier itself, and of the detector To a very good approximation the gain is dependcapacitance and stray input capacitances. ent only on the value of the feedback capacitance, C,, that can be exceedingly stable with respect to time and temperature. A resistance RF connected in parallel with the feedback capacitance discharges it and determines the discharge time constant, R,C,, of the preamplifier output pulse. reference may be made to Chiang (1969), Ayers (1973), For more detailed information, Knoll (1979), Fredericksen (1984) and, or, to the texts listed in 76-10. Very informative and up-to-date literature can also be obtained from the manufacturers of nucleonic equipment.
Radioactivity
890
6.4.2. Main
amolifier
and feedback
measurements:
principles
and practice
loon
partly-shaped detector function is to take the amplified, The linear amplifier's signals from the preamplifier and to amplify and shape them further until they are suitable As can be seen from Fig. 6-8, the for final pulse analysis or for count-rate measurements. linear amplifier consists of a number of amplifier stages, with feedback loops, coupled The shape of the final output pulse must be such as to together by shaping networks. optimize the signal-to-noise ratio and also to be compatible with the equipment used for Improvement of the signal-to-noise ratio is now achieved by the use the data processing. of complex bandpass filters to shape the pulse, and a "Gaussian" pulse shape is often By increasing the duration of the rise time of the pulse, and decreasing that of realized. A "Gaussianits time of fall narrower and more symmetrical pulses will be obtained. shaped" pulse is the limiting result obtained by an infinite number of integrating stages close to of differentiation although a pulse with a shape very following one stage stages of The approximately four integration. can be produced with "Gaussian" and the (CR) attenuates low-frequency components (e.g. hum) differentiating stage integrating stage (RC), which is, however, rarely used, attenuates those of high frequency The optimum noise reduction is generally obtained when the RC time constants (see 76.3). of the differentiating circuits are equal, but there is always a conflict between circuit noise, detector noise and pulse pile-up. One has to choose the optimum pulse shape for It should be realized, however, that minimum noise while retaining spectral information. superior, and complex, filters are used in modern amplifiers. 21 Fl.9,
SW0"d
0 "nlpolar out
Simplified diagram of a typical linear nuclear pulse amplifier with RC integration and both single and double differentiation of the output signal (after Mann et al., 1980).
Fig. 6-8
A primary requirement for a linear amplifier in a radiation-measuring system is possibly be affected by instability in the voltage stability. Its gain could, however, But, as in the case of the supplies, by aging of components and by temperature changes. charge-sensitive preamplifier the effects of such instabilities can be minimized by the application of the principle of negative feedback. As indicated in each of the amplifier stages A,, A, and A,, shown in Fig. 6-8, this is provided by the feedback resistors RF1, Considering one such stage, if, in the absence of feedback, the amplifier has R,, and R,, a gain equal to A, then the amplitude of the output signal V, for an input signal of If a fraction, f, of the output amplitude amplitude V, would be AV,. is applied to the inverting input terminal of the amplifier stage it will be subtracted from Vi, so that V, = A(V, - fVO)
V, = AV,/(l + fA)
or
Thus
,
the closed-loop
gain
V,/V,= compared
with
(6-3)
is
the open-loop
A/(1 + fA)
,
(b-4)
gain A
Af >> 1, so that the 1n general, however, such an amplifier will be designed with But the value of f is set closed-loop gain will be, with good approximation, equal to l/f. by the value of the feedback resistance, R, which can be made to remain constant with time and to be highly insensitive to temperature change, with the result that the closed-loop gain will be equally stable. There are many other circuit functions of the linear amplifier, not shown in Fig. 6-3, that provide for its overall adjustment. These may include, for example, variable-gain pulse-shaping time constants (often by switch settings), baseline restoration controls,
(q.v.),
etc.
An amplifier should have good overload characteristics in order to handle input pulses counter is used to of greatly different amplitudes, as, for example, when a proportional register a spectrum of beta particles. A linear amplifier with a gain of, say, lo3 that produces a maximum output pulse of 10 V will overload for input pulses greater than 10 mV For input signals having amplitudes much greater than 10 mV the from the preamplifier.
Radioactivity measurements: principles and practice
891
tens of microseconds, main amplifier can be driven into saturation and be paralyzed for thereby introducing "dead times" during which it is unable to process further input A wide selection of amplifiers with so-called good overload characteristics is, signals. however, available commercially. Other problems arise in handling the unipolar tail output pulses from preamplifiers. discussed in connection with the need for pulse shaping. This problem has been briefly Fig. 6-8 illustrates the kind of relationship between the signal that is generated across the output terminals of a gas-ionization detector and the output-voltage tail pulse from In this figure the tail-pulse duration is of the order of one-third of a the preamplifier. millisecond. If the pulses were arriving at constant frequency, the preamplifier could not handLe more than the order of 3,000 to 4,000 a second without overlap and consequent distortion; but it could also not handle more than about 1,000 5-l randomly distributed If, in pulses, such as those arising from radioactive decay, without risk of distortion. addition, these events arose from monoenergetic gamma rays interacting with, for example, a solid-state detector, then such distortion would give rise to a broadening of the finally observed gamma-ray peak by the addition of pulses to its high-energy side. Another source of distortion of unipolar pulses passing through a chain of shaping and feedback stages is caused by their depositing short-lived charges of the same sign on the These charges will be dissipated in various coupling and bypass capacitors in the chain. times governed by the various RC time constants of the capacitors in the chain. But these accumulated charges will cause distortion in an amplifier system at high count rates, One way to avoid such charge deposition unless some form of compensation is employed. leave no net charge, the positive and negative would be to use bipolar pulses which would lobes being of equal area. a differentiating Any coupling capacitor with resistance to ground will act as network and convert a unipolar pulse to a bipolar pulse with an undershoot of long Unipolar peaks with long overshoots can be converted by RC differentiation to duration. bipolar peaks, the second lobe of which is an undershoot of equal area to the first. And long undershoots can be removed or turned into undershoots of very short duration by the of pole-zero cancellation and baseline restoration, that are methods, respectively, described in the next section. Where an overshoot or an undershoot of, say, 300 ps would limit pulse-processing rates to the order of 1,000 s-l, an undershoot of the order of 10 ps would permit pulse-processing rates, without serious distortion, of the order of 30,000 s-1. 4.4.3. Pole-zero cancellation and baseline restoration The output pulse from a preamplifier is a tail pulse similar to that shown in Fig. Normally this tail pulse will traverse a coaxial cable to be processed by the input coupling differentiator of the first stage of a linear amplifier (Fig.6-8), from which it will emerge as a bipolar pulse similar to that shown in Fig. 6-9b. The undershoot of this This is achieved by pulse can then be removed by the process of pole-zero cancellation. adding a portion of the original tail pulse to the undershoot by means of a variable The resistor placed across the capacitor C,, (Fig. 6-8), as illustrated in Fig. 6-9c. variable resistor is adjusted, while observing the output pulses from stage A, (Fig. 6-8) on an oscilloscope, until suitable unipolar pulses of short duration (Fig. 6-9d) are obtained. 6-9a.
Time
Pole zero compensation of differential pulse undershoot; Fig. 6-9 a) original tail pulse; b) after passing through a coupling network of short time constant (differentiator); c) dashed line is portion of signal to be added back in; d) resultant pole zero compensated pulse (after Hatch, 1973). Baseline restoration, in its simplest form, is achieved by means of the biased-diodeInitially the diode in this cicuit is biased to be restorer circuit shown in Fig. 6-10. But when a bipolar pulse arrives at the input of this circuit the first non-conducting. lobe will be transmitted and the second will drive the diode into conduction, and the remainder of the signal will be short-circuited to ground, with the undershoot returning rapidly to the baseline, as illustrated in Fig. 6-11. A residual undershoot of much shorter duration survives, but the time during which there is a possibility of pile-up on the undershoot is reduced by a factor equal, in this illustration, to about six This type of restorer does, however, distort low-amplitude pulses. Where such pulses are likely to be present it is necessary to use an amplifier-diode-restorer circuit known as an "active restorer'.
Radioactivity
a92
measurements:
A
I
and practice
AV
Biased-diode restorer Fig. 6-10 (after Hatch, 1973).
I
principles
circuit
I
for baseline
,
I
80
0
Fig. 6-11 Pulse shape, a) before and b) after (after Hatch, 1973).
restoration
T
100 ps
baseline
restoration
6.5. MICROELECTRONICS Three or four decades ago in order to establish a function, such as transmitting or not transmitting a signal above or below a certain amplitude, a function known as "discrimination", one adopted a suitable design, purchased the necessary electronic components such as vacuum tubes, resistors and capacitors, and then assembled the circuit which would perform that function. Now, one normally purchases a completely assembled discriminator from a commercial supplier. Following the development of solid-state-diode detectors described in Chapter 4, complete integrated circuits (IC) can now be created on silicon wafers by the deposition or implantation of appropriate dopants and suitable metallic contacts and connectors. The procedures of modern microelectronic technology permits an electronic component such as a transistor to have dimensions of the order of micrometers, and enable as many as half-a-million transistors to be located on a six-inch-diameter silicon disc, and megabit "chips" may be expected to be in production soon, if not already (see C. Seitz and J. Matisoo, Physics Today, May,1984). Already by 1984, integrated circuits had reached such a degree of excellence that a complete charge-sensitive preamplifier could be purchased as a single module measuring about 3 x 1 x 0.25 cm (advertisement in Physics Today, May, 1984), and pens and pencils are available, containing a small fragment of quartz and single integrated circuits of many components, that give the calendar date, time of day and seconds in a small liquid-crystal digital display. This microelectronic revolution is having a profound effect on both the size and reliability of contemporary multichannel analyzers and other nuclear data-processing equipment, and it therefore behooves the planners of new radionuclide metrological laboratories to take careful note of the free publications of the nuclear industry. The recommended texts must be read to give the principles, but the industrial publications will inform one of their latest applications. It should perhaps be noted that, because a chip complete integrated circuit, the term "chip" is "integrated circuit".
6.6. COINCIDENCE
AND ANTICOINCIDENCE
LOGIC
of a silicon wafer often contains a frequently used synonymously with
CIRCUITS
Two of the most powerful methods for the direct measurement of activity are those of coincidence and anticoincidence counting. Pulse-height analyses by single-channel and multichannel analyzers (SCA and MCA, respectively) also involve the use of anti-coincidence logic circuits. A process
double-coincidence-counting circuit comprises two main detector channels that pulses from two separate detectors (one, for example, of 0 particles and the other
Radioactivity
measurements:
principles
and practice
893
of
A so-called "coincidence mixer" receives inputs from both and records them. 7 rays), channels and registers the number of times that events in each channel are coincident in The principles of coincidence and anticoincidence counting are discussed in Chapter time. 5, but in practice the method requires that the coincidence-mixing circuit shall put out a standard logic signal every time that the signal pulses from the beta and gamma channels as the coincidence to within a controllably short interval of time, known coincide, In the case of the anticoincidence logic circuit it is required that it resolving time. put out a logic signal whenever it receives a signal pulse from the beta-channel input or the gamma-channel input, but never when the two are in coincidence. circuit, coincidence and As with so much else in this age of the integrated anticoincidence circuits are not only available commercially, but they can be obtained with more than two inputs in order to provide an output logic signal when the signals to all Such circuits would be required to inputs are in coincidence, or, in anticoincidence. But in the implement the triple-to-double coincidence method described in 75.4.3.4.2. coincidence and anticoincidence circuits following two sections only simple, two-input, will be described - without any of the embellishments that can be obtained on commercially available models, such as variable resolving times and pulse shapes. 6.6.1.
Standard
loeic uulses
A standard logic pulse is one that conveys the message "yes" (or "1") or "no" (or "O"), as illustrated diagrammatically in the upper part of Fig. 6-12. The corresponding voltage levels of the "yes" and "no" pulses are designated V(1) and V(O), respectively. These pulses are square, and often of the order of 0,5 to 5 ps in duration. The three most important common logic systems are named, respectively, Transistor-Transistor Logic (ECL). Logic (TTL), the Nuclear Instrument Module system (NIM), and Emitter-Coupled Approximate unterminated signal levels in volts for each of these systems areshown in the lower part of Fig. 6-12. These are only approximate ranges as it is, for one thing, necessary that the range of output voltage should be greater than that required to drive If the signal terminates in a characteristic impedance of 50 the input of the next stage. For those who need more definitive information ohms, the levels are specified in amperes. about logic-system specifications, reference may be made, for example, to AEC (1974) or ANSI/IEEE (1982a).
I-----“,o,l 1 1
V(1)
l--
TTL
0
A0
1.8to5V
Coincidence
“No”
or”0” level
NlM;y:;;;;y
EC'dr::a"l;a;
to o.sv
Fig. 6-12 6.6.2.
“Yes” orl'l" level
I----------
Diagram
of a standard
logic
pulse.
or "AND" loeic circuit
diode-logic coincidence circuit (an AND gate) is shown A simple two-input In this figure logic signal pulses are shown arriving at diagrammatically in Fig. 6-13. the two inputs A and B. They could equally well be signal output pulses from two Some will, however, amplifiers and they are arriving at channels A and B randomly in time. arrive coincidentally. +pv(>W
Fig. 6-13
Coincidence
or "AND" logic circuit
(after Chiang,
1969).
If a moment be considered when the whole system is In Fig. 6-13, V(1) > V(O). then the quiescent, with no pulses arriving at A or B and both at the "NO" voltage V(O), If diodes D, and D, will be conducting and the output voltage will be maintained at V(0). a single pulse of amplitude V(1) were now to arrive at either channel A or channel B, the diode in the other channel will continue to conduct and the output of the system will at channels A But if positive logic pulses, V(l), arrive simultaneously remain at V(0). and B then the voltages across both D, and D, will fall to zero and neither diode will A logic pulse of amplitude V(1) will now be generated at the output of the conduct. circuit, indicating that a coincidence has been detected. When the input of either channel voltage will drop back to V(O),and remain so for as A or B drops back to V(0) the output long as either of the diodes D, or D, remains conducting.
Radioactivity measurements: principles and practice
094
A coincidence logic circuit can also be assembled using transistors instead of diodes (see Chiang, 1969). 6.6.3. The "OR" logic circuit The coincidence circuit described above enables an output logic pulse to be generated whenever two input pulses are impressed simultaneously upon channels A and B. An "OR" circuit (an OR gate) gives an output logic pulse whenever a signal pulse arrives at either channel A a channel B. This can also be achieved by means of a simple diode or transistor circuit. The diode circuit for positive input pulses is shown diagrammatically in Fig. 6-14.
IA
-VC
"OR" logic circuit. Fig. 6-14 The diode circuit shown in Fig. 6-14 is similar to the coincidence circuit of Fig. 6-13, but with the diodes reversed and the output biased at V(0) through the resistance R. In fact, if we were considering negative instead of positive input pulses, this OR circuit would act as a coincidence circuit, and the coincidence circuit of Fig. 6-13 would act as an OR circuit for negative pulses. non-conducting, and both In the quiescent state the diodes shown in Fig. 6-14 are If a positive signal V(1) appears at the input of inputs remain at the potential V(0). either channel A or channel B, diode D, or D,, respectively, becomes conducting and a positive logic pulse of amplitude V(1) is generated at the output of the circuit, indicating that non-coincident pulses have arrived at the inputs of channel A or channel B. arrive in In addition, however, an output logic pulse will be generated if signals coincidence at channels A and B. Strictly, therefore, the circuit shown in Fig.6-14, and which is known as an "OR" circuit, is an "and, or" circuit! Both the AND and OR logic circuits shown respectively in Figs. 6-13 and6-14, can be expanded to any number of input channels A, 8, C,..... .N, in parallel (see Chiang, 1969). 5 6 4
The "NOT" ionic sate
The NOT gate gives an output logic pulse that is the inverse of the input signal. Thus if the input signal is a positive pulse V(1) the output signal will be a negative pulse of amplitude V(1). This logic can be achieved for positive input signals by means of the transistor circuit shown diagrammatically in Fig. 6-15.
"NOT" or "NAND" logic gate (after Chiang, 1969). Fig. 6-15 then the transistor is cut off and the If the input to channel A is at voltage V(O), If, however, the input suddenly switches to V(l), then output will be at the level V(1). This is a somewhat the transistor saturates and the output level changes to V(0). simplified presentation of this logic function and for a more detailed description with suggested values for the various components Chiang (1969) should be consulted. 6.6.5. Anticoincidence
loeic circuit
The logic of a two-input anticoincidence circuit is designed so that an output logic pulse is generated only when a signal is received at input A and none simultaneously at input B, m when a signal is received at input B and none at input A. We have seen that this logic was almost achieved by the "OR" circuit described in 76.6.3 above; but, as was pointed out, the "OR" gate did not exclude coincident input signals and could be more The logic circuit required in order to circuit. strictly described as an "and, Or” identify only those signals in two channels that are not coincident in time is known as an "EXCLUSIVE OR gate" (Chiang, 1969); one such circuit is shown as a block diagram in Fig. 6-16 and incorporates one OR gate, one NOT gate and one AND gate.
Radioactivity measurements: principles and practice
a95
"EXCLUSIVE OR" gate (after Chiang, 1969). Fig. 6-16 The symbol for a NOT, or NAND gate comprises that for an AND gate with a small contiguous circle at its output. The special geometrical shapes used to symbolize the AND, OR and NAND (NOT) gates should also be noted as these are in constant use - just as a triangle is used in circuit diagrams to denote an amplifier or buffer. diagram are these symbols labelled as they have been in Fig.6-16.
Nor in a circuit
From Fig. 6-16 it will be seen that the OR gate will transmit logic pulses to the second AND gate for all coincident and anticoincident signals or logic pulses received by the OR gate. But the positive coincident logic pulses received at the second AND gate will be cancelled by the inverted coincidence logic pulses received simultaneously from the first AND gate. 6.7.
DISCRIMINATORS AND OTHER PULSE- AND DATA-PROCESSING EQUIPMENT
Discriminators permit the selection of amplitude voltages above or below which pulses can be either accepted for further processing for data collection, or rejected. Integral discrimators accept all pulses above a selected amplitude and are used in most electronic systems to exclude amplifier or other low-amplitude "noise". Differential discriminators select, for further processing, pulses in a range of amplitude, or u heipht, which is often limited to a small range of interestAV, e.g. a single gamma-ray peak in a gamma-ray spectrum. By the judicious use of one differential discriminator or of very many of them, one can design, respectively, either a single-channel analyzer (SCA), or a multichannel analyzer (MCA) that are used, especially the latter, in almost every branch of radionuclide metrology. 6.7.1. Inteeral discriminator A single discriminator circuit is one that is biased by an external threshold voltage in such a manner as to eliminate all input signal pulses below a selected amplitude or pulse height. The threshold voltage, V,, may be provided by means of the variable potentiometer P. This information is then used to select those incoming signals, with amplitudes greater than V,, for further processing. This circuit, which is illustrated in Fig.6-17, is called an "integral discriminator", and is chiefly used to eliminate unwanted pulses, including noise.
Simple integral-discriminator circuit; a) and b) show the Fig. 6-17 relationship between input pulse amplitude 4, threshold setting K, and discriminator output signal Vo. When Vi>/Vt, Voremains in the "yes" state (after Mann et al., 1980). 6.7.2. Differential discriminatororsinele-channel A
differential
discriminator,
or
analyzer
single-channel
analyzer,
consists
of
a
circuit
Radioactivity
896
network between
measurements:
principles
and practice
that identifies only those signal pulses with amplitudes in a lower threshold V,, and an upper limit VtY, so that AV = V,,
a narrow V,,.
range,AV,
one a lower-level (LLD) and This is accomplished by using two integral discriminators, the other an upper-level discriminator (ULD), in parallel in the manner shown in Fig. 6-18 so that the input signal of amplitude V, from the main amplifier, or other component is fed The output signal from each discriminator is fed to an to both discriminators. anticoincidence logic gate that will generate an output logic pulse a if an output logic pulses, V,, and V,, are received h pulse is received from LLD or ULD, but none if signal coincidence from LLD and LJLD.
v, Time __t
a) Block diagram of a basic singla-channel analyzer; Fig. 6-18 b) operation of the circuit for pulses below, between and above both the lower, VI, and upper, V2, level discriminator thresholdYland V2 in b) are equivalent to l'tl and vt, voltage settings. in a) (after Mann et al., 1980). respectively,
,
Thus the small first pulse shown in Fig. 6-18 will pass neither discriminator; the second pulse will generate an anticoincidence output logic pulse; and the third pulse generates output pulses from both discriminators in coincidence that will therefore be rejected by the anticoincidence circuit. The anticoincidence-output-logic used to permit the further processing amplitude between V,, and V,“. 6.7.3.
Scalers
(Pulse-countinn
pulse generated in the second example can then be and recording of the second signal pulse, V,, with
circuits)
Activity, the amount of a radionuclide is a rate of the quantity that specifies disintegration. After the pulses of electrical charge generated by an ionization type of detector of the radiation from a radioactive source have been processed it is necessary, in order to quantify the amount of radioactivity to measure the rate at which they are being produced. This rate serves as a relative measure of the activity of the source. The same necessity to count electrical output pulses occurring in a given time arises in the case of electron-multiplier phototubes used to detect the light output from scintillation detectors. In the 1930's when low-activity sources were measured at relatively low count rates it was usual to count the number of output pulses from the last stage of the electronic the relays of which circuitry using electromechanical registers required a fairly substantial pulse to operate satisfactorily. As the activities of sources to be measured to reduce increased and the speed of the electronics became greater, it became necessary the rate at which the electromechanical registers were driven in order to avoid overloading to the point of failure. This was accomplished by introducing a binary scaler between the or discrimination and the electro-mechanical register to scale last stage of amplification, The scaling down the pulse output rate to a level that was acceptable to the register. factor was equal to 2" where n could be chosen so as not to exceed the input capacity of Such registers also operated in conjunction with a series the electromechanical register. of neon or incandescent pilot lights that indicated the number of counts stll resident in the scaler when at the end of the chosen duration of the counting run the scaler was switched off.
Radioactivity
measurements:
principles
and practice
a97
In the present era of solid-state light-emitting diodes (LED's) and integrated These circuitry, scalers read out directly in the decimal system, in Arabic numerals. counts numerals are assembled from seven small elongated rectangularly shaped LED's such as digital watches and in many and various instruments are used nowadays in hand calculators, initially Nevertheless, with digital displays. the incoming signal pulses are still stored in a binary scaler and then decoded by means of a binary-coded decimal (BCD) decoder in order to activate the approriate segments of the LED displays to give the Arabic numerals that indicate the number of counts that have been accumulated. Any number Two decades of such a decade-scaler circuit are illustrated in Fig. 6-19. BCD-to-sevensegment decoders that are now of decade stages can be assembled from available commercially as integrated circuits.
Circuit of n-decade scaler with visual display and BCD Fig. 6-19 When a decade-counter stage has already accumuldigital output. ated nine counts, the arrival of another signal pulse causes the BCD to reset to zero and an overflow pulse is transmitted to the The count-enable gate allows the counts next higher decade stage. The reset is to be collected for, usually, a preset selected time. to return all stages to zero before starting counting (after Mann et al., 1980). 6.7.4. Multichannel
pulse-heivht
another
interval
of
analyzers
We have seen that an integral discriminator or a single-channel analyzer can be useful in excluding low-energy noise and, in the case of the single-channel analyzer, for defining a "window" of energy,AV, which will accept, for further processing, only those signals with pulse heights within the amplitude range lying between V and V + AV. Such a capability is very useful when one wishes to quantify a sample that is known to contain radioactivity that emits monoenergetic radiation, as noise and background radiation with energies lying below or above the "window" will be eliminated. Very frequently, however, it is necessary to record a whole spectrum of radiation energy from a single radionuclide, or a mixture of radionuclides, or when testing a special sample for radionuclidic purity. It is also very desirable in cases involving weak sources requiring Long counting times to record a whole spectrum simultaneously in order to minimize the effects of component instability. For this purpose, and in the early days after world-war II, crude multichannel pulse-height analyzers (MCA) were assembled using a series of integral discriminators to divide a given range of energy into a series of adjacent energy "windows", in exactly the same way as two integral discriminators had been used to define a single "window" with a limited range of energy. Thus lo- and ZO-channel pulse-height analyzers were assembled, respectively, from 11 and 21 integral discriminators. Each channel was provided with a scaler and register to record the number of pulses of each given increment of energy. Some of these early MCA's, particularly in Canada and the United Kingdom, were named "kick-sorters", and when they operated with their 11, 21, or more electromechanical registers at full cry, the less interested spectators would rarely prolong their visits. These MCA's were adequate for the detectors of their time, but with the advent of high-resolution solid-state detectors it has been necessary, in order to exploit their resolution, to develop MCA's of much higher resolution and greater storage capacity. Today MCA's can be produced, using integrated circuits and a different technique of pulse-height analysers, with 8192 channels or more. The then new technique was devised by Wilkinson (1950) in 1949, and it involved stretching the signal pulse as it entered the analyser so that the pulse was held st its maximum value during an interval of time during which it was used to charge a capacitor to a voltage equal to the amplitude of the pulse, V, After reaching the voltage V, the capacitor was discharged linearly by means of a source of constant current, and the time required so to discharge it was measured by means of a constant-frequency oscillator built into the MCA. These measured numbers of oscillations were then proportional to the
898
Radioactivity measurements: principles and practice
This technique is known as analogue-to-digital pulse heights of the input-signal pulses. conversion (ADC), "analogue-to-digital" signifying that the energy of the detected event that was initially proportional to a voltage had been converted to proportionality to a number. These whole numbers - the numbers of oscillations proportional to the various pulse heights - are then used to choose their appropriate sequential position in a computer-type Each such location is called a "bin". Thus an memory, known as "addressing the memory". input pulse that generated, say, n oscillations, which might be proportional to a pulse height of V,, would be addressed to the n-th bin and be stored. A second and then a third pulse of the same amplitude would be addressed to the same bin and stored, and so on for But a pulse, say, of amplitude V,,, would be addressed all pulses of the same amplitude. to the (n + 1) bin and stored there, as would also be all subsequently arriving pulses of that amplitude. Thus, as an experiment proceeds, all incoming pulses are assigned to the appropriate to the magnitudes of their respective pulse heights, and the energy bins spectrum of the detected radiation is accumulated. At the end of the experiment the memory is "read" by conventional computer techniques and the energy spectrum can be displayed on the computer-type screen, or a plot of it can be printed, in the form of incoming pulse rate as a function of energy, or channel (i.e. bin) number This type of MCA is also provided, now almost invariably, with a so-called "live timer" because of the long times involved in first converting and then storing large The pulses of greatest amplitude will clearly numbers of pulses of different amplitudes. take the longest time to sort by the Wilkinson method as they will generate the greatest number of oscillations. A loo-MHz oscillator will generate one oscillation every ten This interval of time will therefore approximately represent the shortest nanoseconds. interval of time reqired to increment the analyzer from one bin, or channel, to the next, i.e. one lo-ns pulse will address the first bin, two the second, and so on. Thus it will take about 8.2 /IS to send an event to channel 8192, or to the overflow where the record of stored as one single number, equal to the sum of all all higher-energy events will be events beyond the energy range of the MCA. In addition another 5 to 10 j~s will be needed to store the pulse in its appropriate channel. During this time of from 5 to 18 ps, known as the dead time the MCA will be unable to receive or to process any further pulse. Hence the need for the live timer, or clock, which at the conclusion of an experiment provides the time during which the MCA has been receptive to incoming pulses; and this is the time that must be used in order to calculate the count rate of incoming events. The live-timer circuit is provided with timing pulses from the MCA's constant-frequency oscillator, and the circuit is used to operate a gate that is closed to incoming signal pulses for the time during which the MCA is processing its last input pulse. A typical pulse-height spectrum obtained by a multichannel pulse-height analyzer at the National Bureau of Standards of one of its mixed radionuclide multi-gamma-ray standards Such spectra are usually collected over a measured live time. is shown in Fig. 6-20.
Channel
number
-
Gamma-ray spectra of a mixed radionuclide source consisting Fig. 6-20 of 5 ml of solution in a glass ampoule. Upper spectrum obtained with the source within a 12.7-cm diameter NaI(T1) well crystal. Lower spectrum obtained with the source at the face of a 60-cm3 Ge(Li) detector (from NCRP, 1985). Multichannel pulse-height analyzers now combine so many format-selection functions, such as, for example, linear or logarithmic ordinate (number of events) scale, isolation of a selected energy range, and summation of counts between two selected energies, to name but a few, that most MCA's begin to resemble and begin to perform many of the functions of a modern computer. It is not, therefore, wholly surprising to find that commercial suppliers of nucleonic instruments are now developing ADC's and buffer memories (packaged for compatibility with the NIM standard system) and interfaced, with appropriate programming provided, so that they may be used with several personal computers.
899
Radioactivity measurements: principles and practice
The fastest analyzers in use today use the method of successive aaoroximation to This method is based on building up a "comparison" measure the final output-pulse height. amplitude by means of very fast binary increments and comparing this, and other successive artificially-created amplitudes (when necessary), with the actual output-pulse amplitude, The great advantage of this method is that the time required to using a comparator. process a pulse is independent of its amplitude. Digital buffers that are now available enable one to store the processed pulseamplitude data that can then be transferred by means of a built-in and suitable interface to commercially-available microcomputers. developing era of Once again it must be emphasized that, in this explosively microelectronics and integrated circuits, it is useless to try to give within the limited description of the very complex scope of this report a full and comprehensive pulse-processing equipment now available. As was pointed out in 16.5, at the present time one selects the appropriate function and then aspires to acquire it. To choose an everyday example, few can afford the time to build a radio or a television; except for fun.
For further information and references on the operation and uses pulse-height analyzers, an article by Ross (1973) could be consulted.
of multichannel
6.7.5. Dead-time losses and gates As with MCA's, other pulse-handling electronic equipment and, indeed, the radiation detector itself are unable properly to process incoming signal pulses while they are still engaged in processing an earlier signal. As mentioned in 76.2 and illustrated in Fig. 6-2, an incoming pulse will be distorted if it rides on the tail of a previous pulse, and the pulse height of the riding pulse will no longer be proportional to the energy deposited in the detector by the primary ionizing event. It should also be remembered that, with the various stages of amplification, in a counting system, the time interval from the beginning to the end of the pulse varies from stage to stage. It is therefore of the greatest importance to be sure that all further input pulses are excluded from the system for the longest time that any one component takes to process an incoming pulse. The minimum time required for the whole system to accept a new pulse and to handle it without distortion is In general the dead time of the system will be the called the dead time of the system. dead time of its slowest stage. In order to be sure that no such distortion occurs it is customary to insert an electronic stage that imposes a dead time on the whole system. It is possible, but not always assured, that one of the other components has a dead time that is stable and independent of pulse rate and amplitude, but in lack of such assurance it is prudent to have an independent dead-time gate. Also this gate should be placed as early as possible in the electronic-processing sequence, otherwise pile-up and distortion may have already occurred in an earlier stage. But it is not practical to place the dead-time gate before the preamplifier that should be as close to the detector as possible. Dead-time gates are also extendable or nonextendable. The former occurs when the dead-time gate activates to prevent the processing of further signal pulses for, say a time T , every time that it senses a new pulse. Thus if two input pulses happen to be overlapping in time then the dead-time gate will close on the arrival of the first pulse, and then remain closed for a time T after the arrival of the second. A nonextendable dead-time gate closes on the arrival of a pulse and opens again after a time 'T, irrespective of how many events may have been detected during the period T that the gate was closed. The difference between these two modes of operation of a dead-time gate are A simple circuit used at the National Bureau of Standards to illustrated in Fig. 6-21. provide a nonextendable dead time is shown diagrammatically in Fig.6-22. This dead-time gate uses a retriggerable-monostable-multivibrator integrated circuit SN74122 (see Texas Instruments, 1976). circuit provides an output pulse of fixed, This but adjustable, duration whenever it is triggered by an input event. This pulse is used to block the input for the duration of the output pulse by feeding one of the outputs, ?j, back to the input. Just as in the case of the MCA the existence of dead time in a counting circuit has the effect of decreasing real counting time of an experiment. The end product sought in counting is almost always, one way or another, a count rate. h measurement of time is even explicit in the spectra of Fig. 6-20, and is indeed required if the spectrum has been taken in conjunction with a measurement, say, of nuclear-reaction rates or yields. In the case of an ordinary single-channel count-rate measurement it is also necessary to make a dead-time correction to the count rate. In essence, such a correction is based on using the measured dead time and count rate to calculate the real live time of the experiment. These corrections have been discussed in (3.4.3.5, and also, very fully by J. G. V. Taylor, in 72.7 of NCRP (1985).
Radioactivity measurements: principles and practice
900
ON,i
1
2
NZT
3
4
NT-~--
Relationship between input (N) and output (n) events for Fig. 6-21 systems with nonextendable and extendable dead times. For the system with nonextendable dead time T , events 3 and 6 are lost but events 2. 4. 5 and 7 are recorded because thev are seoarated in time by more than the dead-time interval T from the last preceding event to produce an output. For the system with an extendable dead time, event 4 is also lost because it is seoarated bv less than T from event 3, which extended the dead-time interval initiated by event 2. For extendable dead times all pulses that are not separated by at least the interval T from the preceding event whether this event is recorded or not, are lost (after NCRP, 1985).
Fig
6-22 Nonextendable dead-time circuit based on a single SN 74122 oneshot retriggerable-monostable-multivibrator integrated circuit. The IC itself is shown within the dashed lines with appropriate external connections outside the dashed lines (after Mann et al., 1980). 6.7.6. Count ratemeters Dosimeters used by health physicists to obtain d.c. readings as a measure of exposure in radiation fields are designed to give an instantaneous average reading of the exposure, whether it be from a photon source, or from w or p-particle sources the last two possibly arising from surfaces accidentally contaminated by such sources. A ratemeter usually comprises two stages, namely an input pulse-shaping stage and an output averaging stage. A simple "pump" ratemeter circuit is shown diagrammatically in Fig. 6-23. The input pulses may be logic pulses produced by the last stage of a detector pulse-processing system. The average voltage developed across R, for C,<>w, where n is the input pulse rate, given by c = nCiViR,. A suitably sensitive voltmeter is usually employed with switch-in resistors to provide three or four ranges of magnitude of the radiation exposure. As a and p particles, and 7 rays are emitted randomly, a low-level source of any of them will give widely fluctuating readings of the current- or voltage-reading instrument, or meter. The higher the input pulse rate the steadier will be the deflection of the needle, because it represents an average of a greater number of pulses occurring within the time constant, R,C,, of the output circuit.
Radioactivity
measurements:
principles
and practice
Ratemeter circuit; BJ is the width in units Fig. 6-23 input pulse (after Mann and Garfinkel, 1966). 6.8.
LOW-LEVEL-CURRENT
901
of time of the
MEASUREMENTS
Ionization currents generated in ionization chambers can vary in magnitude from lo-'A to 10-13A. But a current sensitivity of 10 -i5A is desirable because background and leakage currents may be one or two orders of magnitude less than the ionization current due to a radioactive source. Two excellent reviews of the methods available for measuring such small currents,byH: were published in the Proceedings of the First International M. Weiss and K. Zsdanszky, Herceg Novi (1973, pp. 291 and 299). A Summer School on Radionuclide Metrology, held in description of the ionization chamber and associated electronic system used at the Bureau A new edition International des Poids et Mesures has also been published by Rytz (1983). has also been "Electrometer Measurements" (2nd ed., 1977) of Keithley Instruments recently published under the title "Low Level Measurements" (Keithley, 1984). 6.8.1. Townsend
induction
balance
especially at national laboratories, are often made Ionization-chamber measurements, In this method, using some kind of automated version of the Townsend induction balance. the ionization current charges one plate of a capacitor the increase in voltage on which is compensated by maintaining an approximately equal and opposite potential on the other plate This was originally done manually using a potentiometer and some kind of the capacitor. of electrometer to sense whether the potential of the capacitance was departing substantially from zero, but this is now usually achieved by the use of differential-voltagesensing and automatic-compensating systems. If the combined compensating voltage cv/t.
capacitance of the chamber is increased to V in time
output and external capacitor then the ionization current
t,
is C, and the I is equal to
devices earliest differential-voltage-sensing was the one of the types of vibrating-reed electrometer (VRE), which with many refinements is still in use. In a VRE, one plate of a capacitor (the reed) vibrates and thereby generates an a.c.-voltage output voltage input. If the VRE is connected across the from a constant or slowly increasing capacitance C, the output-voltage amplitude is proportional to the out-of-balance potential across the capacitance C. (See, for example, Fig.6-24.)
Fig. 6-24 Townsend balance HN, 1973). The VRE output pulses can next be amplitudes exceed a specified value they and used, by various means, to provide a
with stepwise
compensation
(after Weiss,
fed to an integral discriminator, and when their will be transmitted by the integral discriminator compensating voltage to the capacitor C.
One of the earliest automatic Townsend-balance systems was described by Garfinkel in 1959; its operation is illustrated in Fig. 6-24. As soon as the voltage on the integral discriminator D, reached about 12 mV the timer T was started. When the integral
Radioactivity
902
measurements:
principles
and practice
and -100 mV was supplied to the discriminator D, reached 50 mV, a relay was closed This could be capacitor plate that is shown connected to ground through the resistance R. repeated a selected number of times up to 15, after which the tFmer T was stopped as discriminator D, again started to detect and transmit pulses having an amplitude of 15 mV. several other current-measuring devices for use with Details of the operation of together with information on their efficiency calibration and their ionization chambers, precision of measurement have been given by Weiss (HN., 1973) and ZsdAnszky (HN., 1973) For more recent information, Rytz (1983) and along with references to other publications. Keithley (1984) should be consulted. 6.8.2.
Electrometer
amplifiers
of very There are two types of electrometer amplifier available for the measurement picoammeters", and the small currents, namely the shunt type also known as electrometer coulombmeters". capacitance type also known as "current integrators", or "electrometer There are also two principal types of each, and all four employ the principle of inverse amplifiers have also been developed with input-stage MOS-FET electrometer feedback. resistances of the order of IO'* ohms and voltage gains of about 50,000 (Zsdanszky, HN., 1973). 6.8.2.1.
Electrometer
oicoammeters
in Figs. 6-25 and 6-26, and is This type of electrometer amplifier is illustrated That shown in Fig. 6-25 is described in detail by Zsadnszky (1973) and in Keithley (1984). and that in Fig. 6-26 as the "feedback-type picoammeter", known as the "shunt-type amplifFers picoammeter", although, as mentioned earlier, all four of these electrometer resistance of the shunt type is R, and that of the The input employ inverse feedback. The input voltage V, of the latter configuration is equal to I,R,. feedback type R,/A. Some further details are given in Mann et al. The shunt type is not, however, often used. (1980) and Keithley (1983).
Fig. 6-25
Electrometer
picoamperemeter-shunt
Electrometer Fig. 6-26 Keithley, 1984).
type (after Keithley,
picoamperemeter-feedback
Current integrator Fig. 6-27 Keithley, 1977).
or coulombmeter-shunt
1984).
type (after
type
(after
Radioactivity
measurements:
principles
and practice
903
T
Current integrator Fig. 6-28 Keithley, 1977). 6.8.2.2.
Electrometer
coulombmeters
or coulombmeter-feedback
type (after
or inteerators
In the electrometer coulombmeters illustrated in Figs. 6-27 and6-28, the integration is achieved by charging a capacitor, C, in the former and C, in the latter. The current I, from the ionization chamber is essentially constant when measuring a long-lived source so that in time t the capacitance charges to a voltage V, equal to I,t/C,. As mentioned earlier, an amplifier with inverse feedback operates in such a manner as to reduce the So, for V, tending to be reduced to zero, V, = V, - V, or amplitude of the input signal. v, = -v,. Hence I, = -VOCf/t. "Dose" calibrators
6.8.3.
"DOSI?" calibrators, more known as also properly "activity calibrators" or "radionuclide calibrators", are usually gas-ionization chambers, many types of which are filled with argon at a pressure of about 2 MPa (20 atm). They have a reentrant well that is large enough to accommodate samples of gamma-ray-emitting radiopharmaceuticals in solution, contained in ampoules or serum vials. One type of radionuclide calibrator comprises a large plastic scintillator with a reentrant well. The instrument is usually set for the radionuclide to be checked by means of a selector switch or, sometimes, by means of plug-in resistance modules. Such calibrators, for the convenience of hospital personnel, usually read out the activity of the sample measured in switch-selectable ranges of, say, 0 to 1 mCi, 0 to 10 mCi, 0 to 100 mCi and so on up to perhaps 0 to 10 Ci; but many models can, by means of a two-way switch, also display the measured total activity of the solution in the container in either curies or becquerels. Further, rather clear and detailed, information regarding the principles and operation of such instruments can be found in NCRP (1980, p. 291). 6.9. STANDARDIZATION 6.9.1.
OF NUCLEAR
INSTRUMENTATION
General
Nuclear measuring instruments consist in general of parts which perform well defined separated functions, such as amplific ation or discrimination. This makes it possible also to subdivide nuclear instruments into separate modular subunits, according to their separate electronic functions. if such units can be For general use, it is convenient interchanged between different electronic systems either within a laboratory or between different laboratories. Thus, over the last two or three decades there has been an international effort to standardize all nuclear instrument modules, hence the name of the system, “NIH”, and that of one of its component parts, the "NIMBIN". For many purposes, however, compact instruments are needed, such as for monitoring or field measurements. And with the availability of cheap complex microprocessors, storage discs, and other miniaturized components, it may be less expensive to acquire certain compact, but complex nuclear instruments rather than to use modular systems; although, even with such compact some useful standardization of parts is still possible, equipment especially of connectors, cables and subunits. However, the intrinsic advantages of standardized modular systems are still valid, especially in the case of larger laboratories. These advantages include interchangeability of subunits, ease of servicing, flexibility and easy updating and reuse, availability of a wide range of modules, and so forth. Two standard systems of nuclear electronics are widely in use, firstly NIM, referred to above and which mainly applies to smaller stand-alone instruments, and secondly that for computer automated measurment and control (CAMAC), that applies mainly, as its name implies, to computer-controlled NIM was developed systems. primarily as an analogue-oriented system although it is being increasingly used for digital circuitry. inception, been computer-oriented. CAMAC has, from its Both NIM and sources throughout 6.9.2. Nuclear The
CAMAC instruments and the industrial world.
instrument
specifications
AHI 39/8-M
modules for
the
components
are
widely
modular
system
of
available
from
commercial
(NIM1 standard
nuclear
electronics
NIM
was
Radioactivity
904
measurements:
principles
and practice
produced by the NIM committee (US National Instrumentation Methods Committee), supported by the US Department of Energy and associated with the National Bureau of Standards (AEC, 1974). The NIM system is in widespread use throughout the world. Earlier systems, such for example, the NIM-compatible ESONE (European Standard on Nuclear Electronics) had, as, for example, found only limited acceptance. The NIM specifications pertain to the mechanical dimensions, the electrical power supply and the electrical signals, and were designed to overcome the situation illustrated in Fig. 6-29. Figure 6-30 shows a solution to the problem, namely a typical NIM/CAMAC crate (standard bin and chassis) which houses 12 single modules (or 24 half-width modules), or correspondingly less if double, triple, or more, modules are used. The total width of the standard bin is 19 inches (482.6 mm), the width of a standard module is such that a standard bin will accommodate 12 single-width modules, 6 double-width modules, or 6 single-width and 3 double-width modules, and so on. The height of the bins is 8 3/4 inch (222 mm).
Fig. 6-29 The problem. At the rear of the modules, plug-in units are coupled by a 42.pin connector to the Several power supplies are available with all or some of common power supply of the bins. the standard voltages, such as f 6V, ? 12V and ? 24V. Connections between modules are made through coaxial connectors at the front panels. Detailed recommendations Some fixed connections can also be made via the rear connectors. are made in NIM for logic signals ("O"/"l"), for the transmission of "slow" digital data, for fast logic signals and for linear analogue signals (0 to10V). NIM systems can be easily connected to computers via individual, task-oriented can then be sent automatically to the The collected data (e.g. spectra) interfaces. central computer for further treatment (e.g. peak-area evaluation). 6.9.3.
Cornouter automated
measurement
and control
(CAMACL
The CAMAC specifications (ANSI/IEEE, 1982a, b, c; CAMAC, 1973) for a standardized computer-automated modular nuclear-instrumentation system with digital data handling has been produced by a group of European laboratories organized by the European Standard on Nuclear Electronics (ESONE) Committee, the US NIM Committee, and some other standardization organisations. The mechanical format of the NIM and except that the minimum width of the single NIM module.
CAMAC crates and plug-in units module is 17 mm, half the width
is the same, of the single
Radioactivity
measurements:
principles
and practice
905
Radioactivity
906
measurements:
principles
and practice
CAMAC modules are connected at the rear via 86-contact connectors to a multiwire data latter is part of the crate and carries data, control bus (highway), the "Dataway". The It has a minimum cycle time of 1 ps and is interfaced by the crate signals and power. controller to the input-output (I/O) port of the computer. Up to 7 crates can be interconnected using a branch parallel highway and branch driver (ANSI/IEEE, 1982~). Larger assemblies with up to 62 crates can be combined using a serial highway and serial highway drive with appropriate crate controllers (ANSI/IEEE, 1982b). All operations of a CAMAC system are controlled by the central computer. This must be Standard software routines for CAMAC programmed using the appropriate computer language. are available in different languages (ANSI/IEEE, 1979). 6.9.4.
EASTBUS
A new modular system for data acquisition and control, designated "FASTBUS", has recently been developed by the NIM Committee with the collaboration of the ESONE Committee. Though This system is extremely fast and versatile with very great addressing capability. designed to meet the needs of the high-energy physics community, its superior characteristics make it attractive for many other applications. It is now a standard of the Institute of Electrical and Electronics Engineers and the American National Standards Institute to be published also as standards of ESONE and the (ANSI/IEEE, 1985), and is expected The development of FASTBUS was initially International Electrotechnical Commission (IEC). undertaken to meet the needs posed by the world-wide advent of a new generation of accelerhaving detector outputs numbering up to the ators (e.g. CERN, KEK, SLAC and FERMILAB), Some FASTBUS system currently in operation have data-transfer rates of order of 5 x 105. 160 megabytes per second (Dawson et al., 1985). which operate independently but which A FASTBUS system consists of bus segments dynamically link together as needed for operation passing. FASTBUS is a standardized Its versatility, modular data-bus system for data acquisition and control applications. addressing capability make it attractive for use in a wide variety of and speed consists of bus Segments which operate independently but A FASTBUS system disciplines. dynamically link together as needed for operation passing. This parallel processing feature accounts to a great extent for the high throughput of FASTBUS in multisegment Master modules compete for single or multiple segment control through a bus systems. arbitration scheme using assigned priorities. System speed is limited solely by propagatation and logic delays. . The principal
features
. High
typically
speed -
. Large
address
bus -
. Versatile
multiple
System-wide
Uniform,
l
Arbitration
6.10. FURTHER
parallel master
include:
than 10 MHz;
(32 bits):
processing: capability;
communication:
. Block transfers synchronous); l
greater
and data fields
. Segmented
l
of FASTBUS
-
system-wide
with
and
without
"handshake"
(i.e.
synchronous
or non-
protocol;
and interrupt
features.
READING
in addition to those already referenced in this chapter, There are many publications, that could usefully be available in a nucleonics laboratory for those who wish to study the Among these, in order of date of publication, are subject in somewhat greater depth. (McGraw Hill Publishing Electronic Devices and Circuits, by J. Millman and C.C. Halkias Electronics for Scientists: Principles and Experiments for Those Company, New York, 1967); and E. C. Toren (W. A. Benjamin, Inc, who use Instruments, by H. V. Malmstadt, C. G. Enke PLll.Se, Digital and Switching Waveforms: Devices and Circuits for their New York, 1973); by J. Millman and H. Taub (McGraw Hill Book Company, New York, Generation and Processing, Techniques in Instrumentation, by Ralph Morison (John Grounding and Shielding 1965); Operational Amplifiers: Design and Application, Wiley & Sons, Inc., New York, 1967); edited by G. E. Tobey, J.G. Graeme and L.P. Huelsman (McGraw Hill Book Company, New York, Applications of Operational Amplifiers; Third-Generation Techniques, by J.G. Graeme 1971; Company, New York, 1973). in the Burr-Brown Electronic Series (McGraw Hill Book Further good coverage of the subject may be found in Nuclear ELectronics, by E. Nuclear Electronics, by Kowalski (Springer-Verlag. Berlin, Heidelberg, New York, 1970); P.W. Nicholson (John Wiley & Sons, London, New York, Sydney, Toronto, 1974); and The Art of Electronics by P. Horowitz and W. Hill (Cambridge University Press, Cambridge, London, New York, New Rochelle, Melbourne, Sydney, 1980).
Radioactivity measurements: principles and practice
907
Reference could also be made to the integrated-circuit data sheets and applications literature available from various semiconductor companies such as Fairchild, Harris, Motorola, RCA, Signetics and Texas Instruments.
REFERENCES FOR 76.9. AEC, 1974. "Standard Nuclear Instrument Modules(NIM)," Energy Report TID 20893, 4th revn. (Washington, D.C).
AEC NIM Committee,
US Dept. of
ANSI/IEEE, 1979. "IEEE Subroutines for CAMAC," ANSI/IEEE Std. 758-1981, ESONE Report SR/Ol (1981), IEC Pub1.713 (1981) (Institute of Electrical and Electronic Engineers, Inc., New York). ANSI/IEEE, 1982a. "CAMAC Specifications," ANSI/IEEE Std. 583-1982, CEC Publ. EUR 4100 (1972), IEC Publ. 516 (1975) (Institute of Electrical Engineers, Inc., NewYork).
and Electronic
ANSI/IEEE, 1982b. "CAMAC Serial Highway," ANSI/IEEE Std. 595-1982, CEC Publ. EUR 6100 (1977). IEC Publ. 640 (1979) (Institute of Electrical and Electronic Engineers, Inc., New York). ANSI/IEEE, 1982~. "CAMAC Branch (Parallel) Highway," ANSI/IEEE Std. 596-1982, CEC Publ. EUR 4600 (1972), IEC Publ. 552 (1977) (Institute of Electrical and Electronic Engineers, Inc., New York). ANSI/IEEE, 1985. "FASTBUS," ANSI/IEEE Electronic Engineers,Inc., New York). CAMAC,
1973.
"CAMAC Tutorial
Papers,"
Std.
960-1985
(Institute
of
Electrical
and
IEEE Trans. on Nucl. Science N-20, No. 2, April
1973. Dawson, U.K., Costrell, Louis, Hirokazu Ikeda, Ponting, J. and Walz, H.V., Trans. on Nucl. Science NS-32, No. 5, October 1985, pages 2089 -2091.
IEEE
7.
RADIOACTIVITY
CALIBRATION
LABORATORY:
SCCPE.
STAFF AND EQUIPMENT
7.1. GENERAL All radioactivity measurements consist essentially of two basic operations, namely (i) the quantitative preparation of a suitable radioactive source, or sources, for making a The measurement in specific measurement, and (ii) the carrying out of that measurement. question may relate to any of a large number of different quantities such as activity, (Iparticle, B-ray or photon energies, the interactions of radiation with matter, the detectthe probabilities for the occurrence of ion and identification of radioactive impurities, in the environment, uptakes of different radioactive decay modes, amounts of radioactivity radiopharmaceuticals in animal organs, and so on. And a diversity of applications requires, in turn, a diversity of source forms and of Thus the quantitative preparation of sources almost invariably measuring instruments. films to thick source mounts, and dispensers requires a sensitive balance, "weightless" ranging from approximately Z-ml plastic pycnometers (baby-doll feeding bottles) to electromagnetic mass, or isotope, separators. Radiation-measuring devices range from simple, small, quartz-fibre pocket ionization chambers or very small in viva intercavitary detectors to the 2,300-kg CERN detector system mentioned in Chapter 4.
Fig. 7-l Hoods designed for use in radiochemistry laboratories, actually located in cold-chemistry laboratory as shown above. hoods can be jacked up slightly to take the load and the legs removed so that floor tiles may be replaced in the event of a active spill. Hemispherical source support in nearer hood is evaporation of metal films on to VYNS source mounts (National of Standards, Gaithersburg, Maryland. U.S.A.).
909
but These radiofor Bureau
Radioactivity
910
measurements:
principles
and practice
In general, these two basic operations result in a radionuclide-metrology establishment being functionally divided into high- and low-level source-preparation laboratories and into counting laboratories, often located in separate wings of one building or in separate buildings in order to reduce the possibility of cross-contamination between radioactive sources. The source-preparation laboratories consist of storage rooms, equipped with lead, steel, mercury, or concrete shields, temperature- and humidity-controlled draught-free weighing rooms, and "hot" (radioactive) and "cold" (non-radioactive) chemistry laboratories. The radiochemistry laboratories may be equipped with hoods and work benches, similar to those shown in Fig. 7-1, that have been specially designed by one of the authors to facilitate the clean-up of radioactive contamination underneath them in the event of an accidental spill; mercifully a contingency that has not yet arisen to test their design. The counting laboratories consist of well-ventillated rooms, preferably air-conditionto accommodate detecting or counting systems such as ionization ad, that are designed chambers, Geiger-Miiller and proportional counters, solid-state detectors, liquid-scintillation detectors, and so on, each with its own appropriate electronic current-measuring, pulse-processing, or data-handling systems. All of these laboratories should be kept scrupulously clean at all times, and regularly monitored for stray radioactive contaminatand the health-physics staff. ion, both by the working personnel Bench-top and hood working areas in the source-preparation laboratories should preferably be of stainless steel which should be protected when in use, if not at all times, with clean double-layerSuch covering is commercially available in ad, absorbent paper on plastic, cover sheets. rolls of about l-m width from which strips of the requisite length may be cut. After use, these absorbent-paper on plastic sheets may be disposed of as radioactive waste, if they have been contaminated with any radioactive material. But some discrimination should be shown in distinguishing between high-, low-, and zero-radioactive contamination in order to avoid overloading the world's capacity for radioactive-waste disposal. Radioactive materials should not, in general, be stored in counting laboratories. The exceptions are well-sealed sources for monitoring instrument performance, such as, for These should be stored between use in a well-shielded and example, Ra and its daughters. permanent location to avoid causing fluctuations in the background count rates of detecting systems. In this respect it is also wise, if building low-level counting laboratories below ground, to check for radon in ambient ground water and (whether above or below ground) for radioactivity in the aggregate used in the adjacent structural concrete. In the construction of new counting laboratories and in the installation of new equipment one For extremely low-level radioactivity measurements it may must be wary of many pitfalls. also be essential to remove radon from the air being circulated in the counting room. A couple of examples of unexpected problems that were encountered at NBS may serve as a Initially inexplicable background changes (attributed at first to some cautionary tale: positron emitter in a mercury shield) were traced, after drawn-out and tedious investigation, to s5Kr lingering in a preamplifier diode that had been leak-tested with that gas; and and on another occasion strange fluctuations in counting rate were found to be caused by an elevator counterweight passing up and down the other side of the laboratory wall. Further details can also be found in 813.2.3 and 3.2.4 of this report. 7.2. SCOPE The scope and dictated by several
size of a radioactivity standardizing considerations, such as, for example:
laboratory
will,
of
course,
be
or perhaps population density, of the region; (ii) the extent to which (i) The population, radioactive materials are used in the region for research in physics or medicine; (iii) the to the environment by the mining or the of radioactivity magnitude of the release of power from processing and refining of uranium or thorium ores, by the generation to coal-powered plants or nuclear reactors, or by the controlled release of radioactivity laboratorthe environment from, for example, hospital and industrial radiopharmaceutical ies, or by nearby nuclear tests; (iv) the degree to which accuracy of radioactivity measuror less in research to flO% in medicine to ments is essential, e.g., from the order of U% perhaps +20% in environmental measurements; (v) the extent to which high-quality industrial support is available in the production and distribution of accurately-calibrated measuring instruments such as radionuclide calibrators; (vi) the extent to which these industrial radioactive materials, producers can also supply adequately pure, well-characterized and radioactivity standards, and, therefore the degree to including radiopharmaceuticals which such industrial producers participate in traceability exercises linking them to the regional and international radioactivity standards; and so on. In a predominantly agricultural area or nation there may be but a limited need for but in those nations that are using radioactivity techniques or radionuclide metrology, In this respect, nuclear power extensively there will be a correspondingly greater demand. Atomic Energy Agency's Table 7-1, from the February 1, 1988, issue of the International The need for radioactivity IAEA Newsbriefs No. 22 (Vol. 3, No. 1) is very informative. standards must, to a great extent, be correlated with the magnitude of a country's nuclearpower program and its consequent ability to produce radioactive materials, including radioThe IAEA also gives the in support of its industry and medical services. pharmaceuticals, reactors were newly connected to interesting statistic that, in 1987, 23 nuclear-power electricity grids, and that nuclear power now supplies more than 26% of the world's electricity.
Radioactivity
measurements:
principle*
and practice
From Table 7-l it is readily seen which areas of the world are nuclear-power rich and a new and those that are not. The nuclear-power rich, in order of "watts-electric", Europe and North America at about 110 and 105 GW, potential measure of wealth, are: The respectively, followed by the USSR and Japan with, respectively, about 33 and 27 GW. less nuclear-power-rich parts of the world appear to be South America, the Middle East, But many countries that are Africa, and South-West and South-East Asia, apart from Japan. not yet committed to nuclear power have swimming-pool or equivalent reactors that produce Howsufficient quantities of radioactive materials for medical applications and research. ever, given the present climate of public opinion, it is not surprising to find a trend toThus Canada has recently announced the availability of a new wards smaller reactors. generation of CANDU reactors, the CANDU-300, rated at 320 to 375 MU(e), about one-third the rated power of the CANDU-900 and one-half of that of the CANDU-600, but keeping the safety In Sweden, ASEA-ATOM has designed, using refuelling-under-power features of its ancestors. "SECURE" (fail-safe) reactor rated at 300 a very interesting new principle,* so-called The new principle is that of controlling the criticality and level of power by m(e). adjusting the level of boric acid in the water circulating in the reactor core. But there is also a pool of highly borated water around the reactor core, but separated only by a gas lock that allows the highly borated water to flood the core in the event of a decrease in There are no valves in this svstem within thereactor the flow-rate of the orimarv coolant. itself, so that this automatic shut-down is based only on the laws of physics.
TABLE
7-l Reactors/ total net MWe
Argentina Belgium Brazil Bulgaria Canada Czechoslovakia Finland France German Democratic Rep. Germany, Fed. Rep. of Hungary India Italy World
total:
2 7 1 1; 8 4 53 5 21 4 6 3
417 reactors
7.3. SIZE OF LABORATORY
(935) (5477) (626) (2585) (12 142) (3207) (2310) (49 378) (1694) (18 947) (1645) (1154) (1273)
Reactors/ total net MWe Japan Korea, Rep. of Netherlands Pakistan South Africa Spain Sweden Switzerland Taiwan, China United Kingdom United States USSR Yugoslavia
36 7 2 1 2 9 12 5 6 38 106 55 1
(26 877) (5380) (507) (125) (1842) (6529) (9646) (2932) (4918) (10 214) (92 982) (32 919) (632)
296 876 megawatts-electric (MWe) total net capacity.
AND NUMBER
OF STAFF
7.3.1. General Quite clearly, the magnitude of the effort needed to meet the metrological needs of any given region of the world in the field of radioactivity depends on the extent to which has become involved in its many applications. The needs may also be met by the joint efforts in varying proportions of a strictly standardizing laboratory and of commercial laboratories; and the proportions may change as the development proceeds. Thus the Canadian National Research Council (NRC) started a small radioactivity standardizing laboratory at their nuclear research laboratory at Chalk River in, about, 1946. Initially this standardizing laboratory had about three rooms accommodating one physicist, one chemist, and two technicians, to whom secretarial help was also available when needed. This effort "as continued at Chalk River when Atomic Energy of Canada Limited (AECL) took standardizing group in over the laboratories, but NRC also set up a small radioactivity their Ottawa laboratories. In recent years, however, both activities have declined as the Commercial Products Division of AECL has increased its distribution of calibrated samples, including radiopharmaceuticals, the "traceability" of which to the international reference system is maintained by AECL Commercial Products Division participating in the Atomic Industrial Forum (AIF) and National Bureau of Standards traceability programme. That part of AIF that supported this program has now become the United States Council for Energy Awareness (USCFA), and the name of the NBS/AIF programme changed accordingly. (NCRP, 1985, Chapter 8 may be consulted for information, with references, about this programme.) Radioactivity standardization in the United States since about 1940 "as the responsibility of the NBS Radioactivity Section (now the Radioactivity Group), but the measurement of large numbers of radium needles for medical use dated back, at least, to 1913 when Mme Marie Curie brought the first radium standard, certified by the International Radium Standards Commission, to the U.S. But it "as not until after the nuclear age began in the early 1940's that NBS became involved in the calibration of uranium-bearing ores and artificially-produced radionuclides. It may be instructive to follow the involvement of
911
Radioactivity
912
measurements:
principles
NBS in radioactivity standardization in terms of the size radionuclides were from about 1946, when reactor-produced present time.
and practice
of its becoming
Radioactivity Section available, until the
In 1946 or 1947 the NBS section comprised 9 scientists, 1 technician, and 1 secretary. that for a small radioactivity standardizing laboratory It might be noted, in passing, limited perhaps to one or two professionals and one or twd technicians, the best kind of professional to appoint to the first position filled would probably be a radiochemist. This is so because a well-trained radiochemist would be competent both in source preparation and in the assay of the sources. But it should also be emphasized that the next staff member appointed should probably be a technician. At the present time when personnelhiring ceilings are so often imposed, the staff patterns in so many laboratories become badly out of balance because of the tendency to hire a doctoral research graduate instead of a well-trained and competent technician. Shortly after 1965, at the time NBS moved to new laboratories in Maryland, the section numbered about 20 (including two secretaries), frequently with the addition of one or more long-term (6 to 12 month) visitors from abroad, wishing to gain additional experience before returning to his or her own national laboratory. At this time the numbers programs being carried out in were alSO swollen because of extensive "traceability" partnership with industrial and hospital laboratories, and with environmental monitoring laboratories of the federal government (Mann et al., 1981; NCRP, 1985). At the present time the full-time staff is 10 (including two secretaries), but is supplemented by two part-time retirees (one aging and the other more alert) and an occasional visit from a radiochemist or physicist from abroad under the aegis of international exchange programs. to sharpen our perspectives. In its new location in Maryland the section (group) occupies some 30 laboratories and offices, although only a fraction may be occupied at the same time because many of the laboratories are dedicated to specific activities, such as, high- and low-level radiochemistry and source-preparation laboratories, high- and low-level counting rooms, different kinds of detectors (such as a, j3, and photon), nucleonics (including microprocessing), and so on. For the first few years after 1946 greater numbers of a greater variety of radionuclides were being produced and put to use in scientific and medical research, so that there was an ever increasing demand for standards of these radionuclides. Concurrently more commercial houses became involved in the distribution of radioactive substances, including labelled compounds, and calibrated radioactivity samples, the calibrations of which were not always consistent between the different producers. Thus around 1970 medical laboratories, commercial producers, and regulatory agencies of the federal government started to organize traceability programs with NBS. The best known of such programs, which is still extant, is the NBS-AIF program referred to above, which comprises NBS, the Federal Drug Administration, and from six to eight commercial producers (the number has fluctuated during the years). These traceability programs are carried out monthly between NBS and the other participants. in general use reaches saturation and But, naturally, as the numbers of radionuclides as their producers and users become more skilled in making accurate calibrations, the numbers of standards required from the national laboratory should begin to decrease. Thus any regional radioactivity calibration laboratory that does its job well, may live to see that its services are not so urgently needed with the passage of time, with the advent of a more widely-distributed competence and expertise, and with the almost unlimited availabilility of radioactive materials and calibrated sources from the nuclear-power-rich countries of the world. in the nuclearNor, indeed, is this index of the passage of time without significance world where nuclear measurements have not only become simpler with the power-rich increasing availability of computers and microelectronics, but where the "fashion" has Radiopharmaceutmoved from nuclear physics to molecular biology and genetic engineering. icals do not have to be calibrated to tenths of a percent, and dosimetry, at present or indeed at any future time, probably needs to be accurate to only 10 or 20% in order to match the certainty with which we can predict physiological response. The one thing against which the nuclear-power-rich world has still to be on guard is the occurrence of another Windscale, Three Mile Island or Chernobyl; and it will need to maintain the resources to deal with it, It is now no longer feasible to take such precautions against the devastation of a large nuclear war; but sufficient resources are probably now available to cope with a small one. 7.3.2. A small
radioactivity
laboratory
In a region where there is not even a small reactor or accelerator, or even where a power reactor is coming into operation, radioactive research materials, radiopharmaceuticals, or environmental radioactivity standards may be imported from elsewhere, If this external supplier has a well-organized quality-control and traceability program in place, it may be in a position to supply reliable standards, free of impurity, to the region that is coming into operation. In such
an event,
the monitoring
laboratory
in the
starting
region
might
consist
of
Radioactivity
measurements:
principles
and practice
913
an activitylaboratory, one radiochemist and three rooms, namely a source-preparation This would certainly constitute the minimum calibration laboratory and an office. viable configuration, inclusive of staff! The minimum equipment needed microbalance, suitable glassware bottles.
for and
the source-preparation including dispensers,
laboratory would be a good "baby-doll" small plastic
radionuclide The equipment for the counting room could be at least a commercial one that had been calibrated by a laboratory that was calibrator (9.v.); and preferably Then a NaI(T1) well-crystal directly or indirectly traceable to the international system. detector system would be most desirable for use in both gamma-ray assays and in crude testing for the presence of impurity radionuclides which could also be accomplished, in longer term, by half-life measurements. If funds permitted, a commercial liquid scintilemitters would be a very great lation counter for the relative assay a- and B-particle, asset. If funds did not permit, a resourceful scientist could try his hand at constructing a Lauritsen-type electrometer, which is illustrated in Fig. 4-1, but which is no longer available commercially; a do-it-yourself sketch (without the aluminium enclosure) is also shown in Strong (1940, p. 229; a Later 1946 edition may still also have this sketch). Calibrated a, p or photon (including x-ray) sources on solid mounts can, under the best be calibrated to better than 2% (estimated standard deviation) using this conditions, simple ionization-chamber device. With the addition of a plastic ampoule holder that can be located at any of a variety of fixed distances from the electrometer chamber many photon-emitting nuclides in solution in standard glass ampoules can be assayed by comparison with calibrated sources of the same nuclides in the e.ame geometry. NCRP Report "General-Purpose ories."
No. 58 (NCRP, 1978 and 1985, Section 6.5) has Equipment" and "Minimum Instrument Requirements
useful information on both for Some Specific Laborat-
Most gamma-ray solution standards are distributed in lo-ml or 15.ml glass ampoules, Both the and many radiopharmaceuticals are dispensed in a variety of bottle shapes. standards and radiopharmaceuticals must, before measurement in a radionuclide calibrator, be transferred to a bottle having the same configuration as that for which the instrument was calibrated, or a correction factor must be determined. (See NCRP, 1978 or 1985). Such a laboratory would be able to check prepared Sources for maintenance of quality in a region where there was, initially, a fairly low demand, and its operations would increase as the use of radioactive materials increased. It could also rely on traceable longer-lived standards from other regions, but as its operations expanded it should have adjoining space into which its equipment and staff can expand. 7.3.3. A laree radioactivity
laboratory
In a burgeoning region the growth of a laboratory might approximate the case history, described briefly above, of the National Bureau of Standards, Radioactivity Section. As mentioned, various perturbations arise from the concomitant activities of other metrological laboratories in universities (e.g.. Lawrence Berkeley Laboratory), groups of universities (e.g., Oak Ridge National Laboratory), medical laboratories, and industry. In France there is a strong central standardizing and distributing laboratory, the Laboratoire de Metrologie des Rayonnements Ionisants (UiRI) in the Office des Rayonnements Ionisants, reporting to the Commissariat a 1'Energie Atomique and the Bureau National de Metrologie. IMRI has extensive calibration and production facilities. In the United Kingdom the National Physical Laboratory's (NPL) Acoustic and Radiation Division a group about the same size as that at NBS is responsible for radioactivity measurements, including the acquisition of nuclear-decay data, but the large-scale production of radioactivity standards in the United Kingdom is handled by Amersham International. The monitoring of quality, including that of personnel engaged in calibration functions, is performed by the British Calibration Services. Thus it would seem that there are too many variables, involved in the interplay between national, industrial, and university services in a region, to do more than hazard to fulfill the functions of any regional an estimate of the size and scope required radioactivity standardizing laboratory. A reasonable estimate might be six scientists (physicists and radiochemists) including the head of the laboratory, six technicians, one nucleonics and micro-processing expert, one mechanic, and one secretary, for a total of 15 persons. The ratio of scientists to technicians may be high, as many of the source-preparation and counting operations can nowadays be handled by skilled technicians. 10 technical staff will need nearly twice that number of Judging from experience, rooms. This ratio of rooms to people is not extravagant because, as mentioned earlier, the number of rooms is dictated by the number of "functions" but this ratio should decrease with any increase in the numbers of staff, because many of the "functions" will probably not need to be increased. Thus there will be "hot , ” medium-level and low-level radiochemistry Laboratories, one "cold" chemistry laboratory, perhaps two, or possibly a so-called "white" room. In addition there should be a draught-free humidityand room, one special low-level temperature-controlled balance room, a source-preparation counting room built from monitored activity-free material with circulated radon-free air,
914
Radioactivity
measurements:
principles
and practice
and probably at least three other counting rooms. one computer room, three or four offices for the six scientists and one secretary, a source-storage room, and a workshop, or access As eating and drinking is normally prohibited from radiation to one, will also be needed. areas, a tea rcmmor enlarged area in a "non-active" hallway, with a coffee maker and food At least one secretary is absolutely essential in order to take dispenser may be required. and publications of the group, but also the care, not only the routine correspondence business of ordering materials and dealing with inquiries about calibration services, and The occasional services of a skilled machinist, or access to a orders for standards. nearby machine shop is also almost essential. The equipment needed in any regional laboratory will depend upon the special As already mentioned, section 76.5 activities peculiar to that region and its priorities. of NCRP (1978 or 1985) may help as a guide, as should chapters 3 to 6 of this report.
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WINKLER, G. and PAVLIK, A. (1983). Some aspects of acfivify measurements with Nal(TI) wellrype detectors, Int. J. Appl. Radiat. and Isotopes 34, 547. WU, X.Z., SONG, L., WANG, Z.Y. YANG, Y.D. and WANG, C. (1987). Standardization of j4C by liquid-scintillation coincidence counting, Int. J. Appl. Radiat. and Isotopes 38, 891. YAFFE, L. (1962).
Preparation of thin films, sources and targets, Ann. Rev. Nucl. Sci. 12, 153.
YOSHIZAWA, Y., IWATA, Y., KAKU, T., KATOH, T., RUAN, J.-Z., KOJIMA, T. and KAWADA, Y. (1980). Precision measurements of gamma ray intensities, I. “Co, LoY, lromAg, ‘“Cs and 107Bi, Nucl. Instr. and Meth. 174, 109. ZWEIFEL, P.F. (1957).
Allowed capture-positron branching ratios,
Phys. Rev. 107, 329.
ZYRYANOVA, L.N. and SUSLOV, Yu. P. (1968). Latest data for tVB+ branching ratio values, in Proceedings of a Conference on Electron Capture and Higher Order Processes in Nuclear Decays, Debrecen, Hungary, 12, D. Berbnyi, Ed. (E&v& Lorand Phys. Sot., Budapest).
Radiat.
Isot. Vo1.39,
Int. J. Radiat. Printed
in Great
Appl.
No.8,
Instrum.
pp.717-937,
1988
0883-'2889/88 $3.00+0.00 Pergamon
Part A.
Press plc
Britain
RADIOACTIVITY
PRINCIPLES
MEASUREMENTS
AND PRACTICE
1. INTRODUCTION
1.1. ORGANIZATION
OF LABORATORIES
FOR RADIONUCLIDE
METROLOGY
This report, which was prepared initially at the request of the International Atomic as a guide to laboratories engaged in, or about to become Energy Agency, was written engaged in radionuclide metrology. These may be national laboratories specialized either in measurements of radioactivity or dosimetry of ionizing radiations, or both, which are recognized by national law or international agreement, or they may be newly entering the field in regions of the world that are developing the uses of radioactive materials in the natural sciences or in medicine. These laboratories may collaborate with or be members of the Network of SecondaryStandard Dosimetry Laboratories (SSDL's) established and supported by the International Atomic Energy Agency (IAEA) and the World Health Organization (WHO) (see Eisenlohr, 1978, 1984; IAEA 1978a, 1979b, 1981, 1985,; IAEA/WHO, 1976, 1984). This international collaborative project, which includes top-level basic standardization laboratories as affiliated members (Fig. l-l), maintains a high level of quality of dosimetry work. The worldwide SSDL network consists at present of more than 50 laboratories of very different character, some of them being large national laboratories. The creation of this network was brought about by the basic need for an internationally consistent standard of absorbed dose for use by radiotherapy centres operating increasingly available cobalt-60 teletherapy units for the treatment of malignant turnours, in countries where the understanding of the principles of radiation measurements had not kept pace with the developments in medical methods. In view of the increasing use of radioactive materials, it was realized, as early as 1951, that international cooperation was needed to assure the conformity of international measurements of activity. Accordingly representatives of Canada, the United Kingdom and the United Stateb agreed, at that time, to exchange suitable samples of carbon-14,
Fig.
l-l.
The IAEA/WHO Network of Secondary-Standard Dosimetry Laboratories: AFF.PsoL'~: Affiliated Primary-standard Dosimetry L.bo=.tOTie.; IAEA:InternationaL AtmnlcEnergyAgency; WHO:WorldHealthorganization;
sodium-24, phosphorus-32, cobalt-60, bromine-82, strontium-90-yttrium-90, iodine-131, thallium-204 and gold-198 for intercomparative measurements (Mann and Seliger, 1958). These beginnings have since developed under the aegis, first, of the International Commission on Radiological Units and Measurements (ICRU) and then of the Bureau International des Poids et Mesures (BIPM) into a system of intercomparative activity measurements involving all of the leading national standardizing laboratories (ICRU, 1963; Rytz, 1983). But, as in the case of dosimetric measurements, the progress in radionuclide metrology has not, in some countries, kept pace with the developing technological, biological and medical applications.
717
Radioactivity
718
measurements:
principles
and practice
It is, especially, the aim of this report to provide guidance to any laboratory that is called upon to provide radioactivity standards and calibrations that are in agreement with the international standards, where such services are presently deficient or lacking. The work of the SSDL's, both in radiation dosimetry and in radioactivity, must clearly be continuously adapted to current and future needs, and must conform with different national laws and regulations, and with the precepts of the international hierarchy of standards laboratories (see Fig. 1-Z). It is to be hoped that the radioactivity-measuring laboratories, be they linked to the SSDL network or to some other metrological chain, will also establish firmly recognized transfer channels between the workers in the field and the national and international standards laboratories (Eisenlohr et al., 1981). 1.2. TASKS
OF LABORATORIES
ENGAGED
IN RADIONUCLIDE
METROLOGY
The first "classical" task of the radionuclide-metrology laboratories is to maintain with appropriate limits of uncertainty, and provide standards, for the calibration of Their second task is to maintain consistency of their activity-measuring instruments. activity measurements with other established laboratories, national and international, by means of direct or indirect international comparisons of their measuring competence (see, for example, L.M. Cavallo et al., HN*, 1973, p. 5; Rytz, 1983; NCRP, 1985). By means of such intercomparisons an international hierarchical system of measurements consistency and traceability has been established (Mann et al., 1981). This system that applies both to dosimetry and radioactivity measurements is illustrated in Fig. 1-2: f3lPM (IAEA,
International t
I~RM)
National
I laboratories
Qualitycontrotand I regulatory bodies
State
health
Government
Fig.
1-2.
laboratories, agencies,
Universities
lndustrlal
groups
,
Hospitals,
and
others
Hierarchy of radioactivity-standardization laboratories and organizations (the "Traceability Tree")
calibration services can also provide Laboratories that radioactivity SUPPlY This is indLs.pensible support in most, if not all, applications of radioactive materials. agriculture, archeology, biology, the a very large domain that includes, for example, the building industry, chemistry and the chemical industry, cosmology, energy production, medicine, meteorology, the metal fusion, geology and hydrology, environmental sciences, and the textile industry, mining and cokery. physics, reactor technology and safeguards, scope of industry (including leather, paper, and plastics). But, despite the extensive mo.st radioactivity measurements in these fields can be performed by these applications, very similar procedures, most of which are described or referenced in the following pages. 1.3. PURPOSE
AND SCOPE OF THIS REPORT
This report is written as a concise introduction to the field of radionuclide metrolproblems that may be encountered in ogy. Emphasis is given to the basic and practical although an attempt has been made to cover the whole field at measuring radioactivity, least by the inclusion of recent references.
Radioactivity measurements: principles and practice
719
The report therefore comprises this introductory chapter and six more. Following this introduction. the second chapter gives a brief survey of the basic concepts, definitions, quantities and units, and some useful data and constants used in the treatment and The third chapter treats the most important general problems measurement of radioactivity. in radioactivity measurements, such as radiation protection, source preparation, and the The fourth chapter describes the various treatment of experimental uncertainties. interactions of radiation with matter and detectors based on such interactions. The fifth chapter describes different methods of measuring activity. The sixth chapter gives a brief account of the basic principles of electronic instrumentation as applied to the processing The seventh chapter and recording of electrical pulses generated in radiation detectors. attempts to estimate the possible requirements for staff, space and equipment needed for Extensive references laboratories designed to make routine measurements of radioactivity. A principal reference is the are given in order to facilitate the use of this report. second edition of the U.S. National Council on Radiation Protection and Measurements (NCRP) "A Handbook of Radioactivity Measurements Procedures" (NCRP, 1985). The Report No. 58 present report largely complements NCRP, 1985, that is directed more towards applications in biology and medicine. 1.4. SI UNITS The Syst&me International d'Unit6.s created by BIPM (SI units: BIPM, 1985; NBS, 1986), has been adopted by IAEA and most countries, but as the greater part of the present literature is difficult to understand without any knowledge of the old system of units, both systems are generally used here in parallel (the old mostly within brackets). The SI unit for the quantity activity of a radionuclide, which is one measure of the The term phenomenon or property of radioactivity, is one reciprocal second, s -1 radionuclide metrology covers all aspects of radioactivity measurements, such as those of activity, half life, the atomic energy available and necessary for a nuclear transition to take place, probabilities of different modes of decay, and so forth
The following SI prefixes and symbols are used throughout:
Factor
Prefix
Symbol
Factor
Prefix
Symbol
1018
exa
E
10-l
deci
d
1015
peta
P
10-X
centi
1012
tera
T
10-j
milli
109
giga
G
10-6
micro
106
mega
M
10-9
Ilall0
103
kilo
k
10-12
pica
102
hecto
h
10-15
femto
101
deka
da
10-18
atto
2. DEFINITIONS,
OUANTITIES.
SOME USEFUL
CONSTANTS
SYMBOLS
AND UNITS;
AND REIATIONS
2.1, INTRODUCTION "Radioactivitb" was the name coined by Marie Curie to describe the phenomenon of radiation, atomic transformation, with the emission of corpuscular and, or, electromagnetic A detailed treatment of the phenomenon, or discovered by Antoine Henri Becquerel in 1896. and the underlying principles of atomic and nuclear physics is property, of radioactivity far beyond the scope of this report. Therefore this Chapter 2 seeks only to supply the reader briefly with the essential information needed for the successful performance of in particular. But for this radionuclide metrology, in general, and activity measurements purpose, it is also necessary here to consider the most basic attributes of radioactivity, the law of radioactive decay, the types of such as the statistical nature of radioactivity, their probabilities of emission, and other nuclear data. Further radiations emitted, detailed information may be obtained from several appropriate texts (see, for example, Evans, 1955; Siegbahn, 1965; Herceg Novi, 1973; Knoll, 1979: Mann et al., 1980; NCRP, 1985). 2.2. BASIC
CONCEPTS
2.2.1. Measurement,
AND
PARAMETERS
standardization
USED
IN THE MEASUREMENT
OF RADIOACTIVITY
and calibration
"Measurement" is a set of experimental operations, the purpose of which is to assign magnitude to a physical property, or to quantify it, in terms of a number and a unit.
a
Any physical quantity, such as mass, length or time, is measured in terms of a unit that may be defined in terms of a standard such as the kilogram, just as commercial transactions are measured in terms of one or more basic currencies that are related to one Indeed it is not just by chance that many national standards laboratories have another. the framework of governmental departments of commerce or developed, or remain, within trade. (See, for example, L.M. Cavallo et al., HN, 1973, p. 5.) Following the industrial revolution and the growth of international scientific cooperto tighten up a system that had developed quite randomly in ation, it became necessary of eighteen countries met different parts of the world. Therefore, in 1875 representatives des Poids et and signed the Convention du HBtre that established the Bureau International Mesures at S&vres as the custodian of the international standards of mass and length (and and dissemination (BIPM, later, time), and charged this Bureau with their preservation 1985). All three standards were defined standards, although those of length and time have The standard of mass, been redefined in terms of precisely measurable physical quantities. held in the kilogram, is, however, still the original cylindrical mass of platinum-iridium are measured by careful and precise experimental S&vres. Replicate national kilograms methods relative to the international standard at BIPM, and domestic standards are, in In terms of this hierarchical turn, measured in terms of their own national standard. system a mass of, say, 25 kilograms is a shorthand way of saying that the quantity "mass" system, is, Q of a certain object, in any part of the world using this international within an uncertaintv that can be estimated and should be stated, twenty-five times that of the international kilogram in S&vres. In 1960, the llth Conf&rence Gdnerale des Poids et Mesa-es (CGPM) extended the international system to include base (i.e. defined) units, derived units, and supplementary units, comprising L.e Syst&me International d'Unit8s (SI). The seven base units (and their names and symbols) for the followjng auantities are presently (BIPM, 1985; NBS, 1986): mass (kilogram, kg), length (meter, m), time (second, s), electric current (ampere, A), and luminous thermodynamic temperature (kelvin, K), amount of substance (mole, mol) intensity (candela., cd). standard has often been In the past the accepted standard or the best available defined as the primary standard. National-laboratory standards, although secondary international standards also frequently designated as primary standards. are Such ambiguity can be avoided if standards are designated according to the hierarchical system shown in Fig. 1-2, simply as international, national, laboratory working standard, hospital standard and so forth (NCRP, 1985). Basically, however, the only statements of importance in specifying a standard are its value and a realistic estimate of the uncertainty of that value (see 13.4). In many cases the national standard of a short-lived radionuclide such as, for example, Ia11 is in fact a secondary, or even tertiary standard calibrated very precisely by means of an ionization chamber maintained in the national laboratory or nt BIPM (set? 74.5.1.1.2).
721
Radioactivity
722
measurements:
principles
and practice
Another misused term is "absolute" and every effort should be made to use it unambiguously. Only the defined standards are absolute, in the sense that they have no error. K.F. Gauss has referred to measurements made "in absolute measure", meaning in terms of the defined, and therefore "absolute", standards. But such measurements have varying degrees of uncertainty. Nowadays "absolute" usually means "direct" as opposed to "relative" measurements. Thus the direct method of coincidence counting will give a value in terms of the absolute standard of time without the use of another standard, whereas an ionization chamber gives only a relative measurement, but nonetheless 8, in absolute measure". An "absolute neutron cross section" with an uncertainty attached to it is often a relative measurement, but is probably "in absolute measure" in the sense used by Gauss. In this report, every effort will be made to conform with the statement referring to "Electrical quantities", in BIPM (1985, Appendix 11.4), that "So-called 'absolute' electrical measurements, i.e. those that realize the unit according to its definition, can be undertaken only by laboratories enjoying exceptional facilities." The term calibration normally refers to the relative, or indirect, measurement physical quantity by comparison with a standard that embodies that quantity. 2.2.2. Radioactivity
standards.
reference
and calibration
of a
sources
A standard is, quite generally, a very well characterized sample, instrument, or procedure intended to define, represent, conserve or reproduce the measure (unit) of a physical quantity, in our case activity. There exiqts a great variety of types of calibrated sources of radioactivity, International standards are, in general, maintained by the BIPM; in the case of activity standards chiefly through the "international reference system," known as SIR (72.2.3). National standards are normally recognized by law as the basis for the calibration of all other standards of a quantity in one country. Ideally they should be "traceable" ((2.2.3) International standards to international standards. are of the highest metrological quality and are, in general, checked by intercomparisons betweeen national and international standardization laboratories. A complete hierarchy of national, laboratory, field or calibration standards is derived from, and, in the case of radioactivity, traceable to, the international standards, within stated limits of uncertainty (72.2.3). All activity standards of every kind must be fully documented; that is, they must be accompanied by a certificate issued by the standardizing laboratory that fully describes their preparation, characteristics, and calibration, and, most importantly, states the estimated uncertainties in the certified value, both random and non-random. For a discussion of statements of estimated uncertainty reference may be made to 73.4.1.2, er seq. Field standards, the last level in the hierachical system of standards, should be available for every field instrument. There is no better way to check efficiently and reliably the functioning of field instruments than by using suitable calibration standards; these are often called "reference sources". International cooperation in radionuclide metrology would be greatly facilitated if the forms of standards and sources could themselves be standardized. This has indeed already been done in the SIR program (72.2.3) where standard glass ampoules (for filling with a specified volume of solution) can be obtained from BIPM. Into most European languages the word "standardization" is translated as "normalisation". 2.2.3. Traceability
and aualitv
assurance
Because of all the problems and hazards connected with radioactivity, its measurement should always be extremely reliable. This can be achieved to a considerable extent by measurements-assurance programs and so-called traceability exercises (Mann et al.. 1981; NCRP, 1985, Ch. 8.3). The term "traceability" is not yet fully recognized officially, but within the restraints imposed by the transitory nature of radioactivity, it aims to achieve either exulicit or implicit (NCRP, 1985, Ch. 8.3) measurements assurance within the hierarchical systems (Fig. 1-2). The necessary credibility of measurements and standards of radioactivity is not easy to achieve because of the multitude of radioactive substances used and their different and, frequently short, half lives. Direct verification by special organizations of every standard issued (quality assurance) is not possible for radioactivity standards. Therefore, continuing international, and many national, quality-assurance, or traceability, radioactivity-measurements programs have been established, which allow the achievement of a high degree of reliability of radioactivity standards and measurements at all levels of the hierarchical system (Fig. l-2).
Radioactivity
measurements:
principles
and practice
723
The international system of radioactivity-measurements traceability comprises a close collaboration between many of the outstanding radioactivity-standardization laboratories around the world. It involves two principal activities organized by BIPM, namely (i) frequent interlaboratory comparative measurements of the activity concentrations of radioactive solutions, encapsulated in standard glass ampoules and all prepared from the same master solution (see, for example, Rytz, 1985), and (ii) an international reference system (SIR, Syst&me International de RBfbrence) that allows national laboratories to submit standard glass ampoules containing radioactive solutions with stated activity concentration to BIPM for verification and registration (Rytz, 1983). The SIR program complements and extends the program of international comparisons of activity measurements organized by the BIPM. The participants are, as a rule, national and international laboratories of radionuclide metrology. They are invited to submit samples of solutions of gamma-ray-emitting nuclides, which they have prepared and standardized Two very stable, pressurized wellthemselves, in sealed, and standard, glass ampoules. type ionization chambers have been installed at the BIPM (Rytz, 1983) and used for comparing the current produced by a submitted sample with that produced by a BIPM reference source of very pure radium. From this ratio the activity concentration is calculated. This international traceability and new ideas may still be expected.
program
(SIR)
is still
developing,
so
that
changes
At the national level many standardizing laboratories conduct internal traceability exercises between themselves and the principal domestic radioactivity-measuring laboratories, and especially with those involved in regulation. Such exercises are very similar to those conducted at the international level, except that solid sources of alpha-particle-emitting nuclides may often be included. The national laboratory will usually distribute calibrated radioactive solutions, or solid samples, in the form of "blinds". These are sources of known but undisclosed activity concentration, or activity, and it is incumbent upon the receiving laboratory to measure the activity, and perhaps even identify it, and to return its results to the national laboratory or, in some cases, to the next higher laboratory in the hierarchy. The tested laboratory may then receive a cetificate of traceability stating its achievement in terms of its percentage divergence of its value from that of the national or monitoring laboratory. But this kind of traceability "is usually imulicit, insofar as it only establishes the ability of a laboratory to assay any radionuclide at any given time. In the long term it is the competence and reliability of a laboratory and the skill of its staff that comprise its traceability" (NCRP, 1985, Ch. 8.3). And it is the purpose of any traceability or quality-assurance program, relating to any production process, to provide the necessary assurance that, within certain well-specified limits, that process shall remain in control. Essentially this is also the aim of the SSDL network. With the many uses of radionuclides, especially in medicine, this task can be formidable. And it is interesting to note that in the United Kingdom the National Physical Laboratory has to some extent circumvented the problem of distributing calibrated sources of photon emitters by sponsoring the manufacture of calibrated ionization chambers. These can then be maintained "in control" by monitoring with a few standards calibrated for photon-emission rate over an appropriate range of energy. The United Kingdom has also instituted the British Calibration Service which is charged with the task of assuring the quality and competence of the laboratories and personnel of the laboratories in the hierarchy of measurement standards. 2.3. RADIONLJCLIDES. 2.3.1.
Elements. isomers
RADIOACTIVITY
nuclidas.
radionuclides
(radioisotopes),
isotopes,
isotones,
isobars
and
The different elements were initially recognized by their more distinctive external characteristics, such as state, colour and density (e.g. mercury, copper, silver, gold and lead); and then, with the passing of time, they became characterized by their physical and chemical properties. The elements are subdivided into nuclides. And a nuclide is defined as anv species of atom having specified numbers of protons, 2 (atomic number), and neutrons, N, in its nucleus. The positive nuclear charge, Ze, which, under normal conditions, is compensated by the charge of the electron cloud around the nucleus, -Ze, determines the kind of element (Table 2-l); and the outermost electrons in the cloud, its chemical properties. The sum of the numbers of neutrons and protons gives the mass number, A, of the nuclide. This is expressed in the symbol for a nuclide A (= Z + N), that is designated in the form *X, as, for example, 6oCo and 85mKr (where "m" indicates a metastable state). Sometimes the value of Z may also be included as in $0 or 853;Kr. The atomic mass number, A, of a nuclide is approximately equal to its atomic "weight" relative to 1% = 12.000000. Unstable nuclides, radionuclides, decay stochastically (i.e. randomly) to stable or unstable progeny of lower atomic mass, the difference in mass being radiated in different kinds of energetic radiation according to the Einstein mass-energy relation E = mc2. Radioactive substances are found in nature, but most are now produced by nuclear reactions, Nearly all naturally-occurring radionuclides (except for some unstable nuclides at low
Radioactivity measurements: principles and practice
724
"OK) belong to the four families of radioactive heavy nuclides (a2.3.7). Z-values, e.g. Most artificial radionuclides are produced by neutron irradiation of stable nuclides in reactors, and many by charged-particle bombardment in high-energy accelerators. Sometimes the term radioisotope (implying "radioactive isotopes of') is used instead of the correct term "radionuclide". The different nuclides with the same atomic number, Z, are the isotopes of one well-defined element. Nuclides with the same neutron number, N, are named isotones, and those with the same mass number, A (= N + Z), isobars. If, in radioactive decay, the transition is to an excited state of the daughter nucleus that, in turn, decays to a lowerGround States of Free Neutral Atoms Table Z-l. ELECTRON CONFIGURATIONS OF THE ELEMENTS ----pNumbers of electrons in the different subshells (after Kaye and Laby, 1973). The capltals of the first line refer to the principal quantum numbers, n= 1,2,3...7. The subshells are designated by laxer-case letters, s,p,d,...h,corresponding to the azimuthal quantum numbers P = 0,1,2,...5. Element
K 1s
1. 2. 3. 4. 2: 7. 8. 9. 10.
H
1
He
2
Li Be B c N 0 F Xe
11. Na 12. Mg 13. Al 14. Si 15. P 16. S 17. Cl 18. Ar ---------19. K 20. Ca 21. SC 22. Ti 23. V 24. Cr 25. Mn 26. Fe 27. Co 28. Ni 29. Cu 30. Zn 31. Ga 32. Ge 33. As 34. Se 35. Br 36. Kr 37. 38. 39. 40. 41. 42. 43. 44. 45. 46.
47. 48. 49. 50. 51. 52. 53. 54.
Rb Sr Y Zr Nb MO Tc Ru Rh Pd
Ag Cd In
Sn Sb Te I Xe
L 2s
M 2P
1 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 __-_------ -. 2 2 2 2 2 2 2 2
--_
3p
3d
;
1
2 2 2 2 2
2 3 4 5 6
6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 ----
2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2
6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6
2 3 5 5 6 7 8 10 10 10 10 10 10 10 10
6 6 6 6 6 6 6
2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2
6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6
10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10
----
2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 _-. 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2
3s
N
: 6 6 6 6 6 6 6 6 6
4s
4p
0 4d
4f
5s
5p
5d
_____----5f 5g
1
n
:
1
2 2 2 3 2 4 2 5 2 6 ____________________-__---------_-------_________ 1 2 6 2 6 2 1 2 6 2 2 2 2 6 4 1 2 6 5 1 2 6 5 2 2 6 7 2 6 1 6 8 1 2 10 2 6 2 6 10 1 2 6 10 2 10 2 1 2 6 10 2 2 2 6 2 6 10 2 3 10 2 4 2 6 2 6 10 2 6 10 2 2 continued next page
Radioactivity
meaeurements:
principles
and practice
725
Table 2-l (cont'd) _____________________------------------_______________--_-__-_________________-------___-________ Element
K
L
M
N 4s
4p
4d
4f
5s
5p 6 6 6 6 6 6 6 6 6 6 6 6 : 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6
2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2
8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8
18 18 18 18 18 18 18 18 18 18 18 18 18 18 18 18 18 18 18 18 18 18 18 18 18 18 18 18 18 18 18 18
2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2
6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6
10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10
2 3 4 5 6 7 7 9 10 11 12 13 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14
2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2
Fr Ra AC Th Pa U Kp Pu
2 2 2 2 2 2 2 2
8 8 8 8 8 8 8 8
18 18 18 18 18 18 18 18
2 2 2 2 2 2 2 2
6 6 6 6 6 6 6 6
1014 10 10 10 10 10 10 10
14 14 14 14 14 14 14
2 2 2 2 2 2 2 2
95. Am 96. Cm 97. Bk 98. Cf 99. Es 100. Fm 101. Md 102. No 103. Lr 104.(Rf) 105. (Ha)
2 2 2 2 2 2 2 2 2 2 2
8 8 8 8 8 8 8 8 8 8 8
18 18 18 18 18 18 18 18 18 18 18
2 2 2 2 2 2 2 2 2 2 2
6 6 6 6 6 6 6 6 6 6 6
10 10 10 10 10 10 10 10 10 10 10
14 14 14 14 14 14 14 14 14 14 14
2 2 2 2 2 2 2 2 2 2 2
55. cs 56. Ba 57. La 58. Ce 59. Pr 60. Nd 61. Pm 62. Sm 63. Eu 64. Gd 65. Tb 66. Dy 67. Ho 68. Er 69. Tm 70. Yb 71. Lu 72. Hf 73. Ta 74. Iv’ 75. Re 76. OS 77. Ir 78. Pt 79. Au 80. Hg 81. Tl 82. Pb 83. Bi 84. PO 85. At 86. Rn ------____ 87. 88. 89. 90. 91. 92. 93. 94.
5d
Q
P
0 5f
6s 6p 6d 6f 6g -------------------_--__-___-_______-
%
1 2 3 4 5 6 7 9 10 10 10 10 10 10 10 10
1 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 1 1 2 2 2 2 2 2 2
1 2 3 4 5 6
6 6 6 6 6 6 6 6
10 10 10 10 10 10 10 10
2 3 4 6
2 2 2 2 2 2 2 2
6 6 6 6 6 6 6 6
6 6 6 6 6 6 6 6 6 6 6
10 10 10 10 10 10 10 10 10 10 10
7 7 9 10 11 12 13 14 14 14 14
2 2 2 2 2 2 2 2 2 2 2
6 6 6 6 6 6 6 6 6 6 6
1
1
--.
1 2 1 1 1
1
1 2 3
energy state of the same nucleus with, usually, a short but easily-measured half the latter transition is known as isomeric, and the decaying daughter is called
6h
7s
1 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 life, then an isomer.
Such isomers are denoted by a letter "m" (for metastable) placed after the mass number of the isomeric nuclide. As an example, '\:Cs decays to isomeric 1375:Ba that, in turn,decays with a half life of 2.55 min to stable '\LBa. The assignment of radioactive isomerism is somewhat subjective as decays from all excited states follow the radioactive-decay law, but mostly with half lives that are too short to be easily measured. Thus the 1.3325.MeV excited state of giNi, in the decay of "207Co, has a half life of the order of 1 ps. but the transition is not considered to be isomeric.
726
Radioactivity
Table
measurements:
2-2
principles
Periodic
and practice
table of the elements
The elements can be grouped according to their atomic structure (and, consequently, chemical behaviour) in the periodic table of the elements (Table Z-2). Nuclides are often plotted in a Z-N table of the nuclides, with Z as ordinate and N as abscissa. A part of a typical nuclide chart is shown (with explanations) in Fig. 2-l (see, for example, Walker et al., 1977). Groups in the periodic table having similar configurations of their outermost electron shells have similar chemical properties (e.g. F, Cl and Br). Isotopes of any given element have essentially the same chemical properties.
spm and
parity
0
d
decay
modes I
2.3.2. Radioactivitv
Fig. 2-l. and activity
Part of a nuclide
chart
The phenomenon, or property, "radioactivity" is quantified in terms of the number of Some 60 years ago when radium was the most nuclear transitions occurring in unit time. important radioactive substance, it was quantified by mass, usually in terms of milligrams Later a quantity, the "curie", was defined as the amount of radon-222 in of radium. equilibrium with one gram of radium-226. Further experiments showed that such an amount of radon-222 was emitting alpha particles at a rate of somewhat more than 3.6 x 1O'O per when the use of radioactive materials multiplied, the curie was Subsequently, second. redefined as an activity of a substance such that it was decaying at a rate of 3.700 x lOi0 In SI units the quantity activity has been defined again in terms of a derived SI 5-l. unit of "one per second" (s-l) with the special name (and symbol) of becquerel (Bq). Because of the widespread use of radiopharmaceuticals in the practice of nuclear medicine
Radioactivity measurements: principles and practice
and the almost universal quantification of such radiopharmaceuticals in terms of "curies" or "millicuries", the unit "curie" (symbol Ci) has been temporarily retained by CGPM as a unit of activity "outside SI". In summary 1Bq = Is-', and
1Ci = 3.7~10~' Bq
The quantity activity that is used as a measure of the property radioactivity has been defined as follows (NCRP, 1985, Ch. 1.3): "The activity of the amount of a nuclide in a specified energy state at a given time is the expectation value, at that time, of the number of spontaneous nuclear transitions in unit time from that energy state". By this definition zero activity would be equivalent to stability of the nuclide, and the definition also takes into account that radioactivity is a process involving the && nuclide (or atom) and not just tzhenucleus. This is epitomized in the case of the decay of l"Re to la70s which could not occur but for the binding energy of the extranuclear, atomic, electrons (see 72.5.2). The probability of decay of some radionuclides can also be modified slightly by the effect of changes in chemical composition and pressure on the extranuclear electronic configurations (Harbottle and Maddock, 1979). The activity concentrations in some radioactive substances that occur in nature or derive from industrial applications are given in Table 2-3. Because of the large variations of these data in practice, only orders of magnitude are given. 2.3.3. Ouantities derived from the auantitv activity "Activity" pertains, by definition ((2.3.2), to one type of nuclide only. Therefore a number of secondary quantities must be derived from the general definition of activity for The term "activity" must always be used with caution, and practical applications. preferably in the context of the specific nuclide (e.g. "the activity of a "Co source"). A quantity that should first be exactly defined is the "specific activity". In agreement with the general use of the term "specific" and the definition of activity, the "specific activity" should be the activity of 1 g of the nuclide itself, as, for example, the activity of "Co in 1 g of 6oCo. This should probably preferably be named "specific nuclidic activity", because "specific activity" has already been defined (ICRU, 1963), as the activity per gram "of the element whose radioisotope is considered". This might be The units of any specific activity are Bq g-' called the "specific elemental activity". (old unit; Ci g-l). In practice, a most important quantity is the "activity concentration per unit mass or unit volume," which is defined as the activity per gram (or millilitre) of a sample; for gases it is either per unit volume (cm3 at STP -- Standard Temperature and Pressure, i.e. 0°C and 760 torr, or = IO5 Pa, i.e. lo5 Pascal), or par mole. It may sometimes be important to state, in addition to the activity concentration, the degree of homogeneity of the sample. The units of activity concentration are Bq g-l = se1 g-l (old unit; Ci g-') or Bq cmm3 = 5-l cme3 (old unit; Ci cmW3). For mixtures of radionuclides, the quantity "total activity" although never formally It is the sum of all nuclidic activities in a sample. defined, is of great importance. The same holds for a "total activity concentration". Because some of the quantities defined above are not yet officially adopted, it is always important to state exactly what is meant by the "activity" in question. 2.3.4. Decav schemes All radioactive transformations can be described as transitions of higher-energy atomic states into lower-energy states through reorganizations of the atom and its nucleus. The excess energy is emitted -- depending on the neutron-proton ratio in the nucleus -- in the form of different radiations. The radiations from radioactive atoms consist mainly of: o particles (doubly positively charged He++ ions), @' particles (positrons) and /l- particles, and monoenergetic conversion electrons, nuclear electromagnetic radiations (7 rays), and atomic electromagnetic x rays and Auger electrons following electron capture (of a shell electron by the nucleus), or internal conversion. The different radiation properties of radionuclides and the characteristic parameters of their decay are usually described by decay schemes. These are diagrams with the total energy as ordinate and the nuclear charge as abscissa. Transitions between energy states are shown by arrows. Branching transitions, shown by arrows starting from the same energy state, are decay modes with discrete decay probabilities, the ratios of which are called branching ratios.
727
728
Radioactivity
Table
measurements:
2-3 - Typical
MATERIAL
average
principles
radioactivity
ACTIVITY
(drink) water
of some common
materials
CONCENTRATION
Bq/g Surface
and practice
Remarks
Wg
0.0004 0.04
to
10-14 to 10-12
Mainly "'Rn + daughters
seawater
0.01
3x10-13
Mainly
4oK
Human
0.1
3x10-12
Mainly
4oK and 14C
3x10-14 to 10-11
Mainly 4oK (+U+Th...)
body
Detector construction materials
0.001 0.3
Food (plants) animals)
0.1 to
3 to 30xlo-~~
Dry substance
0.1
3x10-12
40K/87Rb/lJ+Th = 10/1/l
0.1
3x10-12
Mainly 220Rn
0.5
1.5x10-11
K/Rb/Th/U = 10/3/1/l
1.5
5x10-1'
K/Rb/Th/U = 10/1.5/1/l
0.15 to 150
5x10-12 5x10-9
Carbonate
and
rocks
Air (in buildings Mean
to
x 0.7)
soil
Granits (igneus
rocks)
Medical
springs
to
222Rn -I
,%i;?
226Ra +
4oK
Phosphate
fertilizer
40
10-9
Mainly
Low-level
waste
< 400
< 10-8
IAEA (1970) definition
1.2x104
3.3x10-7
Specific Activity
Intermediate-level waste
400 to 4x108
10-8 to 10-2
IAEA (1970) definition
4OK (Th = 1.3x109
2.6~10~
7x10-6
Specific Activity (y act.
238" (T,, = 4.5x109
a)
a)
x 0.1)
> 4x108
>
2.2x109
0.06
Specific Activity
bOCCl (T% = 5.26 a)
4.2~10~~
103
Specific Activity
Burnt LWR fuel element (0)
4x1014
104
Fission products + actinides; t=O
Burnt LWR fuel element (150)
4x1012
24Na
3x1017
High-level
waste
239P, (Q-h = 24,000
10-2
a)
Fission products + actinides; 150d cooling 9x106
(Tb = 15 h)
Numerical data from Castren (1985), Sauter (1983), NCRP Jaeger and Hubner (1974), ICRU (1972) and others. Some examples
of typical
decay
schemes
Solidified; Cooling needed
Specific Activity
(1976b),
are shown and explained
NCRP in
(1975), Fig. 2-2
Radioactivity
measurements:
Typical
Fig. 2-2.
principles
decay
schemes
729
and practice
of radionuclides
Corresponding data in tabular form are given in Table 2-4 together with data for some important radionuclides not included in NCRP (1985), in which nuclear data for many of the not listed here can be found. In special collections of decay schemes further data are given and parameters are discussed in more detail (see, for example, Lederer and Shirley, 1978; Kocher, 1981; NCRP, 1985). Table 2-5 gives preferred methods for measuring the activities of the 13 radionuclides listed in Table 2-4, together with many other important radionuclides. 2.3.5. Disinteeration
probability
As radioactivity is a stochastic one cannot predict when a radioactive phenomenon, atom will decay and exactly how many decays will be counted in a given interval of time. But, for a mean value, or expectation value, E(n) of the number of atoms decaying in a given time the probability distribution, P, around E(n), of the number of decays occurring in that time can be calculated, because the radioactive decay process follows, except for extremely low decay rates, the Poisson probability distribution (see 73.4.2; Haight, 1967; 1974; Mann et al., 1980). This law states that the Feller, 1968, 1971; Frigerio, probability, P,, of n transformations occurring in the given interval of time is [E(n)]" emE(") P,
=
(2-l) n!
where E(n) is the only parameter is not too small.
of the distribution
for integral
For larger values of n the Poisson distribution symmetrical normal ("Gaussian") continuous distribution P, = [2aE(n)]-'
ev-x*/2E(n)
1 ,
can
be
n, and provided
well
that E(n)
approximated
by
the
(2-2)
where x = [n-E(n)] and 1x1 << E(n) (see Fig. 2-3). This distribution function can be much more easily calculated. The difference in the values of n calculated from these two distributions is less than 1% at a mean of 10, about 0.1% at a mean of 100, and so on (see Fig. 2-4).
730
Radioactivity
measurements:
-2
principles
-1
and practice
l2
l1
0
x/u Fig. 2-3
Normal ("Gaussian") distribution of the probability density for a mean p = E(n) = 1 and a standard deviation D = 1
Poisson and normal decay-probability laws may be used to derive The many characteristic orooerties of radioactive decav. The most imoortant is. that the estimated standard deviation of a measured number of events (e.g. counts) is equal to the square root of the number of these events (NCRP, 1985).
t
0 30
I.
40
50
60
,
70
Oo,o
o,q” 80
90
100
110
I20
IO
nx Poisson
The Poisson distribution Fig. 2-4. distribution (vertical bars) for mean values of 50 and 100: Normal distribution (circles) for mean value of 100
The Poisson distribution for count rates is equivalent intervals of time between counts, and each can be derived form of a Poisson time-interval distribution is P (L>d)= exp(-rt)
I
to a similar distribution for from the other. The simplest
(2-3)
the probability that a time interval larger than d will occur for a mean where PC,,,, is Some properties of radioactive decay can better be understood, if count rate of r = l/d. the time distribution is used instead of the event distribution (Miiller, 1973). However, the Poisson distribution holds exactly only for ideal conditions, as, for in the measured interval of time is example, that the number of decays of a radionuclide negligible compared with the number of atoms of the radionuclide present, that there is complete independence of all events from each other, and that the background approximates a Poisson distribution. These conditions are not always fulfilled in practice, especially at low count rates and for dead-time distortions of the Poisson distribution at high count rates. These distortions are best understood, if the time-interval distribution (Eq. 2-3) With a finite dead time, T , of a counting equipment, is considered. the interval distribution can only be finite for times t DT (the truncated Poisson distribution). This leads to a narrowing of the Poisson distribution of the numbers of events (shifted exponential). There are several other effects which distort the observed distribution that must be carefully considered, such as the possibility of perturbations being introduced by scalers.
Radioactivity
Table 31( B-
DmxY
2-4
1 m.i
aw
22NA
II+
DIKXY
Radiation
I,l#IN,=
mtmsity
‘8.600 5.685
10 4
t2.602
Y
A”O.C_K I
mex
aw
545.9 215.50
1 xsak
B’S
*IBIN,=
Intensity
radionuclides
9.20
89.89 CEl#
0.101
5
0.412
Energy
,k*“l _________
AUg*r-I
x-ray K-ray X-ray x-ray
204TL
K.diation
TYPa TYP* ---------
rnt.n.ity
,k.“, _______--
0.0006 0.0004 0.103 0.0198 0.0066
94.43
7
0.344
5.53
I
0.0489
99.96
10
IC
PICAY
Ic.di.tion
t2.,2
,x1 _________
Y 21
-----___-
0.0025
3
1.20
Auger-l Auger-K
Intmslty CX) _________
0.6 5.19
X-ray X-ray K-r*y
I K(I> KO, Kg
x-ray
139 60.7
0.64 5.88765 5.89875 6.49
3 3
I KO, K(1, K#
B-
DSCAY
1ntsnsity
Alg-rad,
(X1 _________
#.Ci-h, ________
7.6
1.23
9
0.0002
10 68.8950 70.8190 80.3
9 12 18 9
0.0002
20 20
0.75 0.420 0.711 0.314
t3.7s
Y 2,
Kn.rgy Ck.“) __----___
4
0.42 8.2 16.3 3.79
21 14 7 12 25
B-
DllCAY
(5.2714
Y
5,
IIIIIN,=
cx, ____--___
0.0011 0.0005
0.101
nlt.n.ity
ACg-r.d/
,I, _____---_
___-
pCi-hl -___
0.506
0.101
ACg-rad, rCi-h) ________
ansrgy , *a”,
0.0018 0.0067 -0 0.0010
0.0020 0.0005
&i-h) ________
11.2 13 23.2 10 6.35 25 2.34 10 0.176 8
0.0013 O.OlS4 0.0071 0.0028 0.0004
0.300 31.7 68.0
0.0328 3.55 7.71
20 9 4
6
0.101 Atg-rad, Ji-h) --______
0.101
Alg-rad,
Intensity (X1 ___ ______
(XII
Intmw.ity
0.0006
III(m)=
12.2 13 0.2011 6OCO
o.oo,o
big-r.d/ &i-hl
3,@!IN>=
Kll.l-JY tkm”, __--_____
VP
---_____-
=0 0.0014
7 12 5
TC”IN,= 55PK
0.398
3
0.061)
TYPt, _________
ml.rgy
5 21 5 3 19
3.68 1.34 85.1
Radiation
Radiation
Atg-r‘sd, )&i-h, ____- ___
1.0 1.99
0.0002
11
=
1nt.nsity IX1 _________ 7.3 0.77 7.78 1.42 0.472
beg-rad, #&i-h’ ________
lx, _________
omitted
selected
731
0.0121
11
5 21
of
and practice
0.10%
100
0.82
principles
ACg-Tdl rCi-hl ___-____
cx, _________
KlIargy Cb”, _________
TYPO _________
Decay data
1,
,k.“, ____-____
TYPO ___-_____
,9’
Y
mmrgy
Il.diati.2”
s-
(12.35
measurements:
=
0.07X)
0.0034 0.0003
732
Radioactivity
measurements:
principles
and practice
_________ _______ __ ce-r-2
0.9 0.4 4.9 cl.21 1.5 0.24
5 4 7
0.7 1.70 4.2 5.0
20 3 5
2.09 1.50 0.22
8 20 3
7.417
1
_________ ________ 12.9
4
P.OO2cl
Radioactivity measurements: principles and practice
Table 2-5.
733
Preferred methods for activity measurements of selected radionuclides
Radionuclide'
Half life2
Radiations3
Methods4 for standardization
3H :? 18; 22Na 24Na ;;A1 33; 35s 36Cl 37Ar 40K 42K 45Ca 46% 51Cr 54Mn 55Fe 56M, 56co 5’CO %o
59Fe 59Ni 60~0 63Ni 64cu 65Zn 6'Ga 68~e+68~a 74As '5% 79Kr 82Br 85Kr i3Sr Y a9Sr ;;sr+90y 91; 94Nb 95Nb 95Zr+95mNb 99Mo+99mTc ;;;%&+'""Rh llOrnAg ;;;sIl+113rnI, I ;;;Sb 129; 13OI 131I 131cs 131nlX, 132T,+132I 133B, 133X, 1%
;;;%;;13'mB, 139C, 140Ba+140La 14OL, 14lC, 144Ce+144Pr
12.35 a 53.28 d 5730 a 109.7 min 2.602 a 14.96 h 7.2 E5 a 14.29 d 25.34 d 87.44 d 3.01 E5 a 35.0 d 1.28 E9 a 12.36 h 163 d 83.79 d 27.70 d 312.1 d 2.72 a 2.577 h 77.9 d 271.7 d 70.82 d 44.51 d 7.5 E4 a 5.271 a 96 a 12.70 h 243.9 d 3.261 d 270.8 d 17.78 d 119.8 d 35.04 h 35.34 h 10.72 a 64.85 d 106.6 d 50.5 d 28.5 a 64.0 h 58.5 d 2.03 E4 a 35.0 d 64.0 d 65.92 h 367 d 462.6 d 249.8d 115.1 d 13.22 h 60.20 d 59.6 d 1.57 E7 a 12.36 h 8.021 d 9.69 d 11.9 d 76.3 h 10.5 a 5.243 d 2.065 a 30.0 a 2.553 min 137.6 d 12.76 d 40.28 h 32.50 d 285.0 d
fl EC p p+ EC
18.6 7 156.5 EC B+ 7
;+7EC 7 /3 1710 fl 249 /3 166.7 j3 709 (EC) EC B EC 7 UJ+) ; 7257 B 7 EC 7 EC 7 a""7 EC B+ 7 EC 7 EC B+ 7 Br 5"7 B 65.9 B EC 8+ EC B+ 7 EC 7 EC B+ 7 B 7 EC 8+ EC 7 EC 7 8+ ;: EC 7 EC 7 B+ B 1463 B (7) ,9 2283 B (7) ;: ;: Pr EC 87 EC EC Br EC
7 7 7 7
;: Br EC ;7 EC 7 ,":: 87 7 EC 7 Br ;: B7
I s I c E E c P P I P I L C P c c c S E E E E E S E M P E El s s El I1 E I E E L P P P E E E E El E E s El E w c E E P 11 P E I E T s E E E E E
0.3 0.3 0.3 0.5 0.3 0.1 0.3 0.3 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.1 0.3 0.3 1 0.1 0.3 0.3 0.3 0.3 1 0.1 0.5 0.5 0.5 1 1
0.3 0.5 0.3 0.3 0.5 0.3 0.3 0.3 0.1 0.3 0.3 0.5 0.5 0.3 0.5 0.3 0.5 0.5 0.3 0.5 0.5 0.5 0.3 0.5 0.3 0.5 0.3 0.5 0.5 0.3 0.5 0.5
M MPT s CW SW s TM TM PTM TM SP SPE TM SW SW SW PM SPE S UP SW ESW PM S ITP SW S SW PW PW CPU SW SW s WC WC PTM WLM WLM WML C SW S CPL CPL US SWL w S WS PCS SPL SWL LS TS S SW SW s EW PTW w W W WP WPT TWL
routine work
Ll s Ll Sl s s s Ll Ll L Ll I2 s s Ll s s s s s s Wl s s s s L Sl s Sl s s s s Sl s s s Ll L L Ll s s s Wl s Pl w Wl W2 w Wl Pl w Wl Wl s2 Wl w s w s s s w s Wl Pl
0.5
0.5 0.5 0.5
2
1 2 0.5 0.5 0.5 2 0.5 0.5 0.5 0.5 2 0.3 3 0.5 2 2 2 2 2 0.5 0.5 0.5 0.5 0.3 0.5 0.5 2 0.5
0.5
0.5
0.5 1 0.5 0.5 0.5 0.5 0.5 0.5
(S) w P(S) w w WL w us P(S) P(S) PSW (S) PLW WPL P(S) WL w w UP WPL w SP UP WL UP WL (S) w w w PW PW UP UP w IW w w WSP SUP SUP SUP WL WL WL SPL PLW us SLW S s s PS LS SL LS SP w SL SPL SL WL w WL SL WL SLW SLW
Radioactivity measurements: principles and practice
Table 2-5 cont'd 14'P, 152EU 154ElJ :;;EU Yb l'OT, '*lHf gTa w 1921, 195AU 198AU 199ALl 2OlTl 202Tl 203Hg 204Tl 207Bi 210Bi D 2lOP0 222Rn D 226R, D 227Ac D ;;;Th D U D 233P, (D) 233U (D) 234U (D) 235U (D) 236Pu D 238U D ;;;Pu (D) U D 23gNp (D) 23gPu (D) 240Pu (D) 241Pu D 24111, (D) 242Pu (D) 243Am D 243Cm (D) 244Cm (D) 24gCf (D) 252Cf (D)
2.623 a 13.4 a 8.55 a 4.72 a 32.03 d 128.6 d 42.4 d 114.4 d 75.1 d 73.83 d 183 d 2.696 d 3.139 d 72.91 h 12.2 d 46.60 d 3.77 a 32.2 a 5.013 d 138.4 d 3.824 d 1600 a 21.77 a 1.4 El0 a 72 a 27.0 d 1.59 E5 a 2.45 E5 a 7.04 Ea a 2.85 a 4.47 E9 a 87.74 a 23.5 min 2.355 d 2.41 E4 a 6564 a 14.4 a 432.2 a 3.76 E5 a 7380 a 28.5 a 18.11 a 351 a 2.64 a
p 224.7 B EC 7 W+) ;; EC -Y B -r (EC) B 7 ; 7432.6 B EC Y EC 7 ;
‘7
EC
7
EC
7
B
7
B
(EC)
EC
7
P a a
(7)
;
;
a
7
;
5
a
7
a
7
0
7
(1
7
a
7
;
;
B
7
a
7
;
a 0
(a)
2i.82 7 -7
: a Q
; (EC) 7
a
7
7 n
P w c Cl w P c c P w c c c c c c P w P s s s s s c s s P s P s P P s s P2 s s s c s c s
0.5 0.3 0.3 0.3 0.5 0.3 0.3 0.5 0.3 0.5 0.3 0.5 0.5 0.3 0.5 0.5 0.3 0.5 0.3 0.5 1 0.5 0.3 0.5 0.1 0.1 0.5 0.3 0.5 0.1 0.5 0.5 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.3
TM L LW LE c TCL SL PWL TLM CP LW SL WL WL WL WL LTM c TL PL PLC PLC LPC LPS LP LP LPS LP LS LP CL CL LP LP TM CLP LP CLP SLP LP SLP LP
Ll s w Wl w s Wl Ll s w s Wl s s s Pl w Ll s I Sl s s s Sl s s s s s s Sl s s s L3 s s s s s s s
0.5 0.5 0.5 1
0.5 0.5 0.5 1 0.5 1 0.5 0.5
P(S) PWL SL LS s PWL SPL PL WPL SL WL L WL WL WL LW SL WP LP PLW
1 1 1 0.5 0.3 0.5 0.5 1 0.3 1 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.5
LP LP WLP LP LP LP LP LP LP PL LP LP LP P LPW LP LP LP LP LP LP
735
Radioactivity measurements: principles and practice
2.3.6. Radioactive-decay
laws
Radioactive decay is exponential in time. This follows simply from the proportionality of the activity (decay rate) to the number of atoms, N, of the radionuclide present; that is A = dN/dt
= -XN ,
(p-4)
where X is the decay constant. Integration of Eq. 2-4 leads to N, = N,exp(-Xt)
,
(Z-5)
where N, (and -AN,) are the numbers of atoms (and activity) of a given radionuclide with the decay constant X in the given sample at the time t = 0, and N, (and -AN,) at the time iY. The decay constant X is, for practical reasons, usually replaced by the half life T%, the time in which an amount of a radionuclide (or its activity) is reduced by a factor of in which the number N, decays to N,/2. Analytically, NJ2 = two, i.e. the time T N,exp(-XT%), therefore'l'% = ln2/X, and, finally, N, = N,exp(t ln2/2'%) = N,exp(-0.69315t/T$
(z-6)
The observed half lives of radionuclides range over more than 40 orders of magnitude, from just measurable parts of a femtosecond (about lo-l6 s) up to about 10zo years. The radionuclides mostly in use have half lives of hours, days, years and up to thousands of It is interesting to remember that after 10 half lives the number of radionuclide years. atoms is reduced by a factor of 2lo = 1024, i.e. about one thousandfold In health physics and nuclear medicine the biological half life, Tb, is of great importance. It is the time required for a biological system to excrete half the amount of any nuclide introduced into it. In health physics or nuclear medicine this is clearly relevant to any injected or ingested radionuclide in the human body and the resulting dose to various organs in that body. If the decay is not negligible and T,,, is the resulting, effective, half life of residence of the nuclide, and Tti is that of the injected or ingested nuclide, then
l/T,,,
= l/Tb + l/Th
,
or, in terms of probabilities, Lff =&+X 2.3.7 Radioactive f&lies
.
(decay chains. series1
The products of radioactive decays are often also radioactive daughter products. high atomic number Z most, and for Z > 83 (Bi), all nuclides are radioactive.
At
Because mass-number changes are only possible by a decay, all heavy nuclides can be grouped into four families (decay chains) with the atomic-mass numbers A = 4n, A=4n+l. A = 4n + 2 and A = 4n + 3 (Table 2-6). Three of these families are found in nature (natural radioactivity), commencing with their very long-lived parents '=Th, “% and 23%l. Many of the members are of importance in the nuclear-fuel cycles. It is often very important, to take the radioactivity of the daughter products into consideration. In some cases, they may cause strange effects due to their physical properties. For example, gaseous or volatile daughter products could contaminate counters or samples. And they contribute, of course, to the total activity of a sample in which they are being generated (see also (2.7.7).
Radioactivity measurements: principles and practice
736
Table 2-6 - The four decay chain of heavy elements (main branches only, Z 5 100)
A = 4n+l Neptunium series (artificial)
A = 4n Thorium series 252 100Fm 25.4 h
CI
257 100Fm 101 d
248 9*Cf 334 d
a
244 96011 18.1 a
A=4n+2 Uranium-Radium series
A=4n+3 Actinium series
o
254 100Fm 3.24 h
a
255 100Fm 20.1 h
a
253 g8Cf 17.8 d
fi(u
250 g8cf 13.1 a
a
251 98Cf 898 a
a
a
253 ggEs 20.5 d
a
246 g6Cm 4730 a
a
247 g6Cm 1.6xlO'a
a
240 94Pu 6564 a
a
249 Bk 320 d 97
P(a
242 94Pu 3.76x105a LI
243 g4Pu 4.96 h
p
236 92U
a
249 g8Cf 351 a
a
238 g2u
243 g5Am 7380 a
o
232 9OTh 1.41~10~~a a
245 g6Cm 8500 a
cz
2;;Th 24.1 d
j?
';;Np 2.36 d
228 88Ra 5.76 a
P
241 g4Pu 14.4 a
P(a
234 glPa 6.70 h
/J
239 g4Pu 24.1x103a a
228 89A~ 6.13 h
B
241 g5Am 432 a
228 90Th 1.91 a
LX
237 g3Np 2.14x106a LL
230 gOTh 7.54x104a a
231 gOTh 25.5 h
224 88Ra 3.66 d
a
233 glPa 27.0 d
p
226 Ra 1600 a 88
a
231 91Pa 3.28x104a a
220 Rn55.6~ 86
a
233 g2u 1.59x105a
a
222 86Rn 3.82 d
a
227 8gA~ 21.8 a
216 84Po 0.145 s
a
229 gOTh 7340 a
a
218 84Po 3.05 min
CI
227 gOTh 18.7 d
a
212 Pb 10.6 h a2
P
225 88Ra 14.8 d
p
214 Pb 26.8 min 82
p
223 88Ra 11.4 d
c1
212 . 83B~ 60.6 min
a,,L
225 8gAc 10.0 d
a
214 83B~ 19.9 minp(a)
219 86Rn 3.96 s
(I
208 81Tl 3.05 min
@
221 87Fr 4.9 min
a
214 84Po 164 ~LS
215 84Po 1.78 ms
c1
212 84Po 0.298 !_Ls a
217 85At 32.3 ms
a
210 82Pb 22.2 a
/3(o)
211 82Pb 36.1 min
p
208 Pb stable 82
213 83B~ 45.6 min p(a
2iiBi 5.01 d
P(a)
211 83B~ 2.14min a(P)
2.34xlO'a
a
234 g2U
4.47x109a a
2.45x105a a
13 84Po 4.2 ps
(I
210 84P0138d
09 Pb3.25h 82
0
206 Pb stable 82
cx
a
P(a:
235 g2u 7.04x10*a
07 81Tl 4.77 min
a
p(o:
P(a)
p
07 82Pb stable
09 83B~ stable Data taken from NCRP (1985), Westmeier and Merklin (1985) and Nuclear Data Sheets Mean tropical year, 1 a = 365.2422 days.
Radioactivity
measurements:
principles
and practice
737
2.4. RADIATIONS 2.4.1.
Introduction
All radionuclides release energy in the form of radiation. Some are primordial, and others are produced by different processes in nature (e.g. cosmic radiation) and technology The naturally-occurring radionuclides are the members of the three (e.g. by accelerators). natural decay series (q2.3.7) the precursors of which, along with 4oK and "Rb, have half lives comparable with the age of the solar system. Most radionuclides in common use are produced artificially by irradiation of selected nuclides by certain kinds of particles, generally by thermal neutrons in reactors or by protons, deuterons, or ionized helium atoms in accelerators. The discussions here are largely electrons substances ~seean~2~~,~arti~~~tr~~~, discussed,
and others
are mentioned
restricted to those radiations, such as a particles, e~~;~:;~,anetic radiations emitted by radioac.tive and fission products are only brlefly only in passing.
All these radiations differ, not only in mass and charge, but especially in their absorption and attenuation in matter, scattering, and, consequently, in their energy deposition and range. Their general properties are described in this chapter while the details of their interactions with matter, which is important for their detection, are discussed in 74.3. Here the terms "radiation", are used interchangeably. 2.4.2, Aloha
"ray" and
"particle"
all have
almost
the same meaning
and
Particles
Alpha particles are the heaviest particles emitted by radionuclides, except for (i) fission products which are only rarely emitted by radioactive species, and (ii) a recently-discovered and puzzling mode of decay, sometimes called "exotic decay". The spontaneous emission of protons and neutrons has been known to occur, for some time. But, more recently, the emission of heavier fragments, predicted by some theoreticans, has been observed, the best known cases being particles of 14C emitted by certain radium isotopes, with a probability of 10m9 or less (see Rose and Jones, 1984). Still heavier fragments, up to magnesium, have since been found with still lower branching ratios. This new decay mode may be interpreted on the basis of a super-asymmetric fission model. But alpha particles are still the heaviest form of spontaneous radiation to lie within the scope of this report. Alpha particles are doubly-charged positive ions, and thus are bare nuclei. Alpha Their mass is 4.001506 u (u = particles from nuclear transitions are always monoenergetic. the atomic-mass unit, relative to lzC = 12), which is equivalent to an energy of 3,727.409 MeV; their kinetic energies, when emitted from radioactive sources, are mostly around 5 MeV (with energies ranging between 2 and 11 MeV). Alpha-particle energies for calibration purposes are discussed in ~4.11.2.5. The kinetic energies of o particles are approximately equal to the mass-equivalentenergy difference between parent and daughter atoms minus the mass-equivalent-energy of the He atom, and minus the recoil energy of the residual nucleus (about 2%). Monoenergetic groups of alpha particles of slightly different energy are often emitted from the same nuclide, indicating branching decays to different excited states of the daughter (or from different excited states of the parent). The energies of alpha particles and the half life of the emitting nucleus are strongly interconnected, the latter being shorter for higher energies (Geiger-Nuttall rule). The half life can be calculated using a simple barrier-penetration theory. Because of their relatively large mass and charge, a particles suffer strong energy absorption and low scattering during their passage through matter (74.2.2). Therefore, they have short ranges and nearly straight paths in matter. Fig. 2-5 shows the ranges of (I particles of different energies in different materials (Northcliffe and Schilling, 1970). Five-MeV alpha particles, the most common alpha-particle energy, have a range of about 3.5 cm in air at STP which is equivalent to about 4 mg/cm' or 0.03 mm (35 pm) of tissue. (The protective dead-cell skin layer is about 70 pm,) Alpha particles are emitted by most nuclides used as nuclear fuels. Therefore their accurate measurement is of great practical importance. For this and many other standardization purposes 241Am (Fig. 2-6) is an ideal reference nuclide. Its half life (432 a) and consequently its specific activity are very convenient for accurate measurements and its decay scheme allows these to be carried out by different methods, especially by 4s~7 coincidence and by low-geometry defined-solid-angle counting. Furthermore, stable and very thin z41Am sources can be rather easily prepared, e.g. by electrolysis, < "Beta terms used
particles" (@‘) and "electrons" (e-), also sometimes called "negatrons", are for identically the same particles that carry the negative elementary charge.
738
Radioactivity measurements: principles and practice
l/IlIIlIl 0.1
Fig. 2-5.
Fig. 2-6.
0.2
I 0.5
1
2
5
10
2-3
50
100
Mean range of protons and alpha particles in different materials (numerical data taken from Barkas and Berger, 1964; Williamson et al., 1966; Bichael, 1967; and Northcliffe and Schillings, 1970).
Typical alpha-particle energy spectra (241Am) taken with a high-resolution surface-barrier and a low-resolution thin plastic detector.
The first term is used if the particle originates in a nucleus, and the second for particles emitted from atomic shells. Electrons, stemming from decay interactions with atomic shells, namely internal conversion and the Auger effect, are monoenergetic, while beta particles always show an energy distribution from zero to a maximum, Em, that is typical for a given pure beta emitter (Fig. 2-7). Positrons (8') are positively-charged beta particles with continuous-energy spectra; monoenergetic positive electrons are never emitted from the nucleus in a radioactive transition.
Radioactivity measurements: principles and practice
-6
94.6 % E.. 511.6 keV 5.4 % E,; 1173 keV
-5
739
conversion electrons
-4
dN(E)/(dE
‘dt)
1
n
-2
54 -1
E CkeV)
\i
-rJ10
Fig. 2-7.
20
30
40
100
300
500
’
600
620
630
640
High-resolution spectrum of electron radiation from the 137Cs decay.
Beta particles are emitted with different energies, the remainder of the beta-decay energy being removed by neutrinos that have zero charge and very small, if not zero, mass. The neutrino is emitted in fl+decay, and the antineutrino in p decay. The shapes of the resulting beta-ray spectra (e.g. Fig. 2-8) can be rather accurately described by modern theory (Behrens and JBnecke, 1969). They depend on the degree of forbiddenness of the decay (super-allowed, allowed, first-order, second-order, third-order or fourth-order forbidden), which is determined by the difference of the nuclear spins and angular momenta of the involved parent and daughter nuclei. With a shape factor related to the degree of forbiddenness, S(E,E,), such spectra can be plotted versus particle energy E as straight lines terminating in the endpoint of the spectrum (Kurie plots), if the equation for the emission probability N(E) is written in the form: [N(E)/(f(z,E)E(E'-l)~ S(.E,.&,,) II’
=
K(E,-E) ,
(2-8)
where f(Z,E) is the Fermi factor from theory and K is a constant. Integration of the decay probability N(E) (Eq. 2-8) with respect to energy leads to the "comparative half life", ft a constant, where f(Z,E,,,)is the Fermi integral function and t = Tb is the half life of the B-decaying nucleus. The value of ft characterizes the forbiddenness of the decay. The measured log ft values vary between about 3 and about 20.
3
Fig. 2-8.
6
9
12
15
Beta-particle spectra of tritium: theoretical differential spectrum n(E) and integral spectrum N(E) derived from it (and reduced by a factor of 10).
The charge of all electrons is + e = 1.60218 x 10-l' C, the elementary charge, and their rest mass 5.48580 x 10e3 u is equivalent to 0.51100 MeV (u = atomic-mass unit). Beta-particle endpoint energies range from zero to about 2 MeV, e.g. the maximum B-decay energy of tritium is 18.6 keV, and that of "Y 2.28 MeV. Positrons are unstable and annihilate with electrons, partially even before coming to rest (annihilation in flight). The subsequent annihilation radiation consists of two photons having an energy of 511 keV each, emitted in opposite directions. This is much more penetrating than the original positrons. Otherwise positrons are similar to beta particles, but show different spectra at low energies. Monoenergetic electrons are produced through the internal and external conversion of 7 rays and in the Auger effect after electron capture or other vacancy formation in atomic shells ((2.4.5). Because of their relatively low mass and single charge, electrons are much more easily scattered and less readily absorbed in matter than a particles. Consequently their paths in matter are not linear and are much shorter in range (maximum distance from origin), and the range straggling is considerable (up to 10%). The ranges of monoenergetic electrons, which can be defined in different ways are shown in Fig. 2-9 for different absorbing
Radioactivity
740
measurements:
principles
and practice
materials as a function of energy. Because of the relative independence of electron absorption on atomic number the average range may be used for any material when the thickness is expressed in terms of superficial density. For non-monoenergetic beta particles the range can be best extrapolated using the nearly exponential transmission function of number of particles versws thickness of the absorber. The extrapolated ranges of monoenergetic electrons and of beta particle of the same maximum energy are equal within the rather large experimental uncertainties.
XT'
10-l Fig. 2-9.
12
XT'
51020
Maximum range, practical (extrapolated) range and path lengths of mono-energetic electrons (and beta radiations) in narrow-beam geometry (Kanter and Sternglass, 1962; Pages et al., 1972).
Some practical examples of the maximum ranges of ,9 particles from 3H (E,,,,, = 18 keV), 14c (E,,,,, = 155 kev), Is11 (E,,, = 0.81 MeV) and 3zP (EgmsX = 1.71 MeV), are, approximately 0.6 mg/cm', 30 m&m', 240 mg/cm' and 800 mg/cm', respectively; and these are approximately equal to the ranges of monoenergetic electrons having energies equal to E,,,,,. 2.4.4.
Electromagnetic
radiations
The radiations most often met in radioactivity are -y rays, x rays (Helmer et al., which all belong to the immense spectrum of the massless and 1978), and bremsstrahlung, of electromagnetic (Fig. 2-10). The energies electromagnetic radiations chargeless or of their quantum-theoretical counterparts (particles) can be expressed by radiation, If h is Planck's constant then the energy E is their wavelength, X, or frequency, u. given by
E=hu,
v-9)
hc E=-
or
where c is the speed in particle physics,
1n terms of the unit, electron volt, that of light. the relation between wavelength and energy is that
Thus, for example, when x is expressed in Angstram units. The corresponding wavelength of 12.398 A or 1'2.398 x lo-" m. (Hz).
&
lfJ8 10’ 106 105 104 103 102 8
I
lo' I,
1
cm lo-‘2 lo-” lo-‘0 10-9 1l.-s 10-7 10-610-510-d
x rays
Tra_nsition radia(ion
Y rays Fig. 2-10.
10-l 1o-2 I1
10-a 10-2
I
I
l-keV photon radiation has a frequency is 2.42 x 1O1' 5-l
10-a I
10-J
I
1o-4 10-5 I
1
I
1 Synchrotron radiation
The types of electromagnetic
Gamma rays originate in nuclei as a result extend from a few to several million electron typical y-ray spectrum is shown in Fig. 2-11. izations and, accordingly, their energies are shells, which is about energy in atomic The deexcitation of an excited monoenergetic.
a
is commonly used E = 12398/X,
I
10
1o-5 I
lo2
I
I
10-T I
lo3
I
Radio waves
--_
Television
radiations.
of nuclear deexcitations, and their energies volts if emitted by radioactive sources. A The x rays are due to atomic-shell reorgan-smaller than the highest electron-binding 100 keV. Gamma and x rays are always nuclear or atomic-shell state can also take
Radioactivity measurements: principles and practice
741
place by emission of atomic electrons instead of by 7 or x rays by the process of internal Radiative and non-radiative deexcitation processes are conversion or the Auger effect. always competitive (72.4.5).
0 02 04 06 08 10 12 14 16 18 20 22 24 26 Fig. 2-11.
60 Typical gamma-ray spectra of Co taken with a NaI(T1) or a Ge detector (with the source close to the shielded detector).
The probability of gamma-ray emission depends strongly on spins, angular momenta and The gamma-ray-emission processes are therefore parities of the involved nuclear states. classified according to these parameters, as is shown in Table 2-7 fable 2-7
Selection rules for gamma-ray transitions
1
Multipole order
Symbol
AI1)
i2)
An3)
Possible small admixture
Electric dipole
El
0,l
1
Yes
M 2;4)
Magnetic dipole
Ml
0,l
1
TlO
E 2;4)
Electric quadrupole
E2
2
2
IlO
M 3:5)
Magnetic quadrupole
M2
2
2
Yes
E 3;5)
Electric octupole
E3
3
3
Yes
M 4;5)
Electric 2'-pole
El
1
1
no for even P yes for odd I
M(P+1);5)
Magnetic 2'-pole
M1
P
P
yes for even 1 no for odd 1
(a+1);5)
-
1
1) Vector difference of the initial (Ii) and final I(f) angular momentum of nucleus; Ii = If = 0 absolutely forbidden 2) Angular momentum of predominant radiation 3) Parity change in nucleus 4) Absent if Ii = If = l/2 for AI = 0 and if Ii or If = 0 5) Absent if Ii or If = 0 The third electromagnetic radiation, bremsstrahlung, is quite common in radioactivity but is mostly only of very low intensity. It is produced whenever electrons, or other charged particles, are decelerated or accelerated, and can originate in the nucleus (internal bremsstrahlung) or, but with higher intensity, outside the emitting nucleus (external
Radioactivity
742
measurements:
principles
and practice
Unlike 7 and x rays, bremsstrahlung shows a continuous energy spectrum bremsstrshlung). extending to the maximum electron energy and its intensity is orders of magnitude smaller than that of the original process (e.g. p-ray emission). But it can dominate when other for example the radiation outside %r - "Y or i4'Pm heat radiations are suppressed; sources, or outside ampoules containing solutions of pure ,9 emitters, is often exclusively bremsstrahlung. The deexcitation of an excited level can not only take place there is always competition between internal-conversion electron (see 172.4.5 and 2.4.3). emission Other electromagnetic radiations can be encountered in annihilation radiation (y2.4.3) and Eerenkov radiation (74.7). The millions detector)
attenuation of electromagnetic radiation geometry" (collimation in a "narrow-beam follows the exponential law N = N,e-llx
by -r-ray emission, as emission and y-ray
radionuclide
metrology
are
in the range of electron volts to before the absorber and before the
,
(2-10)
where N, and N are the numbers of photons before and after attenuation, and p may be given or better linear attenuation coefficient" "narrow-beam linear in cm-' as the "total attenuation coefficient", or in c&/g as "mass-attenuation coefficient" replacing JJ by p/p, In the first case the thickness x of the absorber where p is the density of the absorber. the "surface, or superficial, in SI units must be given in cm, in the second in g/c&, Fig. 2-12 shows examples of mass attenuation density" (i.e. mass per unit surface). The attenuation law (Eq. 2-10) can be also written in terms of a half-value coefficients. thickness X~ (reduction of the photon flux by one half): N = N e-O.@3Wx, 0 Also
(2-11)
see 75.2.2.3.
Fig.
2-12.
Gamma radiation (narrow beam) mass-attenuation coefficients for different materials and energies (numerical data taken from Grodstein, 1957; McMaster et al., 1969; Hubbell, 1977).
In general one has broad beams comprising The narrow-beam case is rather unrealistic. In this case all the secondary radiations from the absorption and scattering processes. the exponential attenuation law must be supplemented by a build-up factor B, which yields (2-12)
N = N,Be-'x The calculations of build-up factors are difficult, high values, of up to 1000 in extreme situations.
but very
important,
because
B can reach
Of the other known electromagnetic radiations, only cerenkov radiation (T4.7) may be 1975; Kleinknecht, 1984). Eerenkov important in radioactivity measurements (Randolph, ultraviolet region of light, is always with a spectrum in the visible and radiation, emitted when a charged particle traverses a medium, of refractive index n, with a velocity In media with high n (e.g. Perspex v greater than the speed of light in the medium (c/n). radiation is already generated by for which n = 1.51, or water with n = 1.34) &renkov 230 keV for Perspex electrons of rather low energy (Egmln = v/c = l/n), of approximately
Radioactivity
and 260 keV for water. the Eerenkov radiation activity of p emitters
measurements:
principles
and practice
743
Although the intensity of the radiation is very low, measurement of may, in some cases, be the most suitable method for measuring the (Kleinknecht,l984).
Bremsstrahlung can also be used advantageously in radionuclide example the assay of tritium in bulk (Curtis, 1972) or the measurement solutions if high-energy beta emitters in ampoules (A. Spernol et al., Annihilation radiation is less frequently used in radionuclide properties are utilized for many useful applications.
metrology, as, for of the activities of HN, p. 169, 1973).
metrology,
but
its special
Other electromagnetic radiations, such as transition radiation (emitted if high-energy particles traverse the boundary zone between two media) or synchrotron radiation (a kind of very low-energy bremsstrahlung in magnetic fields; Watson and Perlman, 1978) play no role in radioactivity measurements. 2.4.5. Atomic-shell
radiations
followinp. nuclear
orocesses
As the atom is normally in its energetically most favorable state, a minimum-energy equilibrium between the positive nucleus and the negative electronic cloud around it, every transformation also affects the atomic-shell structure, and causes atomic nuclear radiations. The usual classical atomic model provides an explanation for the atomic-shell radiations. It assumes that the electrons surround the nucleus in well-defined stable shells, The electronic binding energies depend on the atomic named K, L, M, etc. (Fig. Z-13). number, 2, and vary between fractions of an electron volt and a maximum of about 100 keV nuclides (Table 2-8) Therefore, in general, the radiations from atomic for very heavy shells are of low energy and are often negligible compared with the energies of the nuclear radiations. But in some cases, especially for electron capture (EC) by the nucleus. atomic radiations may be the only observable effects of the nuclear transformations.
M V
M
IV III II
I
L
Ill II
K Fig. 2-13.
/
i
2
512 312
3
2
3 3 3
1 1 0
3/2 j/2 v2
2 2 2
1 1
3/2 v2
0
l/2
1
0
l/2
Innermost atomic shells (K, L, M) and main possible x radiations; n and 1 are the principal and azimuthal quantum numbers, respectively, and j = J?++ is the inner quantum number.
Radioactivity
744
Table
measurements:
2-8 - Some atomic binding
:1ement
K
Ll....L3
principles
energies,
and practice
in keV,
Nl....N7
Ml....M5
in the different
01...,05
1H
0.016
10Ne
0.870
0.049 0.022
to
2oC=
4.038
0.438 0.346
to
0.044 0.025
to
3oZn
9.659
1.201 to 1.022
0.140 0.010
to
4oZr
18.00
2.532 2.223
to
0.430 0.179
to
0.051 0.028
to
508n
29.20
4.465 3.929
to
8.885 0.485
to
0.137 0.024
to
bONd
43.57
7.126 6.208
to
1.575 to 0.980
0.319 0.002
to
0.038 0.022
to
7o=J
61.33
10.49 to 8.94
2.398 to 1.528
0.480 0.001
to
0.052 0.024
to
80Hg
83.10
14.84 to 12.28
3.562 2.295
to
0.802 0.100
to
0.127 0.008
to
9OTh
109.65
20.47 to 16.30
5.182 3.332
to
1.330 to 0.333
0.290 0.085
to
1ooFm
143.1
7.205 4.498
to
1.937
27.70 20.90
to
* Extrapolated
values
shells
Pl....P3
0.041 0.017
to
*
for fermium
If a shell electron is captured by a nucleus, a vacancy is left in the shell, which is shell with the quickly (within approximately 10-'3s) filled by electrons from an outer emission of energy in the form of a succession of Auger electrons (Burhop and Assad, 1972) The number, kind and energies of these radiations depend on the and x rays (Dyson, 1973). capture probabilities P,, P,, P,, ___ (P,/P,/P,/... are approximately l.O/O.l/O.Ol/...), and the fluorescence yields for the different shells K, L, etc. (Bambynek et respectively, fractio:1 emitted The sum of the fluorescence yield, w1 (the al., 1972; see Fig. 2-14). yield, ai, is equal to one (w, + ai = 1). for an ith-shell vacancy), and the Auger-electron The filling of a vacancy by the Auger effect yields two further vacancies in outer shells conserves the (inclusive of all secondary processes), while x-ray emission (fluorescence) Both electron capture and positron emission reduce the nuclear charge number of vacancies. these two decay modes are competitive transitions, provided they are Therefore, by one. Fig. 2-15 shows some typical EC(K)/fl' ratios (Band et al., 1976, energetically possible. 1978) as predicted by theory.
0 Fig. Z-14.
10
20
30
40
50
60
70
80
90
Fluorescence yields, w , in the different atomic shells (numerical data mainly from Bambynek et al., 1972).
Radioactivity measurements: principles and practice
Fig. 2-15.
745
2 34 OS 1 0.2 0.02 0.05 01 Examples of theoretical estimations of K-electron-capture to positron-emission ratios, EC(K)/fl+, for allowed and firstforbidden non-unique transitions (numerical data taken from Zweifel, 1957,and Zyryanova and Suslov, 1968).
Very similar atomic-shell effects, to those following electron capture, occur if an atomic-electron-shell vacancy is formed by internal conversion (IC) instead of emission In this case the whole energy of the electromagnetic of a nuclear 7 ray (72.4.4). radiation is transferred to a shell electron, and in addition to the emitted monoenergetic conversion electron, the whole cascade of shell processes takes place, as in the case of electron capture. The probability of internal conversion, P,, relative to the probability of -y ray emission, P,, is given by the internal-conversion coefficient, a, which is equal The total internal-conversion coefficient is the sum of the conversion coefficto PJP,. ients in the different shells, namely ot = oK + uL + oM + . . . . . where czK= PK,/P,, etc. The numerical values of the total internal-conversion coefficients range between the measurable limits 10m5 to lo5 (Carlson, 1975). All atomic-shell or nuclear processes in which electrons are involved, are accompanied by very-low-intensity internal bremsstrahlung, and cause external bremsstrahlung (q2.4.4). 2.4.6. Neutrons. fission Droducts and other radiations Many of the very heavy nuclides also decay by spontaneous fission, in competition with the "normal" decay modes. This fission process is quite similar to the induced fission in "fissile" (induced by thermal or fast neutrons) or in "fissionable" (induced by fast such as 235U, '%, 23sPu, or WJ, respectively. neutrons only) materials, When undergoing fission, nuclei generally emit two fission products per fission (of The mass distribution of nearly equal energy and mass) and several neutrons and y rays. the fission particles (Vandenbosch and Huizenga, 1973) and their yields (Blachot and Fiche, as are also the 1977) are well known for the most important fissile nuclides, fission-product absorption properties. Spontaneously fissioning radionuclides are often used as convenient sources of neutrons or fission products. Such a nuclide of special interest is "'Cf with its useful Other frequently used "radioactive" neutron sources are based on half life of 2.65 a. (e.g. Ra+Be, Pu+Be). For (a,n) or (7,n) reactions in beryllium or other light elements (Schneider, 1973; the emitted neutron spectra are of importance many applications Cierjacks, 1983). Neutrons are not only useful in radionuclide metrology in the form of radioactive and spontaneous-fission neutron sources; but they may also disturb radioactivity measurements Because the absorption of in the vicinity of neutron-producing accelerators or reactors. (elastic and inelastic scattering and neutrons happens only by nuclear reactions transmutations (capture, etc.)), the cross sections of which are much lower than those of So, it is not reactions between charged particles, their mean free paths are very long. that NaI(T1) detectors, installed several hundred metres away from powerful surprising linear accelerators, show annihilation-radiation peaks due to "Na from neutron activation of Na, and short-lived activity due to "'1 from l"I. Sometimes, therefore, the shielding of radioactivity detectors must be reinforced by highly neutron-absorbing low-2 materials. mentioned The radiations and radioactivity measurements
above are the only immediately Many others are applications.
important ones known, but are
for too
Radioactivity
746
measurements:
principles
and practice
short-lived (proton emitters), show too little interaction with matter energies far away from the energy range useful for radioactivity leptons, mesons, trachons, transition radiation, etc.). Nevertheless, necessary to make measurements on them too (e.g. meson therapy).
(neutrinos), or have measurements (heavy it may sometimes be
2.5. ENERGY 2.5.1. Kinetic.
total
and rest enereies
of oarticles
The term energy is normally used in atomic physics for the kinetic energy (E,.) of particles. For non-relativistic massive particles (moving with a velocity v that is very small compared with the speed of light, v/c = p << 1) Ek is equal to mOvz = p2/2m,, where momentum. m, is the rest mass (for v = 0) of the particle and p its non-relativistic The kinetic the total energy is simply
energy of relativistic particles can be derived from the expression for E, = mc', and its rest mass energy E, = moc2, where m = m,(l - &+-'". It
Ek = E, - E, = mc' - m,c2 = m,c'[( 1
=
8').
,
m,c'[(l + +9'/2)-l - l] = m,vZ/2
This relation can also be derived or its equivalent
from
the relativistic
r, -
11
for fl << 1
mass
equation
(2-13) m = m,(l
EZ = E,z + p2cz.
equal
- p2)-
shows the relative of kinetic energy. Table
Z-9
velocity
p
=
v/c
of
electrons
and
Q
particles
are
for
Relative velocity of electrons and a particles for selected values of kinetic energy, E
E (keV)
1 10 100 1000 10000 2.5.2. Binding.
,
(2-14)
For particles with zero rest mass (photons, for example) kinetic and total energy and E, = Ek = pc = hv, where h is Planck's constant and u the frequency.
Table 2-9 selected values
4
disintegration
- 1)_2]% /3 = v/c = [l-(E/E, electron (2 particle E,=0.511 MeV E,=3727 MeV
0.0625 0.1950 0.5482 0.9411 0.9988
and reaction
0.0007 0.0023 0.0073 0.0232 0.0731
energies
(0 values1
The energy of a radiation is one of its most important properties, especially for its measurements are an integral and important part of Therefore, energy identification. They are therefore treated in some detail in 94.11. Here only radionuclide metrology. the basic concepts relating to energy are outlined. Some further and more specific energy definitions are necessary for the description of The binding energy (Eb) is released when two or more certain radioactivity phenomena. the small to form one common particle of mass m, and, neglecting particles combine difference in mass resulting from from the rearrangement of the atomic electrons, is given by E, = (2%
+ Nm, - m)c2
"mass defect", the difference The binding energy is therefore the energy equivalent to the IMKle0n masses (at rest) of the initial individual between the sum of the individual It is also equal, of particle and the mass of the resulting final compound particle. supplied to the compound particle in order course, to the amount of energy, which must be to break it into its nucleonic constituents. The reaction energy (Q value) of a nuclear reaction (or transformation) 1(2,3)4 is the net energy set free or absorbed in the reaction Q = (ml + m, - m3 - m,)c'
,
of
the type
(2-15)
incoming, outgoing and m, being the masses of the neutral ground states of the target, Similarly, the disintegration product particles, respectively. (decay, transition) energy also tabulated as Q, values, is the maximum available energy, i.e. radionuclide, of a
Radioactivity
measurements:
principles
and practice
available to be shared by all the radiations emitted in the ground state of a parent atom to that of the daughter. The following two examples will energy calculations:
serve to illustrate
a radioactive
the
principles
747
transition from
of such mass-
(i) *l'Po decays to the ground state of 'OsPb by emission of a 5.304-MeV a particle. The difference between the atomic masses of the parent and daughter atoms is (209.982848 205.974440)~ = 4,008408u, lu being equivalent in energy to 931.5016 MeV (Wapstra and Audi, (a particle plus two 1985). Then subtracting 4,002603u, the mass of one 4He atom electrons), and multiplying by the ratio of MeV/u gives Q, = 5.407 MeV. The difference of 0.103 MeV from the experimentally observed 5.304 MeV should represent the recoil energy of the residual ZOsPb atom (see y2.4.2). (ii) 6oCo with an atomic mass of 59.933820 u in the ground state decays by @- emission to one of several energy states of s0Ni that has a ground-state atomic mass of 59.930789 u. The sum of the maximum energy of any /? branch plus the T-ray energy emitted, in the decay of the excited level of s0Ni to which the p decay occurs, is 2.8234 MeV, which is equivalent to the mass difference. Here the recoil energy is negligible. 2.5.3. Units and svmbols. conversion factors The special name of the SI unit of energy is the joule (J), expressed units by J = Nm (N: newton, the special name for the SI unit of force), and units J = m'kg s?. It may be noted that the the pascal, the special name for of pressure (used elsewhere in this report), is equal to one newton per square
in other SI in basic SI the SI unit metre.
In atomic physics the conventional unit of energy, also temporarily retained with SI, is the electron volt, the energy acquired by an electron when it traverses a potential difference of one volt in vacuum. One electron volt, 1 eV, is equal to 1.60219.10-19 J. Atomic masses (equivalent to energies, according to Einstein's law, E = mc') are often also expressed in multiples of the electron rest mass, m, = 511.003 keV, or of the atomic mass unit u (l/12 of the mass of a % atom); 1 u = 1.66054 x 1O-27 kg, approximately or, as stated above, 931.502 MeV. The conversion factors between the most important units are collected in Table Z-10.
microscopic and macroscopic energy
2.6. DOSIMETRY 2.6.1. Definitions and concerts Dosimetry is the body of knowledge concerned with the measurement of ionizing radiations for the purpose of quantifying some radiation effects. Dosimetry is usually concerned with the assessment of absorbed dose or related quantities (exposure, kerma) arising from the interaction of radiation with matter. Radiation dosimetry response functions are usually expressed in terms of dose-vs-effect relationships, that are intended to give a means of assessing the upper and lower measureable limits of such dosimetric effects. Dosimetry is therefore a prerequisite for all radiation applications, especially for radiation therapy and for radiation protection. The principles and applications of dosimetry have been discussed in many publications (see, for example, Attix et al., 1968; Jaeger and Hiibner, 1974; Kase and Nelson, 1978; McLaughlin, 1982; Greening, 1985; Kase ec al., 1985, 1987; Attix, 1986; IAEA, 19&e). In the final analysis, the quantification of radiation effects demands an understanding of the interactions of charged corpuscular radiation with matter, because sufficiently energetic photons interact with structured matter only through their corpuscular surrogates, such as photoelectrons, Auger and Compton-recoil electrons, and electron-positron pairs; and neutrons mainly through recoils. The concepts, quantities and units of dosimetry have been defined by the International
748
Radioactivity
Commission be grouped 2.6.1.1.
on Radiation as follows:
Ouantities
Units
and Measurements
characterizinp
Particle
principles
(ICRU,
the radiation
energy
Energy
imparted
(by particles)
(of particles)
Energy
flux
Fluence Energy
(particle) fluence
Fluence
rate
and practice
1980).
The
relevant
quantities
may
field
number
Radiant
Flux
measurements:
(particle)
N
1
R
J
e
J
i
s-1
d
w
*
mm2
0
J me2
i
*-2 s-1
W mm2 Energy fluence rate $ The definitions of flux and fluence are not necessarily or exactly the same as they are, or were, in other branches of physics; the former, in the past, has been associated with area or volume and confused with flux density, and the latter differs in that it pertains to particles incident upon the cross-sectional area of a sphere. (See ICRU, 1980, for definitions.) 2.6.1.2.
Ouantities
Cross
used
in characterizine
section
Mass attenuation coefficient (photons)
the interaction
of radiation
Svmbol
Special Unit Used with SI
o
b (1 "barn" = 10-28 mz
mzkg-'
Mass energy-transfer coefficient (photons)
mz kg-'
Mass energy-absorption coefficient (photons)
m2 kg-'
Linear stopping power (charged particles)
with matter
*
J m-l
eV mm1
Total mass stopping power (charged particles)
J III' kg-'
eV l m z kg-'
Collision mas.s stopping power (charged particles)
J mz kg-'
eV+m' kg-l
Radiative mass stopping power (charged particles)
J mz kg-'
eV*m' kg-1
Linear energy transfer (LET), upper energy h. (L, = SC011 + S,,d)
J m-l
Radiation chemical yield
mol J-'
Mean energy expended ion pair formed
per
J
aVf&
(100
l
e”;-’
aV* = 1.60219.10-'g J
J.H. Hubbell (in McLaughlin, 1982, p 1269) has supplied useful tabulations of massattenuation and energy-absorption coefficients for photons (energies 0.001 through 20 MeV in their interactions with many elements and compounds. ICRU Report 37 (ICRU, 1984b)als.o tabulates stopping powers for electrons and positrons in many elements and compounds for a large number of energies in the range from 0.01 through 1.00 GeV.
Radioactivity
2.6.1.3. Energy
Dosimetric
Symbol:
z.
principles
749
and practice
auantities
(to
imparted
measurements:
unit volume)
SI unit: J. c
R,, - R,,t + 1 Q,,>
=
(excluding rest energies) of all those charged and where R,, is the sum of the energies uncharged ionizing particles that enter the volume, Rout is the sum of energies (excluding rest energies) of all those charged and uncharged ionizing particles that leave the volume, and C Q., is the sum of all changes (decreases, positive sign; increases, negative sign) of the rest-mass energy of nuclei and elementary particles in any nuclear transformations that occur in the volume. Absorbed Symbol:
dose SI unit:
D
J kg-' D
where
dP is the
mean
Absorbed-dose
rate
Symbol:
SI unit:
b
Kerma
(kinetic
Symbol:
K
=
SI derived
imparted
J kg-' se1
SI unit:
released
by ionizing
names:
Gy; rad
SI derived
radiation
units with
to
special
matter
names:
units with
special
names:
of mass
dm.
Gy s-l; rad s-'
Gy; rad
= d&,/h,
where dEt, is the sum of the initial kinetic energies of all the charged liberated by uncharged ionizing particles in a material of mass dm. Kerma
(= 1 cGy)
in unit mass of absorber) SI derived
J kg-l K
special
dT/dm,
energy
energy
units with
ionizing
particles
rate
Symbol:
ic
SI unit:
J kg-' 5-l
X
SI unit:
C kg-l
SI derived
units with
special
names:
Gy 5-l; rad S-I
Exposure Symbol:
X
=
where IdQl is the "absolute air when all the electrons in air.
SI derived
unit with
special
name:
R
IdQl/W value" of the total charge of the ions of one sign produced in completely stopped liberated by photons in air of mass dm are
bremsstrahlung emitted by the electrons is The ionization arising from the absorption of not to be included in IdQl. Except for this difference, significant only at high energies, the exposure is the ionization equivalent of the air kerma. X = qp_,e/pW where ~,,/p is Exposure, X, and the photon energy fluence, q, are related by the mass energy-absorption coefficient in air, e is the elementary charge and W is the mean relation is only valid if W is assumed energy expended in air per ion pair formed. This and if p_,/p is a mean value weighted by the spectral energy to be energy-independent, fluence. Exposure Symbol:
rate i
Air kerma-rate Symbol:
I’,
SI unit:
C kg-l 5-l
SI unit with
special
name:
R s-l
m2 J kg-'
SI unit with
special
name:
m'Gy; Bq-ls-'
constant SI unit:
l-6 =
&/A.
of a radionuclide emitting photons of energy greater than where i, is the air-kerma rate 6, at a distance 1 from a point source of this nuclide having an activity A. It is assumed that the attenuation in the source and along the path length 1 is negligible. This is an dosimetry to radioactivity. important quantity, that links This quantity replaces (ICRU, constant or the specific gamma-ray 1980), but is not identical to, the exposure-rate constant, previously recommended by ICRU (1962, 1971).
Radioactivity
750
measurements:
principles
and practice
Km-ma factor Symbol:
k,
SI unit:
J mz kg-l
SI units with
special
names:
Gy m2; rad mz
k, = KU1
where K is the kerma for a given kind of particle (usually neutrons), and @ is the particle fluence; it is also related to the mass-energy-transfer coefficient, for monoP’t,/P I energetic neutrons of energy E (see R.S. Caswell et al., in McLaughlin, 1982, p. 1227). A dosimetric quantity that is of great interest to most users of ionizing radiation is the absorbed dose (at a point in a specified medium). However, it has long been established practice to measure, using ionization chambers, another, more readily accessible quantity, namely the exposure, and to derive from it, by application of certain conversion and correction factors, the absorbed dose to the medium at the point of interest. Detailed protocols for this conversion are available (ICRU, 1969, 1970, 1973, 1984b; IAEA, 1986b). Closely related to exposure, but based on energy transfer rather than charge production, is air kerma. Its unit, the gray, is the same as that for absorbed dose. Air kerma, apart from a usually small correction that takes account of energy loss by bremstrahlung, equals the energy equivalent of exposure. While exposure is conceptually limited to photon radiation, kerma is defined for all types of uncharged radiations. Absorbed dose may be derived from air kerma in the same way as it is derived from exposure (IAEA, 1987). 2.6.1.4.
Ouantities
used
in radiation
protection
Svmbol
Dose equivalent
H = DQ
J kg-l
Quality
Q
1 (for photons)
factor
Effective
dose equivalent
Dose-equivalent Absorbed-dose
index
Absorbed-dose-index Dose-equivalent
rate
index
Dose-equivalent-index Shallow
rate
dose-equivalent
Deep dose-equivalent
index
index
SV
rem
(=
1 c.J kg-')
Sv
H, = xI,H, *
rate
SI Derived Units with Soecial Names
SI Unit
H
J kg-' s-l
Sv s-l
DI
J kg-'
GY
DI
.J kg-l s-l
HI
J kg-'
HI
J kg-' s-l
Gy 5-l SV Sv s-l
rem 5-l rad
(= 1 cJ kg-l)
rad 5-l rem rem 5-l
H,,,
HI,,
* gT ir the mean dose*qui"Ble"t in an organ.or tissue.T, and WT 15 B weighting factor
Two new concepts, ambient dose equivalent and directional dose equivalent have been introduced (ICRU, 1985) to link the external radiation field to the effective dose equivalent and to the dose equivalent in the skin. For purposes of individual monitoring the two concepts individual dose equivalent, penetrating and individual dose equivalent, superficial were introduced (ICRU, 1985). For the definition of these and other important quantities used in radiation protection the reader is referred to ICRU Report 39 (ICRU, 1985). Also see IAEA (19863).
it is not sufficient to know just For biological and radiation-protection applications, the quantity of the radiation energy that has been absorbed, but also how the biological effect on the tissue irradiated varies with both the nature and energy (and energy range) of the radiation. Thus the biological effect will be different for electrons, protons and alpha particles and will also vary with the energy (and hence LET) of each. For this reason, the quantity absorbed dose is multiplied by the quality factor Q to give the dose equivalent listed above. In other words, the quality factor Q is used to weight the absorbed dose to give the biological effectiveness of the charged particles producing the absorbed dose, and is equal to 1 for photons, and for a charged particle is a function of the stopping power in water, Lo, for that particle (for electrons and positrons, see ICRP, 1977). While values of the quality factor Q are generally used for the purposes of routine radiation protection, its predecessor, the relative biological effectiveness (RBE), is still widely used in radiobiology. RBE is defined as the quantity of 250.keV x rays needed to produce a given
Radioactivity measurements: principles and practice
biological effect divided same effect.
751
the quantity of the radiation of interest that produces the
The quantities absorbed-dose index D,, and dose-equivalent index H,, also listed above, have been introduced in order to estimate maximum absorbed doses or dose equivalents to all, or parts, of a human body after exposure to ionizing radiation. For further information concerning these dosimetric concepts and quantities, reference should be made to ICRP (1977, 1979) and to ICRU (1980, 1985), or to any of the other references given in 72.6.1. 2.6.2
Methods of absorbed-dose measurement
In many absorbing media the radiation energy imparted is ultimately degraded to heat Assuming that no heat defect and will cause a temperature rise that can be measured. occurs (gain or loss due to exothermic or endothermic radiation-induced reactions), or that its amount is known with sufficient accuracy, and that the specific heat of the absorbing medium is known, such a calorimetric method may be used as a dosimeter. Absorbed-dose calorimeters have been built by standardizing laboratories and are being used as dose standards (Domen, 1969; Domen and Lamperti, 1974; Domen, 1987). However, they are not recommended for day-to-day laboratory use, except for measuring high doses when electron accelerators are used for radiation processing (Morris, 1988; Miller and Kova&, 1986). For practical use a dosimeter should meet a number of requirements, such as suitability for the type of radiation to be measured, suitable range of dose and dose rate, matching the dosimeter to the medium of interest, size of the detector, ability to integrate dose or to measure dose rate, stability, accuracy and precision, and simplicity. Ionization chambers are most widely used for dose measurements in radiotherapy and radiation protection. They offer high accuracy, cover a wide dose range, and may be used Ionization chambers are fragile and need sophisticated for different types of radiation. They may serve as reference instruments, as well as field electronic readout devices. instruments (Attix et al., 1968; Burlin, 1970; Jaeger and Hiibner, 1974; Greening, 1981; IAEA, 1981; Kase et al, 1985; Boag, 1987). (Also see Ta4.4.1 and 5.4.6.) There are many chemical systems (mostly aqueous solutions) in which absorption of radiation energy leads to the formation of initially-absent compounds, ions or radicals, related to absorbed dose. quantitative measurement of which can be The best known and most widely used aqueous chemical dosimeter is the Fricke dosimeter, composed of a solution It is very nearly water-equivalent, of FeSO, in diluted H,SO, (Fricke and Hart, 1966). relatively easy to handle and has high accuracy. A spectrophotometer is required for its The radiation chemical yield (G-value) of readout (Helm and Berry, 1970; Attix, 1986). optically-absorbing species (ferric ion, Fe"), is related to the molar linear-absorption coefficient (c,) for that species at a given optical wavelength (X = 304 nm). The product of the two is well established for electrons and for x and 1 radiation (G.r, = 352 x lo-' m2 kg-' Gy-I; see ICRU, 1984b). This dosimeter requires the use of ultrapure water and reagents as well as ultra-clean glass containers. A disadvantage in its use in radiology and radiation protection lies in its limited range of response, namely from lOI to 4 x 10' GY. Thermoluminescence dosimetry (TLD) has become one of the most widely used dosimetry systems in recent years. It involves the use of a solid-state dosimeter, the sensitive material being LiF or some other thermoluminescent substance (74.6.2). The energy stored by the radiation-induced filling of electron and hole traps in these crystalline materials is released as luminescence when the dosimeters are subjected to heating at a controlled rate. The intensity of this luminescence is plotted as a function of time to give a "glow curve", its amplitude at a given temperature, or integrated over a given temperature range (thermoluminescence intensity), being a reproducible function of absorbed dose. Its main advantage is that the dosimeter can be made very small, providing a means for "point" dosimetry. Another advantage is the relatively wide range of absorbed-dose response of different thermoluminescent materials, from nanograys to kilograys. The dosimeters can also be used over and over again by the use of repetitive cycles of annealing at elevated temperatures. A disadvantage is the difference in their response from that of water or tissue over broad spectral distributions: for example, the photoelectric effect for lowenergy x rays in TL materials has a distinctly different spectral distribution from that of hydrogenous materials. There is also a marked difference in electron stopping powers in the two types of material; the stopping power in hydrogen being about double that in other For readout the TL probe must be heated in an elements and non-hydrogenous materials. oven, and the light emitted measured by a phototube. Automated TLD systems are largely replacing film systems in national radiation-protection services (Helm and Berry, 1970; IAEA, 1981; Oberhofer and Scharmann, 1981; McLaughlin, 1982; McKinley, 1983; Horowitz, 1984; Kase et al., 1985; Attix, 1986). A promising dosimeter material that simulates many biological tissues, and one that can be utilizes in a form small enough for in viva dosimetry in radiotherapy (with a dose range from and above 1 Gy) is the amino acid, alanine (Regulla and Deffner, 1982). When pellets of alanine are irradiated, stable free radicals are produced, the concentrations of
752
Radioactivity
measurements:
principles
and practice
which can be measured, in terms of populations of unpaired electrons, by means of electronspin-resonance (ESR) spectrometry. The amplitude of the resulting ESR signal is proportional to the absorbed dose. The response of this dosimeter can be calibrated by comparison with crystalline samples having known numbers of unpaired electron spins per unit mass (Regulla and Deffner, 1982). 2.6.3
Doses
from distributed
internal
radioactive
sources
It is often necessary to calculate the dose to different tissues of the body from an administered radiopharmaceutical that becomes distributed around the body with varying amounts concentrated in different organs. For this purpose it is usual to evaluate the dose to the rest of the body due to the activity residing in each of the most active organs in turn, such, as for example, that arising from the thyroid in the case of 1311, If A, is the activity of the radiopharmaceutical, administered at time t = 0, then the activity residing in the source organ of interest, A,(t) at time t, will be equal to ~cune fraction f(t) of the administered activity, i.e. A,(t) = A,f(t), and the time integral of the administered activity, in the source organ, is given by m
/
A,(t) dt = A, 0
J
fm(t) dt = A,rr
,
(2-16)
0
the time integral of the fraction f(t) being the residence time T,. In effect, Aor, is the total number of disintegrations that will occur in the source organ during the time that any significant amount of the radiopharmaceutical remains in it. This is called the cumulative activity. Group OR Reference Man (ICRP, As pointed out in Appendix I of the Report of the Task such as alpha particles and beta rays will be 1975), shallow-penetrating radiation, But in the source organ or within relatively short distances from it. absorbed within the organ, much of the body may be case of photons emitted by a radionuclide in the source Following the schema developed by Loevinger and Berman (1968), the task group irradiated. (ICRP, 1975) denoted that fraction of the decay energy produced in the source organ, S, This is called the absorbed that is absorbed in any given target organ T, as $(T + S). fraction. The fraction of energy absorbed per unit mass of the target organ, the specwhich is equal to Q(T + S)/m,, where mr ific absorbed fraction is denoted by Q(T + S), is the mass of the target organ. In the last column of decay data shown in Table 2-4, as an example for a few radiois given for the ith type nuclides, the mean energy, Ai in gram-rads per microcurie-hour, of radiation emitted by each radionuclide. Similar data are given for 279 radionuclides in belong to the older system of The units of Aiv g-rad/&i-h, Appendix A.3 of NCRP (1985). In the SI system A1 = PiE,, where units that is, however, still widely used in medicine. Pi is the probability of emission per nuclear transition of an i-type radiation of mean energy Ei, with units J Bq-' 5-l. As one Bq.s is one nuclear transition, A1 is the mean energy per ith transition in joules. For any given radionuclide the mean energy emitted per nuclear transition, A, is the sum of all A,'s, that is (2-17)
A=CA,. i The product of the cumulative specific absorbed fraction gives designated target organ, i.e.
activity, the mean
A,?,, the mean energy per decay, energy absorbed per unit mass,
A, and the D, of the
D(T + S) = A, TT.C A, +,(T + S)
I
In order to enable the calculation of D for explicit target organs due to photons emitted from specified source organs the Task Group on Reference Man has published extensive tables of the specific absorbed fraction for the target organ for photons (with energies ranging between 0.01 and 4.00 MeV), and for 16 source organs (plus total body) and 20 target organs (including total body, skeleton and skin) (ICRP, 1975; Appendix I, Table Most of the data were obtained using Monte Carlo calculations and an anthropomorphic 1.2). This publication also tabulated values of phantom described by Snyder et al. (1979). for 20 target organs and 10 source organs, absorbed fractions, as its title implies, including whole body, for a number of specified monoenergetic photon emitters such as laF. The 1985). 2.6.4.
above
concepts
Further
have
also
been
discussed
by
R.
Loevinger
in NCRP
Report
58
(NCRP,
reading
In addition to the references given in 72.6.1, Volumes I and II of The Dosimetry of Ionizing Radiation, edited by Kase, Bjarngard and Attix (1985, 1987) contain eleven reviews of the theory and practice of the measurement of both external and internal radiation. These reviews are thorough in their treatment of several important dosimetry topics, including radiation protection, environmental radiation, external photons and ,9 rays, external
753
Radioactivity measurements: principles and practice
beams of heavy particles, microdosimetry calorimetry, and ionization chambers.
(also with applications
in biological
systems),
charged-particle, Twenty-four papers dealing with many aspects of ionizing-photon, and neutron dosimetry have been published in a special issue of the International Journal of Applied Radiation and Isotopes entitled Trends in Radiation Dosimetry, edited by W. L. McLaughlin (1982). Subjects include dosimetry in biology, medicine and in the environment, systems, tables of stopping powers (energy range 0.01 radiation protection, dosimetry energy-absorption coefficients (energy range through 1,000 MeV), of mass-attenuation and 0.001 through 20 MeV), and of neutron kerma factors of elements and compounds for neutrons (energy range 8 eV through 29 MeV). Recent ICRU reports, from 1980 through 1986, have focused on radiation dosimetry quantities and units (1980), the dosimetry of pulsed radiation (1982), microdosimetry (1983), the dosimetry of electron beams (energies 1 to 50 MeV) (1984a), stopping powers for electrons and positrons (0.01 to 1,000 MeV) (1984b), dose equivalents (1985), and the quality factor (1986). 2.7. SOME USEFUL CONSTANTS AND MATHEMATICAL RELATIONS 2.7.1. Introduction All figures given in aq2.7.2 and 2.7.3 are certain, in the sense that the uncertainty More exact data with discussion of the of the last figures is negligibly small. uncertainties can be found in the literature (see, for example, Petley, 1985; Wapstra and Audi, 1985; Cohen and Taylor, 1987). 2.7.2. Constants useful in the calculation of atomic-decay processes
In 2 = 0.6931472
log e = 0.434294
e = 2.718282
7r= 3.141593
1 d = 8.6400.104 s [Half lives, of radionuclides, that are longer than 365 days are usually given in For convenience however, especially in tables of years, but the unit year is not SI. nuclear data, the unit of one mean tropical year taken as 365.2422 days, is used. In the published literature it is desirable that the quantity year should be specifically defined The most commonly used symbols are "y" or "a" (for and the symbol denoting it described. an&s or annum), but "Y" also appears frequently in computer printouts.] The mole (symbol mol) defined as the amount of substance of a system that contains as many elementary entities as there are atoms (unbound and at rest in their ground state) in 0.012 kg of carbon-12. The Avogadro constant, NA, = 6.0221 x 10z3 mole' of 1%)
(equals the number of atoms in 0.012 kg
The unified atomic mass unit, u, = l/12 of the mass of one atom of "C state = (O.O12/N,)/12 = 1.66054 x lo-*' kg.
in the ground
u/c* I 931.50 MeV (see Wapstra and Audi, 1985). The Faraday Planck's
constant,
constant,
Elementary
charge,
NAe, = 9.64853
x 10' C mol.'.
h, = 6.62607 x 10m3" J s. e, = 1.60218
Speed of light
in vacuum.
Fine-structure
constant,
x 10-r' C.
c, = 2.99792458
x lo* m s-l.
a, = poce2/2h = 7.29735 x 1O-3
(l/a = 137.036)
(dimensionless),
Permeability of vacuum, pO, = 4?rx lo-' N A-'. 2.7.3. Mass-enerw
relations
Energy and mass are related to each other, in any consistent system of units, by the Einstein equation, E = mc'. In SI units, for a mass of 1 kg, 1 cz = 8.9875518 x 10's J. But the electron volt, 1 eV, is also a unit of energy used with SI (72.5.3), and is the kinetic energy acquired by an electron in passing through a potential difference of 1 volt in a vacuum. In SI, one electronvolt of energy is 1.60218 x lo-'s J; the electron charge being 1.60218 x 10‘I9 C and one volt being 1 J/C (BIPM, 1985; NBS, 1986). The conversion factor from kilograms to units of electron volt is
754
Radioactivity measurements: principles and practice
5.6095 x 10z9 MeV/kg. m, = electron rest mass = 0.91094 x 10m3c kg = 5.48580 x lo+ u. m,,c2- 0.51100 MeV. mr = proton rest mass = 1.67262 x 10-z' kg = 1.007276 U. mscz = 930.27 MeV. m,,= neutron rest mass = 1.67493 x 1O-27 kg = 1.008665 u m,,c'= 939.57 MeV. m, = alpha-particle rest mass = 6.64478 x 10-r' kg = 4.001506 u. m&s - 3727.41 MeV. 2.7.4. Decay and erouth of radioactivity The law governing the decay of radioactivity, discussed in 72.3.6, applies also to induced radioactivity. This term is used when an appropriate material is irradiated by activating particles (neutrons, protons, etc.) which transform atoms of the target substance (subscript 1) into atoms of the radioactive product (subscript 2). The competitive processes of production and decay of the radioactive atoms are described at any given time, per gram of the target material, by dn,/dt = -X,ri,+ a12~hl , (2-18) where n2 is the number of product atoms per gram of target material, is the X, = In 2/T decay constant of the product nuclide, 4 the average fluence rate (flux density!I of the activating particles, n1 = N,/A, the number of atoms per gram of target material, N, the Avogadro constant, A, the molar mass, and g12 is the cross section for the reaction considered. Integration over the activation time ti and introduction of the waiting time t, (time between the end of irradiation and the onset of counting) yields, for t, = 0 and IQ(O) = 0, the activity, A,, at the time ti + t, as Ac = +t,+t,)
= o,,4n,
(1 - e
-In 2.t,/TQ) e-ln 2.t,/r&$
2.7.5. Snecific activitv of nure nuclides and of nu&&c
(2-19)
mixtures
For a pure radionuclide of atomic mass A, decay constant X, half life TG and number of atoms per gram n (= NA/A; NA = the Avogadro constant), the specific (nuclidic) activity A s' is
A*
=
An
NA In 2 ___
=
(2-20)
ATk
in s),
= 4.1742 x 10z3 (AT%)-'
(A, in Bq g-' = s-lg-', if Tb
= 1.3228 x 10's (AT&l
(A, in Bq g-', if T% in years; "a"),
lo5 (AT%,-1
(A, in Ci g-l, if Tti in years; "a").
= 3.575
X
For a mixture of n nuclides with mass numbers AI.......%, half lives III,.......% (in g), the formula for A,, in Bq g-', is
T,.......T,
(in a) and masses
A,
=
[1.3228 x 10's i m,/(TiAi)] /t m, i
(2-21)
2.7.6. Mass and atom nercentages of nuclide mixtures Sometimes the nuclidic composition of a mixture is only known by atom percent (a,) and not by mass percent (pi). The mass percent can easily be calculated from the atom percent and vice versa by means of the following two equations
and
100
gi
=
ai
= 100 [&/(A,
I
(2-22)
“cgjAJ)l
(2-23)
[a,A,/ "c aj Aj] j=l
j=l
Radioactivity measurements: principles and practice
755
2.7.7. Activity of dauehter oroducts in radioactive families Let N: (parent), and N,O, ...NO., ...N.O be the numbers of atoms each of the family at time t are X,N,, members present at the time t = 0. Then their respective activities, . &N,. .A&, and one has (Bateman, 1910)
=
Y
(2-24)
;s., n=l a-%t
k-l k N,O lI Xi 1 i=n i=n
(2-25) k lI (X,-X,) m=n wi If we now consider the important case where, at t = 0, only the freshly separated parent is present, and which may be expressed by Ni = 0 for n > 1. We obtain S,
where
=
Nk
=
S,
=
k k-l Nyll Xi 1 i=l i=l
e-&t (2-26) k n (X,-X,) m=l tii
The activity of the daughter thus becomes
4
=
X,N, Al% N,
-
(e
_ e-x t
-x,t
2),
(2-27)
AZ - Al and that of the "granddaughter",
4
= X,N, =
e-&t
NT X,X,
e-&t +
+
[
(&-A,) l&-Q
C&-X,) (X,-Q
e-w 1 .
(2-28)
(X,-X,) (&-&) If the half life of a daughter product is much shorter than that of the parent, their activities, when measured several half lives of the daughter later, become equal, and This is known as secular equilibrium (from both decay with the half life of the parent. Latin saeculum, an age), and is best exemplified by the growth of zzzRn into freshly separated 226Ra. In the case of a radioactive parent decaying to a shorter-lived radioactive daughter, and with the time t after separation being long enough that exp(-X,t) can be neglected compared with exp(-X,t), their activities are related by the following simple approximation of equation (2-27): 4
:.
4
=
X,N,
=
NYX,e -X1t[&,/(X,
= 4
L&/(-h
- &)I
- A,)1 ,
(2-29)
at time t. In other words, for large values of t the activity of the daughter merges with This state of equilibrium is known as transient and merges with the that of the parent. secular as the ratio X,/X, becomes so large that the activities A, and A, are essentially equal. But if X, is not significantly greater than X,, as in the case of '&OLa (T& = 40.3 hours) and lroBa (Tb = 12.7 days), then the daughter grows and then decays with an activity greater than that of the parent by the significant ratio X,/(X, - X,). In the case of a short-lived parent and longer-lived daughter, the former decays to "zero" while the daughter grows to a maximum and then decays with its own half life. But in both cases
156
Radioactivity measurements: principles and practice
the decay curve of the parent crosses the growth-and-decay maximum of the latter curve.
curve of the daughter at the
Examples of both of these types of parent-daughter activity freshly separated 14OBa decaying to 140La, and for a sample hours) decaying to lz31 (Tk = 6.6 hours), are given in Mann ec 2-7). The latter example would typify the accelerator production for medical purposes.
decay-growth curves, for of lz3Xe (T+ = 2.08 al. (1980, Figs 2-6 and of lz3Xe to provide lz31
Another important example is that of the isotopes of uranium, where there is a daughter alpha-particle activity ingrowth per annum of about 0.05% for 233U, 0.001% for 234U, and 0.056% for 235U.
3.
GENERAL
PROBLEMS
IN RADIONUCLIDE
METROLOGY
3.1. INTRODUCTION Radioactivity measurements can be rather complex and can also be very different for But several problems and procedures are common to different modes of radioactive decay. Some of them are discussed in this chapter in connection with most types of measurement. and handling of radioactive sources (73.3), radiation protection (13.2), the preparation and the evaluation of radioactivity measurements (73.4). 3.2. RADIATION 3.2.1. Basic 3.2.1.1.
PROTECTION
facts
General
dosimetry has produced a. profuse and sometimes The subject of "cause-and-effect" mysterious literature, in which the number of terms has proliferated and the values of certain adjusting factors have, from time to time, changed. In 72.6 measurable dosimetric quantities have been defined. But in this chapter we will be dealing with the somewhat At the lowest levels qualitative assessment of effects arising from exposure to radiation. this assessment is largely a matter of probability: If a single unit of of radiation, electromagnetic radiation interacts with a single biological cell, will a chromosome be And is affected, and, if it is, will a possibly resulting mutant be beneficial or not? there a threshold or not? At higher radiation levels, data from, and calculations based such as those given in nuclear accidents no" enable estimates, on, several unfortunate Table 3-1, to be made for the onset of the effects for different levels of radiation dose equivalent. Table 3-l Somatic effects due to different levels of radiation Dose equivalent received (Sv) Radiation Effect 0 to 0.25
0.25
to 0.5
no detectable improbable
clinical
effects:
late effects
very
slight transient blood changes (reduction in the lymphocyte number, etc.): late effects improbable
0.5 to 1.0
marked changes in blood picture with delayed recovery; temporary nausea and fatigue; late effects not improbable, but no serious shortening of life expectancy
1.0 to 2.0
nausea and fatigue with possible vomiting within 24 hours; marked changes in blood picture; following latent period of 1 to 2 weeks,pallor, epilation, general weakness with very probable recovery; few deaths possible in 2 to 6 weeks; shortening of life expectancy due to late effects by about one percent
2.0 to 3.0
nausea, vomiting and possible diarrhea within few hours; strong changes in blood picture: following latent period of about 1 week,epilation, loss of appetite, pallor, sore throat, general weakening and fever; in general,recovery within 3 months, but some probability of death within 2 to 6 weeks; about a few percent shortening of life expectancy due to delayed effects (cancer)
3.0 to 6.0
nausea, vomiting and diarrhea in 1 to 2 hours; strong changes in blood picture, after latent period of up to one week,epilation, fever, general weakness, severe inflammations of mouth and throat, emaciation, hemorrhage, purpura, petechia; at about 4.5 Sv 50% death probability, at 6 Sv nearly certain death within 2 to 6 weeks due to failure of blood-forming organs; serious delayed effects of survivors
6.0 to 12
above
12
above ~100
as above; epilation weeks due walls as above; damage to
nausea etc. within one hour; redness of skin; etc. within a few days; death within 2 to 3 to loss of body fluids from damage to intestinal peeling central
as above;
immediate
of skin; death within nervous system coma;
757
death within
a few days due to
hours
750
Radioactivity
measurements:
principles
and practice
In this report the discussion of this subject will be limited to a brief explanation, for the benefit of dosimetric neophytes, of some of terms used in the field of radiation dosimetry dealing with cause and effect, and to currently recommended upper limits of expthat are contemporaneous with their proposed use of radioactive osure. For recommendations materials, readers should consult the frequent reports issued by the International Commission on Radiological Protection (ICRP) and the International Commission on Radiation Units and Measurements (ICRU); and also those issued by their own national radiation-protection in the Federal Republic of organizations such as, for example, the Bundesgesundsheitsamt the National Radiation Protection Board in the United Kingdom or the National Germany, Council on Radiation Protection and Measurements (NCRP) in the United States. For the neophyte it may also be helpful to explain three terms that appear frequently in the literature of radiation dosimetry, but that do not always find their way into the "Committed" is essentially the glossaries. They are committed, effective and equivalent. In radiation as used in the term "cumulative activity" in 72.6.3. same as "cumulative" protection it refers to the effects due to an ingested or inhaled radionuclide during the The term "effective" refers to the time of residence of that nuclide in the body (82.3.6). normalizing the effects of a radiation dose absorbed by one tissue to the process of These ICRP risk to the whole person, using a weighting factor appropriate to that tissue. "Equivalent" is used in weighting factors (ICRP, 1977,1981) are quoted in 73.2.2.2 below. the same sense as it was many years ago to define the unit "rem" (radiation-equivalent man) whereby the absorbed dose was multiplied by a "quality factor" (and sometimes an additional "adjusting" factor that has varied between 1 and 5) in order to allow for the variation in biological effectiveness of u, /3 and photon radiations, and to reduce the absorbed dose to A useful discussion of these terms is given by J.R. a common base (see NCRP, 1987a). Johnson in Kase et al. (1985, Chapter 6). Persons handling radioactive materials should be aware of the principles of radiation protection and observe the related regulatory precautions, because excessive exposure to radiation can be harmful. The aim of all such protective measures (IAEA, 1973a,b; Jaeger and Hiibner, 1974; NCRP, 1978a; IAEA, 1979a; Martin and Harbison, 1980; PTB, 1980; Stewart, is to limit any radiation exposure to as low as reasonably possible, 1981; Sauter, 1983) or to "acceptable" levels. These are aimed at excluding any detrimental effects (ya3.2.1.2 natural radiation and 3.2.1.3), but must also be chosen in relation to the irreducible background (73.2.1.4) in order to permit the beneficial uses of radiation. The damage caused by the irradiation of human tissue derives from atomic and molecular which lead, eventually, to interactions, such as ionization, excitation and dissociation, cellular damage. The resulting biological effects of exposure of man to radiation are well known (from experiments, accidents, medical treatment, Hiroshima and Nagasaki (Hiroshima 1981). They are subdivided into somatic effects (Gk. soma, body) which are and Nagasaki, manifest in the exposed individual itself (and are immediate or late) and into genetic Hazardous radiation can also to descendants. effects, which, in general, are transmitted The effects of low-level from ingested sources. derive external sources, or internally radiation are not yet completely understood (NAS, 1980; NCRP, 1981). 3.2.1.2.
Somatic
The
somatic
biological effects
effects
due
of radiation
to different
exoosure
levels
of
radiation
received
are
summarized
in
Table 3-1, and in references such as those given in 73.2.1.1. It must be emphasized that all statements and figures in this table are hypothetical averages, from which rather large deviations occur in individual cases. The late effects of radiation exposure are difficult to distinguish from natural illnesses and often vary considerably from individual to individual. Therefore an estimate of 1 to 2 lethal cases 10 to 30 years after whole-body irradiation per 10' person-sievert average dose-equivalent can only be regarded as valid to an order of magnitude (ICRP, 1977; and Nagasaki, 1981; NCRP, 1987a). IAEA, 1978a; Hiroshima [l rem = 0.01 sievert (Sv); dosimetric definitions are given in 72.6.1 3.2.1.3.
Genetic
effects
of radiation
exDo.sure
The genetic damage to a population caused by radiation is, for the same reasons, also difficult to quantify. A rough global estimate can therefore only be given, namely that the natural background radiation is responsible for a few percent (
The natural
radiation
background
and "beneficial"
radiation
The whole biosphere is continuously exposed to natural background radiation (Eisenbud, 1973; NCRP, 1976b, 1987c; KovaCs, 1984). This comprises three main components of nearly equal risk to man, namely (i) cosmic radiation coming from the universe. (ii) terrestrial radiation from radioactive materials in the earth's surface, and (iii) "internal" radiation from the radionuclides contained in the human body (see Tables 3-2a and 3-2b, the former based on worldwide estimates and the latter on U.S.). The total natural radiation
Radioactivity
measurements:
principles
and practice
background leads to an effective dose equivalent for the individual man of about 1 to 2 mSv per year at sea level. This value is a rough world mean based on the (100 to 200 mrem) 1977; Jacobi, 1982; Sauter,1983). It data from many sources (NCRP, 1971, 1975; UNSCEAR, by less than 30 percent, but can reach up to ten times the "normal" varies, in general, value in proximity, for example, to monazite sands (without observable biological effects). The cosmic-radiation component increases rapidly with altitude above sea level, e.g. by a factor of from 3 to 4 at 2 km, and of from 25 to 40 at 8 km. The internal component can vary considerably and reach rather high values (Table 3-2a) if the inhalation of decay products of the natural radioactive series from the construction materials in badly ventilated houses is taken into consideration (Jacobi, 1982). Since the beginning of nuclear-bomb testing, radiation due to fall-out has to be added to the "natural" radiation It is expected to contribute in the northern hemisphere a whole-body mean background. dose-equivalent commitment of 750 ~SV , accumulated over the period through the year 2,000 (NCRP, 1987a; Table 6.3). But this quantity varies considerably from one organ to another and can reach 650 @J for the endosteal bone from 'OSr alone (NCRP, lot. cit.). About one third of the "natural" background is due to radon and arises from the recent propensity of many of the world to live in brick, and air-tight, houses (Jacobi, 1982; Cast&n, 1985). Recently the general public has become increasingly concerned with the risk from radon, even though it dates to some degree from primordial times as part of the environment that fashioned what we are. The increased risk arises in well-sealed houses into which radon (mainly its isotope "'Rn) can penetrate through brick or concrete, from the surrounding soil through pores and cracks in the walls, or from the domestic water supply. The draughtier the building the less the risk, at least from radon, although other risks may arise. On the other hand, simple expedients such as withdrawing air from the basement, or from channels under the lowest floor of the house can lower any accumulation of radon in the living quarters. With regard to the water supply, one of the authors has, for decades, preserved the genetic purity of the yeast that brewed his beer, by the very simple expedient of first boiling the water to drive off the radon. Table 3-2 (a and b) - Average effective dose equivalent to adult man per year due to the different sources of radiation (a) Worldwide (NCRP, 1975; Jacobi, 1982; Sauter, 1983). and (b) in the United States (after Fig. 8-l of NCRP, 1987).
(a)
Radiation
mrem (1 mrem = 0.01 mSv)
source
Total natural
radiation
100 to 200
Cosmic
30
Terrestrial
40
Total internal (inhalation
5 100 included)
40K ^^ U series (2zz Rn + daughters) Th series (220Rn + daughters) Others (14C etc.) Fall-out Medical
applications
Industrial
applications
Coal and nuclear
= = = =
20 65 15 1
=
1
= 100 5
1
energy
(b)
FIHI
39/H-D
The percentage contribution of various radiation murces to the total average effective dose equivalent in the U.S. pop&Cm.
759
Radioactivity
760
measurements:
principles
and practice
The sources and risks of radon have been well described in a recent report published by the U.S. Department of Energy entitled Radon (DOE, 1987). Radon, by virtue of its short half life and multiplicity of short-lived daughters cannot be assayed directly, as by, for example, internal gas counting. It is usually measured in terms of solution standard of "'Ra from which known quantities of radon can be withdrawn after complete de-emanation the radon reaches 97% of equilibrium (see, e.g., Mann et al., 1980). The principal ways to measure radon concentrations is to compare them with the "radon standard" (i.e. the "sRa solution) by means of a pulse ionization chamber or scintillation counting using an enclosure into which the radon sample can be introduced; the walls of the enclosure are coated with ZnS(Ag) except for a transparent window through which a phototube can record the scintillations generated by the a particles from the short-lived 222Rn progeny. Both these devices must be calibrated; they are described, along with other measuring methods, in a recent comprehensive review by Co116 and Hutchinson (1988). While the methods are relative, the inherent uncertainties are well within the limits needed for radiation protection. The principal exposure of man from medical applications of radiation is due to x-ray diagnosis and cancer therapy, and the use of a variety of other ionizing radiations, such as gamma rays, electrons, ?r mesons, neutrons, protons and heavier charged particles. small contributions to radiation exposure arise from the radioactive Further substances that are emitted from the combustion of coal and from nuclear electric-power and from radioactive industrial products such as fire alarms and fertilizers, production, Table 3-2a refers to two recant estimates of radiation exposure and occupational exposure. table 3-2b includes them under "consumer products" and of man from all these sources: "other" (NCRP,1987d ); for all aspects of nuclear-power production see NCRP (1987e). 3.2.1.5.
Non-radiation
hazards
from radioactive
materials
It is often overlooked that radioactive substances may be chemical the case for uranium and plutonium; the chemical toxicity especially, rather higher than its radiotoxicity (Medical Research Council, 1975).
poisons. This is, of the latter is
Radiation can also be indirectly hazardous. For example, intense irradiation of some plastics could lead to the formation of toxic (e.g. halogenated) gases, which could introduce an occupational hazard unless precautions are taken. 3.2.2. Legal 3.2.2.1.
radiation-urotection
Princiules
regulations
and concerts
The serious hazards associated with the use of ionizing radiation has given rise to The basic regulations set limits for legal protection regulations in different countries. the absorbed-dose equivalent received by the different groups of the population, which is radiation-protection quantity. For practical purposes, secondary limits, the basic reference levels, etc., can be derived from the basic data, using models. And, finally, specific regulations are necessary for special situations involved, e.g. licensing of radiation installations and working conditions, transportation and storage of radiation use of specific sources in industry, agriculture and industry, sources, the occupational considerations include authorized control and handling personnel and etc. Other procedures, insurance, and emergency measures in case of accidents. Most countries have approved such legal regulations. All are based on the pertinent ICRP and IAEA recommendations and are sometimes supplemented by national laws (for the USA These basic ICRP and IAEA recommendations have been see, for example, Stewart, 1981). This has caused some continually developed and often changed during the last decades. the present situation is discussed here. This is, confusion and therefore only characterized by the dose-limitation concept (ICRP, 1977, 1979/1980; IAEA, essentially, 1982c). 3.2.2.2.
The system
of dose
limitation
and urimarv
limits
The aim of the dose-limitation concept is to minimize the absorbed-dose equivalent received by the different groups of the population, while still allowing the "beneficial" This implies the prevention of non-stochastic effects uses of radiation (IAEA, 1982d). (as defined in ICRP, 1977X) and the limitation of the occurrence of stochastic effects* to This is achieved by adhering to three criteria: (i) no practice an acceptable level. involving exposure to radiation (after comparison with available alternative methods, with regard to dose) shall be permitted by the competent authorities unless it produces a net benefit, assessed on a "risk-benefit" analysis for the individual, or a "cost-benefit" society; (ii) any radiation work must be performed in such a manner that analysis for exposures are As Low &s Reasonably Achievable, ALARA (ICRP, 1973); and (iii) as the limits (in terms of the radiation-protection quantities of interest) essential element, must be defined and not exceeded. The primary (effective) dose-equivalent limits (the weighted-mean whole-body dose-equivalent limits) are the most important ones, and are the basis for the derivation ICRP recommends different limits (ICRP, 1979/1980; IAEA, 1982c) of all others. for
Radioactivity
measurements:
principles
761
and practice
stochastic and non-stochastic effects and distinguishes between uniform and non-uniform intake of radioactive exposure to external radiation and that due to substances. Furthermore, the limits must be different for the different groups of the population, such as radiation workers, critical groups with more than natural-background exposure and the general public including everybody. For occupational workers exposed to external and uniform radiation, the annual dose-equivalent limit with respect to non-stochastic effects is 0.5 Sv (50 rem), except for the eye lens, for which it is 0.15 Sv (15 rem). This limit applies only to individual tissues or organs, which do not show stochastic effects such as carcinogenesis. For stochastic effects the dose-equivalent limit for uniform and non-uniform external irradiation of the whole body, HWb,L, is 50 mSv (5 rem) for any year. To obtain the effective dose equiv-
where wr is equal to 0.25 for gonads, 0.15 for breast, 0.12 each for red bone marrow and lung, 0.03 each for thyroid and bone surface, and 0.30 for the remaining organs, total 1.00 (also see 72.6.1.4). The committed (i.e. cumulative) dose equivalent to tissue T, H,,,,, is the dose to tissue T resulting from the total intake of radioactive materials during the year considered, with summation of the dose over the next 50 years as a function of the residual activity resident in that tissue. This represents a lifetime effective-dose equivalent. NCRP (1985) recommends observance of the limits 1 "THs, T 5 Hwb T ’ for stochastic
=
0.05 sv
,
(3-l)
effects,
and for non-stochastic
H 50 T 5 0.5 sv
(3-2)
effects.
In order to allow for deviations from uniformity in total-body irradiations, all ICRP limits are intended, the effective dose equivalent has been defined as
for which
HE = 1 "THT T
The committed effective dose equivalent for a given time t, Ht,T, defined by the ICRP (ICRP, 1977; NCRP, 1985, 1987a), refers to an effective dose equivalent from one dose to tissue T and accumulated over the subsequent time t. Thus, the lifetime dose equivalent, H 50.T, is used to describe the effective dose equivalent from all ingestions of a given radioactive material during the year considered, and accumulated over the 50 years following ingestion. The committed effective whole-body dose equivalent,
should not exceed 0.05 Sv, and that for a limited volume of one organ should not exceed 0.5 Sv. The ICRU has named these limits "stochastic" and "non-stochastic", respectively (ICRU, 1980). The National Council on Radiation Protection and Measurements (NCRP, 1985a; Appendix A) now defines two quantities, H,,, and H,,,, for single and continuous intakes. NCRP (1987a; Appendix A) also has a useful glossary of radiation-protection terms and quantities. Where workers receive radiation from external sources and from intake of radioactive materials together (e.g. in uranium mines), the effective dose equivalent from the external exposure and the 50.years committed dose equivalent from total intake during the year in question must be added and kept below the limit of H, for stochastic effects and 0.5 Sv (50 rem) for non-stochastic effects. that all limits are standard It must be emphasized. mean values, independent of any consideration such as age or sex. For members of critical groups of the population, e.g. those living near to a nuclear-power plant, the annual limits have been set ten times smaller than those for workers, i.e. 5 mSv (500 mrem) for stochastic effects and 50 mSv (5 rem) for non-stochastic effects of individual tissues or organs. For the annual mean effective-dose equivalent of
762
Radioactivity
measurements:
principles
and practice
the total population a limit of 0.5 mSv (50 mrem) is recommended by ICRP (ICRP, 1979/1980) while IAEA recommends a limit of 1 mSv (100 mrem) (IAEA, 1982d). This limit is not critical, it is not regarded as a genetic limit, which would be higher, but as a limit to all exposures from justified practices. Exposure arising from medical treatment and "normal" radiation background are not included in the limits, but the first should also be reasonably minimized and the second must be taken into account if it is enhanced (e.g. by high-altitude flights). These basic primary limits call for a precise and more detailed statement, as for for women of example, exposure exceeding the limits (e.g. life-saving emergency measures), reproductive capacity or pregnant women, child workers in condition A (e.g. special medical care), etc. They can be found in the literature (ICRP, 1979/1980; IAEA, 1982d). 3.2.2.3.
Secondary.
derived
and authorized
limits,
reference
levels
The primary limits cannot always be directly used in practice. In these cases secondary and derived limits are applied which must always be lower or equal to the corresponding primary limits. Secondary limits can be expressed for external exposure in terms of dose-equivalent indices (H,, H,, and if,,; where I is the annual intake in becquerels), and, for intake of radioactive material, by ALI's (&uual Limit on Intake) (ICRP, 1977, 1979/1980; IAEA, 1982d). limits are for radiation In accordance with the primary limits, these secondary workers and external exposure H, = 50 mSv (ICRP, 1979/1980) or better H,, = 0.5 Sv (50 rem) for non-stochastic effects and H,, < 50 mSv (5 rem) for stochastic effects. For intakes the ALI's are the highest value of the annual intake I (in Bq) of a specified nuclide which satisfies both the inequalities: 1 w,I (H 5.,T per unit T for stochastic
effects.
intake)
5
0.05 sv,
(3-3)
and I (H,,,, per unit
intake)
5
0.5 sv,
(3-4)
for non-stochastic effects. (H,,T per unit intake) is here the 50 years committed dose equivalent in tissue T from the intake of unit activity of the radionuclide considered by the specified route, and wT are the weighting factors for the effective-dose equivalent. Consequently, for external exposure and intake of several radionuclides by ingestion (ING) and inhalation (INH), the following relation must always be respected (with H,, in Sv):
The secondary limits for critical groups of the population and for the general public are one tenth and one hundredth of the limits for workers, respectively, but if these limits do not correspond to the primary limits, they must be reduced accordingly. With additional model parameters, e.g. the volume of air breathed by workers (0.02 m3 min-I), further limits can be derived from the ALI's, namely the Derived limits of Air Concentration for a radionuclide during any year (DAC'S). DAC (Submersion) values are limits for operations in a cloud of a radioactive gas, and can be derived from ALI's and additional data. The recommended limits for the dose-equivalent indices are the same as for the dose equivalent (73.2.2.2), or lower. The recommended ALI's vary (ICRP, 1979/1980; NCRP, 1985) from 3.10' Bq (80 mCi) for 3H to l/20 of that for % (except CO and CO,), 1 to 3.10' for 3zP, 1 to 2.106 for 1311, 4 to 6.106 for 13'Cs and 8.106 to 5.104 for ingestion and 5.104 to 2.10' for inhalation of The corresponding DACs vary from 8.105 Bq 226Ra, 25iCf and most of the U and Pu isotopes. mm3 (20 PCi mm3) for 3H to l/20 of it for 14C (except CO and CO,), lo4 to 6.103 Bq mm3 for 32P, 7.10' Bq mm3 for 1311, 2.103 Bq mm3 for 137Cs, and 2.10-l to 8.10.' Bq me3 for most of the alpha-particle-emitting heavy nuclides. The ALI's for ingestion and inhalation of a radionuclide are, in general, not very different, except for alpha-particle emitters for which the difference is 2 to 3 orders of magnitude. For the calculation of the inhalation limits, the radionuclides are classified in three groups (D, W, Y), those with biological half lives of less than 10 days (D), 10 to 100 days (W) and above 1.00 days (Y), There are no generally accepted standards yet on surface contamination, although detailed regulations have been established by several national laws. A distinction must be made here between the limits of contamination of the skin or clothes of persons (national limits about 4 to 0.4 Bq cme2) and the tolerable limits of surface contamination of laboratory equipment (national limits about 400 to 0.4 Bq cm-*. There is also no international agreement yet on the limits of contamination of food, which turned out to be The present national, mostly provisional, a serious problem after the Chernobyl accident.
763
Radioactivity measurements: principles and practice
limits vary between a few hundred and a few thousand of bequerels per kilogram. Further limits used in radiation protection are the authorized limits, which are authorized by a competent authority or management for a certain purpose (operational Finally the They should be lower than primary, secondary or derived limits. levels). They are recommended by an authority frequently used reference levels must be mentioned. or management and indicate which level has to be applied for a given purpose. e.g. recording of dose equivalents received, investigation of the reasons for a larger value (greater than l/20 of the dose-equivalent limit), intervention, etc. 3.2.2.4. Further lea.1 reeulations Besides these most important regulations for limits of exposure, several other regulations are needed at different levels, international, national, and the working place itself. Considerable agreement exists worldwide on the application of IAEA recommendations The IAEA for the transport and packaging of radioactive sources (IAEA, 1979a, 1982b). rules are very detailed and contain many special restrictions (e.g. for fissile materials) The radiation dose-equivalent rate at the and exemptions (e.g. for low activities). surface of the packages is limited to 5 pSv/h (0.5 mrem/h; Cat. I, white label), 0.5 nSv/h 2 mSv/h (200 mrem/h; Cat. III, yellow label). A (50 mrem/h: Cat. II, yellow label) and typical label is sho& in Fig. 3-l. 1.5 cm
--
A
10cm
1_. I
I
5R
10
I
--I
t
Left: IAEA recommended symbol for the presence of ionizing radiation Fig. 3-l. Label for shipping containers of radioactive Right: (black on yellow ground. materials (text and symbol in black on yellow ground, with red bars indicating the category; yellow ground under the symbol for categories 2 and 3).
of any purchase of Several necessary national regulations pertain to licensing radioactive materials and any radiation work (except for very low activities), registration and notification of all radiation operations and exposure, maintenance of inventories of radioactive materials, financial insurance against radiation accidents, as.surance of the competence and the controls of the working environment of radiation installations, waste treatment, medical and social measures. But on These regulations must be observed in all laboratories and other facilities. the laboratory level still further regulations apply, such as a clear definition of the responsibilities, the installation of a widely responsible radiation-protection officer (RPO), clear and optimized organization of the work, recording of work performed and of doses received, the maintenance of health-physics records (that should be kept for 30 years after cessation of work), safe storage of radioactive materials (also safe from theft), emergency measures. 3.2.3. Safe handline of radioactive sources 3.2.3.1. General The success of all radiation-protection regulations and recommendations depends on Therefore, a well-organized and the manner in which the actual laboratory work is done. detailed operational radiation-safety philosophy and program is important for every laboratories the laboratory (e.g. NCRP, 1978b). For metrological radioactivity requirements are still more severe, because, in this case, not only the exposure and the
Radioactivity
764
measurements:
principles
and practice
possibility of accidents must be minimized, but also every disturbance of the measurements Some of the most important problems must be avoided, especially any cross-contamination. connected with the operation of radioactivity laboratories are discussed in detail in the following paragraphs. Radioactive sources may be sealed or unsealed, and solid, liquid or gaseous; they may weigh from fractions of micrograms to kilograms (fuel elements), may emit quite different activities from parts of picocuries to many megacuries. radiations, and may have Consequently, radioactivity work is, in general, very complex and involves very different But there are several general principles. Thus, for every experimental procedures. operation detailed procedures should be established and trial, "blank", experiments performed. Further, the minimum activity needed and the minimum operating time should be and maximum distance between source and operator, and as much shielding as chosen, The use of tweezers, pincers, tongs and gloves is almost always reasonably possible used. of advantage. The optimization of an operation is often very difficult and calls for much which may Lead to accidents. For example, a experience, and should avoid over-protection, short but safe operation with high exposure may give rise to a Lower acquired dose than a longer operation with much less exposure, which may also have larger accident probability. 3.2.3.2.
Laboratories
and working
areas
While even rather active sealed radioactive sources may be used with precaution in suitable locations (e.g. for industrial radiography), unsealed radioactive material of not IAEA proposes to distinguish, very low activity must be handled in special laboratories. three classes of radioactivity laboratory, A, B and C (Table 3-3), in general, between depending on the activity and radiotoxicity of the sources handled. For special purposes, outside this classification. For example, for special laboratories may be designated, metrology laboratories the permitted source activities could be more severely limited, or strong criticality precautions must be for laboratories working with fissile materials taken. Table
3-3 - Classification
of radioactivity
laboratories
Activity Radiotoxicity of nuclide (IAEA, 1973b))
Minimum significant quantity $ib)
Well Chem.
limitsc)
C equipped Laboratory
a)
for Laboratory B Radionuclide Laboratory
very highd)
0.1
< 10 &i
10 PCi-10
high
1
100 &i-LOO
moderatee) low
10 100
<
1mCi
< 10 mCi
1 &i-l 10 mCi-10
of type A Hot Laboratory
mCi mCi Ci Ci
> 10 mCi >lOO mCi >
1 Ci
> 10 Ci
FOOTNOTES
=) Special criteria for fissile materials; b) This quantity may be free from licensing; c) These limits should be multiplied by the following factors; 100 for simple storage, 10 for very simple wet operations, 1 for normal chemical operations, 0.1 for complex wet operations, 0.01 for dry and dusty operations; (1 &i = 37,000 Bq); d) most alpha-particle emitters; e) most radionuclides. to a high degree on its design and Safety in a radioactivity laboratory depends important principles of the design of radioactivity equipment. One of the most laboratories is a reasonable zoning, with a clear classification of the different working areas, according to the level and type of activity handled, and an optimum location of the different zones according to activity levels. The IAEA recommends (IAEA, 1973a) that a They could be named: inactive (i.e. distinction be made between classes of working areas. cold chemistry, detector systems; class 4), environmental (clean, "white administration, counting rooms with possibly room," for samples with low or no activity, and well-shielded activities; class '2.)and hot (high radon-free air supply; class 3), warm (intermediate controlled air flow; class 1). Garment-changing and control rooms may be activities, required between the zones. Access to the environmental laboratory should be through an air lock where laboratory coats and clean footware can be donned. The changing room between zones 3 and 2 should also allow for some foot-wear change and hand and foot monitoring. The entrance zone to any class 1 laboratory should be provided with a safety
Radioactivity measurements: principles and practice
shower and radiation-monitoring equipment. Areas where quite different activities are handled should not be directly accessible to each other. Essential facilities include a source preparation room, a draught-free, temperature- and humidity-controlled weighing room, and counting rooms with low-level detectors, and ventilated source-storage space All zones should be quite Useful facilities are mechanical and electronics workshops. clearly labelled, not only with the radiation warning sign, when necessary (Fig. 3-l), but also with information about the type of work performed therein. Special attention must be paid to all problems connected with the HVAC system (Heating, yentilation, and Air Conditioning), the water supply. the waste- treatment area, and the air and environmental monitoring. Finally, it is a part of radiation protection that radioactivity laboratories be constructed as safely as possible also against natural catastrophes, such as fire, earthquakes and floods. 3.2.3.3. Tvuical radioactivitv work. safe handline. storaEe and waste disuosal The handling of radioactive materials usually begins with the arrival of a shipment, followed by contamination monitoring and the unpacking of the parcel. It is important to prepare carefully for such shipments, to become acquainted with the standard packages (Fig. The unpacked samples must 3-2), and to make provision for adequate handling equipment. always be checked for damage and contamination, and may need undergo further checks. The next step is storage of the unpacked sample (usually a radioactive solution in an This storage area must be sufficiently ampoule or bottle) in a central storage facility. shielded and ventilated if samples in vented vessels are to be stored, in order to avoid damage due to overpressure caused by radiolysis (decomposition of water into hydrogen and oxygen under irradiation). This pertains especially to radioactive solutions emitting alpha particles with activities above about 1 mCi/mL (40 MBq/mL) and beta-particle store all breakable It is also wise to activities above about 100 mCi/mL (4GBq/mL). containers with radioactive solutions in additional vessels large enough to hold the contents of the bottle in case of breakage. In addition to a central storage facility, These auxiliary local storage facilities should be available in all experimental rooms. could be small, but must be well shielded (to minimize influence on counting background) and would be preferably placed in a fume hood in a corner of the room. It is obligatory and vary useful to keep exact records of the stored radioactive samples. This includes all data on the type of source, its container, the position in the storage area, times of removal and return, and any handling of it together with the names of those responsible for
Fig. 3-2. Examples of typical returnable (a) and non-returnable (b) packages for the transport of radioactive materials (different scales).
765
Radioactivity
766
In its "se and custody. radiation-protection officer
measurements:
many cases such or health-physics
principles
records group.
are
and practice
lodged
with
the
staff
of
the
When moving radioactive samples from storage areas to the experimental rooms, it is a few standard containers very advantageous to have, for such within-laboratory transfers, available, and care should be taken not to cause background problems, in the transfer, for other radiation detectors. They will not be The experiments performed with the sample can vary considerably. described here; but one procedure is always necessary, the opening of containment vessels. in order to avoid contamination. Every care must be given to this critical manipulation, a possible overpressure in an ampoule or bottle could cause serious and In particular, The most important experiments in a metrology laboratory are, harmful contamination. in 73.3. It is important besides counting, dilution and source preparation, as described to record all such operations in a logbook or on appropriate forms for standard procedures. especially for a metrology measurements, A very important aspect of radioactivity e.g. by "se of the same pipette for is the avoidance of cross-contamination, laboratory, Therefore disposable instruments should be used wherever possible. different solutions. it, concentrate and confine it as If contamination occurs, it is important to understand much as possible, and to remove it as soon as possible (ICRP, 1978; NCRP, 1980). A crucial problem with radioactivity work is waste disposal (IAEA, 1979a,1983a, 1984; As the activity of wastes can vary over many orders of magnitude, they must Moore, 1981). be carefully contained and suitable arrangements made for their collection from the place The classification of wastes recommended by the IAEA (Gera, 1974) can of their production. a distinction must be made between solid Especially, be used for their segregation. and gaseous waste, and between Liquid (inorganic or organic) (compact or powder), and long-lived intermediate-level and high-level activity, between short-lived low-Level, activity, between combustible and noncombustible waste, and between waste with or without 1n a laboratory, in general, not all categories of waste will be fissile material. there in amounts and which are not shortcollected, but only those which are produced In any individual case the most important criterion for the separation of the lived. The final waste- conditioning and disposal wastes is the method of their later processing. Radioactivity laboratories have, is mostly carried out by regional or national agencies. This pertains also to to collaborate closely with these institutions. consequently, for which local possible release of effluents to drains, sewers or to the atmosphere, regulations must be observed. 3.2.3.4.
Some special
practical
Due to the complexity intricate problems.
nroblems
of radioactive
decay modes,
radiation
protection
may pose
rather
The obviously most important nonclassical problem is the avoidance of a nuclear This is criticality situation, i.e. a spontaneous nuclear chain reaction (Stewart, 1981). done by keeping the mass of any fissile material considerably below the minimum mass necessary for a critical excursion, the critical mass, The critical masses of the common fissile materials are: 6.7 kg for a%~ 20.1 kg for 235U and 4.9 kg for a3'Pu, if the materials are pure metals, have the form of a sphere and are fully reflective (e.g. surrounded by sufficient water to reflect all neutrons). The neutron reflection by water reduces the critical masts by a factor greater than one and up to nearly ten. Therefore, every possibility that a subcritical system could be flooded must be eliminated, The critical mass is still smaller by a factor of about 10 if the fissile material is in solution. when, in the future, greater amounts of heavier fissile nuclides will be available, still smaller critical mase.es will have to be taken into account, e.g. about 10 in solution and fully reflective, g of *%n Sometimes radioactivity measurements can be considerably disturbed by secondary radiations, such as the external electromagnetic bremsstrahlung (q2.4.4) from beta-ray emitters. While beta radiation indicated in the decay scheme is absorbed by thin Layers of material, bremsstrahlung may penetrate these absorbers easily and pose a shielding problem; a typical example is provided by 3zP that gives rise to bremsstrahlung of maximum energies equal to 1.71 MeV. Another penetrating secondary radiation is annihilation radiation, two photons of 511 keV emitted in opposite directions, following positron-electron annihilation (772.4.3 and 2.4.4). Among the most important of the secondary radiations are the x rays and Auger electrons following electron capture (EC) by the nucleus or internal-conversion (IC) electrons (72.4.5). Thus the x rays can often create shielding problems when working with electron-capturing nuclides. Many different secondary radiations are emitted in and following nuclear fission, also several strongly- penetrating gamma rays. Secondary radiations can also be produced by nuclear reactions of the primary particles (activation). This pertains especially to neutrons which produce, for example, positron-emitting 13N around all fast-neutron sources, such as linacs and other accelerators). But (a. n + 1) reactions can also disturb experiments with radioactive alpha-particle sources.
ed
Another potentially hazardous below or above a shield and
type of interfering secondary radiation is that scatterproducing a high radiation level at the place of the
Radioactivity measurements: principles and practice
767
operator in front of the shield (e.g. the "skyshine" effect; Borak, 1975). Scattered radiations can also seriously interfere with measurements of radioactive sources. An absolutely unwanted occurrence in a radioactivity laboratory is an accident. Even if all possible precautions are taken, accidents do happen, mostly due to human error. Any deviation from the foreseen course of an experiment must be considered to be an Many accidents, especially the accident, but the accidents are of different gravity. "usual" ones like fume-hood fires, could be avoided, if sufficient attention were always to be given to the prescribed routines. Most important is the rapid recognition and identification of an accident, which allows one immediately to summon trained personnel and to take, as quickly as possible, previously planned and well prepared countermeasures. When urgent first measures have been taken, the accident should be thoroughly analyzed, and reported in detail so that further preventive measures can be planned and carried out. The detailed initial and later measures, which depend on the individual circumstances, are described in the literature (ICRP, 1978; NCRP, 1980, 1987f; IAEA, 1982d).
It happens that radioactivity laboratories have also to handle neutron sources, especially sources of spontaneously fissioning radionuclides such as zszCf or "radioactive" neutron sources, such as Ra-Be, Pu-Be or Sb-Be sources (Cierjacks, 1983). In this case, special precautions should be taken and, if necessary. special monitors used. 3.2.4. Instruments and materials 3.2.4.1. Radiation monitorine instrumentation Radiation monitoring is an unavoidable daily necessity when handling radioactive materials. The necessary instrumentation used for monitoring varies from simple pocket dose meters (Fig. 3-3) to elaborate systems with many functions controlled by a central computer (NCRP, 1978a; IAEA, 1980). Because different radiation-monitoring instruments can be used for different purposes, if their responses are suitable, it is more important to classify them according to their characteristic measuring properties, namely: The principal radiation measured, namely alpha, beta, x and gamma radiations, (1) neutrons, fission products and combinations of these different radiations; (ii) quantity measured: absorbed dose rate (in rad/s, Gy s-l, or .J kg“ s-l), exposure rate (in R/h, i.e. 7.17.10-s A kg-l, C kg-' s-l, or A kg-l) or accumulated (cumulative) exposure (in R, i.e. 2.58.10m4 C kg-', or C kg-l), or count rate or counts corresponding to dose rate and dose; (iii) detector characteristics: type (see chapter 4), size, efficiency with respect to the main radiation and unwanted radiations, selectivity for desired radiation; (iv) response to the energy spectrum of the measured radiation, especially the energy threshold, below which the instrument is ineffective (often as high as 50 keV), and the energy resolution, if possible; (v)
directional response;
range (vi) (background);
of
measurement
(e.g.
0.1
mR/h,...
to
1000
R/h)
and
detection
limit
(vii) read-out system and speed of indication, i.e. immediate (scale reading) or after treatment (film); and such as compactness, weight, long life, (viii) construction and utilization details : fail-safe provision, portable or fixed location, internal test source, energy supply (mains and, or, battery). An essential The best choice of a suitable detector is often rather difficult. For condition is an exact definition of the purposes that the instrument has to serve. many purposes equipment with exchangeable detector heads are often the best solution. Therefore, but also for general convenience and efficiency, a certain standardization of the monitoring equipment and, especially, of all connectors is most advantageous. equipment, Because of the importance of proper functioning of the monitoring Calibration calibration and regular maintenance and testing should be a normal routine. can be performed in an appropriate radiation field by comparison with an instrument with known response, or by using a calibrated radioactive source and calculating the radiation The calibration of the monitor should also be field to which the monitor is exposed. preserved by checking it regularly against a sealed long-lived radioactive source emitting similar radiations to those for which the monitor was calibrated, and always under the same conditions. The duplication of monitors is reasonable in case of hazardous operations.
768
Radioactivity
3.2.4.2.
Suecial
monitoring
measurements:
principles
and practice
instrumentation
Most radiation-protection surveys are performed using monitoring equipment designed for this purpose. But these may not be suitable in all circumstances, because special instrument properties may be needed in some cases, such as for example, to monitor neutrons (which can only be detected through secondary nuclear reactions) or fission products (with extremely short ranges in matter). Radionuclides which emit radiations of extremely low energy can only be measured with special monitoring instruments, e.g. gaseous tritium using internal gas counters (Budnitz, 197413; NCRP, 197ba), windowless proportional counters or ionization chambers, or "*I with special thin-window or windowless detectors (IAEA, 1978b). A very special radionuclide is "'Rn, which is measured, in general, by means of its several daughter products, and needs, specialized equipment therefore, (Budnitz, 1974a). Many special monitoring instruments are constructed for one application only, e.g. whole-body counting, hand-and-foot monitoring, large-area-contamination monitoring, Filter systems are specially developed for the measurement of low contamination of air (IAEA, 1978a). Special instruments are also needed for the measurement of extreme count rates; low-level systems for highest sensitivity (NCRP, 197ba) and high-level instruments for monitoring of accidents (IAEA, 1982a). 3.2.4.3.
Other
radiation-urotection
eauiDment
Radioactivity laboratories often need special equipment which is not always used in a normal, well-equipped chemistry laboratory. This equipment can vary considerably, depending on the kind of experiment that is planned and the activity level involved. Only the most important special equipment needed in a radioactivity laboratory can be briefly discussed in this report. For work at low activity levels, ordinary laboratory coats are normally used and clean shoes and head coverings may be desirable, but light-weight surgeon-type gloves should always be worn and adequate monitoring instruments should be available. At higher activity levels, changes of clothing may be required for work in "warm-" and "hot-" laboratory areas. For work at the highest levels of activity, respirators, face masks with air SUPPlY? or completely ventilated suits may become necessary. The emergency equipment, such as showers, and first-aid chemistry laboratories should also be available in radioactivity by decontamination materials and equipment (NCRP, 1980). shielding is always required Proper shielding for gamma radiation (Sauermann,
in
radioactivity
kits found in "inactive" laboratories, supplemented
laboratories,
especially
A transparent a sufficient
A simple a
lead-loaded-glass
a radioactivity
a
good
a set a set
, the open sources (such as Am and Fe) should best be metallic layers electrodeposited on standard source supports, the gamma-ray sources should be easy to handle.
Radioactivity measurements: principles and practice
769
Fig. 3-3 Examples of typical monitoring instruments: a) Film badge, about 4 cm x 3 cm; b) quartz-fibre electrometer, typical ranges 100 mR, 200 mR and 1 R; c) finger-ring TLD dose meter; d) personal pocket dosimeter, with indication of exposure and accumulated dose and an audible alarm; e) portable survey meter with exchangeable detectors, typical range 1 to 10 mR/h. 3.2.4.4. Minimum radiation-urotection
equipment for a small radioactivitv laboratory
The radiation-protection equipment needed in a radioactivity laboratory depends entirely on the size of the laboratory and its specific work. But every laboratory requires a minimum of general-purpose equipment, which will be briefly discussed in the following four paragraphs. An important requirement for laboratories of any size, but especially for small ones is, as far as possible, the standardization of the radioprotection equipment and, in particular, of their electrical connectors and cables. The minimum personnel-monitoring equipment could be a thermoluminiscence dosimeter for which processing is often commercially available) and a (or a film badge, The pocket direct-reading pocket monitor for everybody working with radioactivity. monitors could be penlike quartz-fibre electrometers, similar pocket ionization chambers or, better, "beepers" or "chirpers" that are pocket instruments, equipped with a small Geiger-Miiller counter, which give an audible alarm signal at a certain, adjustable radiation intensity. Modern instruments combine a warning "beeper" to indicate exposure rate and a cumulative direct-reading dosimeter. Such an instrument is the "Canary II",
with a piezoelectric beeper and silicon p-i-n
diode detector, that is now available in a package about the same size as a medical pager. It has an exposure-rate range of 10 @R/h to 10 R/h and beeps for every 10 rR accumulated. Survey monitors are also indispensable. They should be as versatile as possible (with exchangeable detector probes), and should be especially suited to the task at hand, having, for example, the necessary range intervals, and showing a suitable response to the radiations to be detected (also see li3.2.4.1). For work with sealed radioactive sources some further items of equipment may be needed, such as more shielding, including a lead shield with a lead-glass window and tongs The for remote handling, additional shielding material and a set of standard sources. handling of open sources may require additional equipment, such as surface monitors (preferably with a large area, and a, +9, and 7 discrimination), an air monitor, personnel protection material, and provision for decontamination. It is always desirable to have available, even in a small laboratory, instrumentation for the identification of radioactive substances, by spectral-energy analysis of the For this, a versatile lOOO-channel analysing system with a different radiations emitted. set of suitable detectors should suffice. This latter set could consist of a high-resolution, average-size alpha-particle detector (surface-barrier or drifted Si), a Si(Li) or thin Ge detector for beta- and x-ray detection, a medium-size Ge gamma-ray detector (Ge(Li) or HPGe), and a 3" x 3" NaI(T1) crystal.
Radioactivity measurements: principles and practice
770
3.3
RADIOACTIVITY SOURCE PREPARATION
3.3.1. Sources for radioactivity measurements 3.3.1.1. General: The need for calibrated radioactive sources The radioactive samples met in practice can be of very different origin, They may stem from field-sampling (73.3.2.1) environmental for controls, from geological prospecting, from irradiation of suitable materials in reactors or accelerators (Servian, 1975), from research work (e.g. TLC plates (Thin Layer Chromatography; Chapman and Ayrey, 1981)), or from commercial suppliers (73.3.1.3). All artificial radioactivity is produced by some kind of irradiation, so that many procedures have been worked out for the preparation of targets for irradiation and for their successive processing (Harley, 1972; Kobisk and Adair, 1982). These procedures cannot be described here, where discussions are limited to the sources for preparation of radionuclide metrology. the But target-preparation procedures related to the source-preparation techniques must always be taken into consideration when metrological sources are prepared. Radioactive samples and sources are used for many different purposes. Consequently, they can vary widely; their activities from much less than 1 pCi (0.04 Bq) (e.g. samples for % dating) to many MCi (tens of PBq; for e.g. food processing or medical radiation; and their mass from much less than 1 picogram (e.g. sources prepared in an isotope (mass) separator) to many kilograms (e.g. fuel elements). They may be sealed, or unsealed, solid, liquid or gaseous; their shapes may be completely different (from irradiated foils such as cobalt to such chemical systems as radionuclide generators). Only those sources prepared for normal radionuclide metrology are discussed in the following sections in detail. In general, the original radioactive samples received by a laboratory, such as many environmental samples, are not in a form that can be measured accurately. Their activities are often too high or too low, and their configuration may be unsuitable for the counting method selected. Therefore, a quantitative preparation of sources for measurement must frequently be carried out using the original samples. This "source preparation" can be very complex, sometimes beginning with the purification of the primary material, followed by chemical treatment (e.g. combustion of organic matter (Gorsuch, 1970) or separation (Trautmann and Hermann,l976), dilution or enrichment (e.g. by electrolysis) and quantitative deposition on a suitable support for counting or, for example, mixing with a liquid scintillator. Some problems, unknown in the chemistry of stable elements, complicate the situation, e.g. the need to add sufficient carrier element or compound to prevent losses Therefore, the final accuracy of a whole radioactivityfrom solution by adsorption. measuring procedure can depend, to a high degree, on the quality of the source preparation which must always be carried out with the greatest care. Here, only the most important techniques of source preparation for metrological purposes can be discussed in detail, namely the quantitative preparation of thin-solid, homogeneous-liquid, and gaseous sources from well- characterized aqueous solutions or solid materials (773.3.3 and 3.3.4). Some interesting special source-preparation techniques are discussed only briefly (a3.3.5). 3.3.1.2.
TYDe
and calibration of radioactivitv sources
Laboratory sources including all types of research sources may vary considerably in their properties, but all may ultimately be needed for accurate radioactivity measurements. Typical laboratory sources are: calibrated radioactive solutions, solid reference sources, liquid reference sources (quenched and unquenched) for liquid-scintillation counting, calibrated sources of mixed radionuclides used to simulate another ("mock" sources), sources for special applications (e.g. for energy measurements, measurement of surface contamination, calibration of radionuclide ("dose") calibrators, and so on). Some of these sources are shown in Fig. 3-4. As calibrated laboratory sources serve mostly for accurate measurements, their relevant properties must be well defined, but the most important property of a source is, of course, its emitted radiation. Current calibrated alpha-particle sources are chiefly s41Am,andthen, less frequently, 'i"Po (but chemically unstable and contaminating), ssgPu (with a few accompanying radiations) and Z44Cm. Alpha-particle radiation is almost always accompanied by electrons and x rays of low to high intensity and low-energy gamma rays. Widely used beta-particle sources (pure beta-particle radiation or beta rays with accompanying gamma rays) are 'H, l"C, "P, 35S, %l, 'sSr + "Y, 147Pm, ""Tl and sl"Bi. s2Na and %o are most often used as positron sources and i3'Cs and sloBi as single-energy As x-ray sources pure electron-capture nuclides (e.g. 55Fe) or photoelectron sources. stable nuclides excited by alpha particles or by other radiations can be used. Many radionuclides serve as gamma-ray sources in the energy range of a few keV to 2.7 MeV, especially the following, listed in the order of increasing energy, '"'Am, ""Cd, 57Co, sOsHg, %r, 137C~, 54Mn, s"Co, sZNa, s8Y (see NCRP 1985). Higher energies can be reached by (a,n+y) sources, e.g. 6.13 MeV with (238Pu>13C). Neutron sources are prepared from spontaneously fissioning from mixtures which s%f or produce (o,n) processes (e.g.r4iAm/Be, 'ssRa/Be, *i'Po/Be) or (7,n) processes (e.g. lz4Sb/Be). Californium-252 can, of course, also be used as a versatile fission-product source.
Radioactivity measurements: principles and practice
Fig. 3-4.
771
Examples of commercially available calibrated radioactivity sources; (a) standard solutions in vials, ampoules or bottles: (b) calibrated (for activity), open sources on foils; (c) calibrated (for emission rate), open sources on thick supports; (d) sealed reference sources; (e) sealed sources for industrial applications; (f) set of calibrated sources; (g) large-surface reference sources; (h) gaseous sources.(Also see IAEA, 1986c)
Other characteristics of laboratory sources which should be known with an appropriate accuracy are: all geometrical dimensions of the source and the source support or capsule, mass, chemical composition (including carrier concentration, which is important for dilutions), isotopic composition (i.e. the relative numbers of atoms of the different isotopes of the element concerned), source activity (or emission rate for gamma-ray sources), uncertainty of the stated source activity, radionuclidic and radiochemical The first points are self-explanatimpurities and stability (including hygroscopicity). ory, and the last two are discussed in the next sections ((73.3.2.3 and 3.3.2.4). But, in each individual case, some of the listed characteristics will have to be known with high, and others with less, accuracy. The high quality of international radionuclide metrology is to a large extent due to In such interintercomparisons organized by BIPM (and also, earlier, by ICRU and IAEA). comparisons of source-activity or activity-concentration measurements, but also on many This is only reasonably other occasions, sources must be circulated amongst laboratories. possible, if the properties of the sources, especially their geometrical dimensions, used Although this aim may never be achieved in different laboratories, are the same. Some promising results have been completely, it should be sought with perseverance. obtained, as most commercial suppliers offer solid sources with the same diameters (25, 30, 38, 50 and 75 mm) and, in international comparisons, standard ampoules (NCRP, 1985; 74.4.7) are a matter of course for the international reference system, SIR (Rytz, 1983). 3.3.1.3. Suuuliers of calibrated radioactivitv sources Many labelled radioactive chemicals and calibrated radioactivity sources are Their addresses can be found in the trade available from commercial and other suppliers. It is impressive and also very directories published by many of the scientific societies. instructive to read the brochures and catalogues of the big commercial and other suppliers (see Table 3-4). Calibrated sources of high quality are available in many countries from The Fachinformationszentrum of Karlsruhe has also published their national laboratories. an "International Directory of Certified Radioactivity Sources" (Grosse and Bambynek, 1983) prepared by IAEA and CBNM, which lists many more suppliers and their products. 3.3.2. Main urocedures and uroblems with radioactivitv sources 3.3.2.1. Samoling and sample treatment
Radioactivity
772
measurements:
principles
and practice
An essential part of radioactivity measurements begins with the field collection of terrestrial, aquatic or atmospheric samples of different type, which are to be processed for measurement and analvsed. This samoline is often the crucial step of the whole measurement (IAEA, 1970, 1$78a; NCRP, 1976;). ”The chief objective of the sampling is to Table
3-4.
suppliers
Some
of
AACC
calibrated IPEN
radioactivity ,ns,um,ode
sources
Perquwar
EnergCncar
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SAO PAULO.
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Products
I,OC”pe Producls Labora1ones 18oU Nonh Ke,smne
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ENGLAND
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Corporamn
Amerrhm 2636 South Arlmgmn
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Radtarmn
Beljmg PEOPLES
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Radioactivity
measurements:
principles
and practice
773
ensure that the collected sample, or samples, be representative of the wider distribution of material to be analyzed, and the sampling should follow a well-devised and tested program. When filters are Another essential problem is the effectiveness of the sampling. used, their effectiveness can simply be tested by using several equal filters in series. But, in general, the problem is more complicated, especially if low activities are present, which can lead to losses by adsorption to the walls of the reagent vessels during ignition and dissolution. Therefore, the addition of an appropriate carrier at every critical point of the procedure is of great importance. Furthermore, the collected samples must be stable between the time of collection and that of the preparation of the final sources for counting. cleaned, combusted, Most of the original samples must be processed, extracted, dissolved, precipitated, or otherwise treated chemically or physically, in order to be measurable ((NAS-NRC, 1965-1987; Harley, 1972; Spinks and Woods, 1976; Friedlander et al., 1981; IAEA, 1981). The end product of these procedures should be stable, homogeneous, sufficiently-active and easily-measurable sources. As losses are inevitable in such as few steps as possible should, however, be used. manipulations, Only minimal treatment may be needed if the samples can be measured using high-resolution gamma-ray spectrometry. 3.3.2.2.
Dilution
and dispensing
A procedure which is quite often needed during source preparations is quantitative dilution of an original "master" solution (by aliquoting and aliquanting) to solutions with lower radioactivity concentrations (Van der Eijk and Vaninbroukx, 1972; Campion, 1975; NCRP, 1985). The parent "master" solutions, prepared from field samples or irradiated materials or simply purchased are, in general, aqueous solutions of HCl or HNO,, about 0.1 mol/L of acid and 100 pg of inactive salt per dm3 of solution. The latter is a minimum carrier concentration to avoid wall adsorption, but it still allows one to prepare sources with small self-absorption. The activities of master solutions are in general rather high, in order to allow for the preparation of sources which are sufficiently active for all counting methods. For example, the measurement of photon emitters in glass ampoules in a reentrant ionization chamber or with NaI(T1) detectors is best made with solutions of from
Diluent,with
proper
t
catnercontent. acidity,
etc....
7 c._-.
_
\ “Master”solution
6111
6112
(A)
8113
Third
Fourth
dilution
dilution
level
(D)
D12nl
level
(E)
E12nll
Fig. 3-5. General scheme for the dilution of a liquid sample. The ampoules Bill, Blkm, C1211, C12np,... could be saved, if filled quantitatively, further measurements.
A2, for
Radioactivity
774
measurements:
principles
and practice
0.4 to 4MBq g-= (10 to 100 &i/g); considerably higher activities still are needed for making good measurements with Ge detectors. For most methods these master solutions must be diluted, e.g. by a factor of about ten, for the preparation of sourcea for 4a measurements. dilution procedure should always be The performed according to a well-devised scheme (Fig. 3-5) with at least two, but preferably three or more, samples at every dilution level. Other samples, at a suitable dilution, can be sealed, and then used to check the half life or dilution factor (i.e. the volume or mass ratio between the final and the original solutions). Volumetric dilution using calibrated pipettes, burettes and flasks is the simplest and fastest dilution technique. However, for small samples, as are mostly used in radioactivity work, it is often not accurate enough, so that weighing techniques must be In this case, applied. an empty dilution flask is first weighed, with or without stopper (mass A), then the diluent is poured into it from a dispensing vessel and the dilution flask reweighed (mass B). Finally the required amount of the master solution is added, preferably by using a "pycnometer" for smaller (Campion, 1975; NCRP, 1985) or a pipette for larger quantities, and the total mas.s of the flask is again measured (mass C). The dilution factor is then DF = (C-A)/(C-B) If pycnometers are used for the dispensing of the master solution their mass before (D) and after (E) dispensing give the dilution factor (C-A)/(D-E). Splashing should be avoided by all means. For very accurate measurements the weighings could be repeated every 10 or 20 seconds in order to account for evaporation (extrapolation method). The contents of the dilution flask should be thoroughly mixed (by shaking or stirring) and, therefore, the flasks should never be filled to more than half of their capacity. A well-equipped chemistry laboratory is the basic condition for precise source-preparation work. It should include a separate balance room with at least two balances. The balance room should be as draught-free as possible (perforated false ceiling), and air conditioned with a temperature constant to within 0.5OC (top warmer), and a relative humidity around 50 to 60 percent, constant to within about 5%. All equipment should be in thermal equilibrium when in use and, therefore, be placed in the balance room at least two hours before use, and the operators should enter the room 15 to 30 minutes The balances should be mounted on vibration-free tables in direct prior to weighing. contact with the ground and without contact to the building. One balance, mainly used for drop weighing (73.3.3.), should cover the range of about 1 mg to 1 g with a precision of better than 10 hg. (Drop masses are about 20 mg.) Such microbalances are now often automatic electro-balances. The second balance must serve many purposes, especially for the preparation of dilutions and dispensing. It should therefore cover an approximate range from 0.1 g to 200 g with a precision of better than 0.1 mg. Regular cleaning and testing of the balances and of their "weights" are mandatory for continuous high-quality work (J.S. Merritt, HN., 1973, p. 325). A set of well-maintained standard "weights," down to the milligram range, can be of great help for the testing and could be used for the substitution method. Some types of balances need recalibration of their optical scale, .some need static-charge elimination (best accomplished with an alpha-particle source of at least 1 MBq). The buoyancy correction (about + 0.1% for brass or stainless steel "weights") must always be applied. And it cannot be stressed enough, that all equipment used must be extremely clean (Campion, 1975). 3.3.2.3.
Purity
of radioactive
An important general samples being measured.
other
samules
problem
Radiochemical impurity refers than those which are desired.
Radionuclidic impurity refers daughters) which is certified.
in
radioactivity
to chemical
measurements
compounds
to radionuclides
is
the
of a radionuclide
that are present,
other
purity
of
the
(and daughters),
than
that
(and
Chemical impurity refers to chemical compounds other than that in which the certified radionuclide is stated to be present; they may be radiochemical impurities or even stable The term isotopic impurity can be used instead of radionuclidic chemical impurities. impurity, that by definition includes isotopic impurity, when the impurity nuclides happen also to consist only of isotopes of the certified radionuclide. As the above terms are not always used in the same manner (e.g. daughter may or may not be included), the intent should always be clearly stated.
activities
should always be accompanied by a statement of all measurable A metrological source impurities and by any relevant high-resolution energy and possible future radioactive It is also important that purity checks be continued from time to time during the spectra. whole working life of a radioactive reference source, because long-lived impurities in shorter-lived sources. For instance, old lJ"Cs sources usually increase in proportion, become, within several years, l"Cs sources and lg7Hg sources, within a few weeks, '03Hg
Radioactivity measurements: principles and practice
775
Further, it should not be forgotten that the purities of most radioactive samples sources. deteriorate continuously because of the radioactive decay itself ("primary internal radiation effect") and due to radiation damage in the surroundings of the active material, (Bayly and 'Evans, especially in labelled compounds ("primary external radiation effect") 1968; Evans, 1976). 3.3.2.4. Stability of radioactive samples with radioactivity samples is Another general, sometimes underestimated, problem In principle, radioactive compounds and solutions are never their long-term stability. stable, as the number of their radioactive atoms decreases and that of the impurities This cannot be avoided but caused by radiation effects increases in the course of time. may be taken partially into account; however, other ageing effects could be prevented. The adsorption of activity on the container walls and impurity centers such as dust particles (and resulting possible chemical changes) can be avoided, or reduced, by adding suitable amounts of carrier to the solutions (0.02 to 10 pg per gram of solution, in general). Also the action of microorganisms can be avoided by addition of suitable reagents, and careful The following effects which cannot be avoided cleaning and sterilization of containers. radiolysis should be considered, minimized as far as possible, or a correctionmade: (hydrolysis, water decomposition by radiation), hydration of solid sources, self-decomposition due to radiation (e.g. of labelled compounds), production of radioactive gases such as Rn isotopes, contamination by recoil atoms or agglomerates from alpha-particle sources, Finally, the continuous exposure to ingrowth of daughters with all secondary effects. radiation and the intense irradiation of sources and source supports may cause mechanical instabilities, which also must be checked thoroughly in order to avoid contamination. For all these reasons, the "useful working life" of a calibrated radioactive sample or source may be of limited duration, and is often specified in terms of the half life of the radionuclide considered. 3.3.2.5. Oualitv and safetv control Contamination by radioactive sources presents a hazard to man and the possibility of Therefore, every prototype commercial error in other calibrated radioactivity sources. source should undergo severe safety tests during development, and all its progeny should be routinely tested during preparation. Leakage tests of sealed sources are particularly important, because such sources are used rather freely. Standard procedures for such tests have been proposed internationally (ISO, 1979). The recommended tests for routine checks during production include wipe tests, bubble tests (at reduced pressure), immersion tests (at different temperatures), and emanation tests. Prototype sources may be tested by impact, heat, pressure, vibration, percussion, etc. And the long-term behaviour of radioactive sources must always be periodically checked. Open sources for laboratory use differ so much from each other, that standard procedures for testing and quality control cannot be indicated. Where possible, the criteria developed for sealed sources may be applied. However, open sources must be handled with special care, owing to the greater contamination danger. Laboratory sources are characterized by their geometrical form, self-absorption, radionuclidic purity and other relevant characteristics. Often, the most important characterization of a laboratory source following that of the activity or activity concentration is that of its uncertainty. Such a statement is even more credible, if the calibration of a source is traceable (72.2.3.) to a national or international laboratory. 3.3.3. Preoaration of thin solid laboratory sources 3.3.3.1. TVDGS of solid source needed for metroloau. Radionuclide-metrology laboratories must prepare and calibrate many different kinds of solid sources, sealed and unsealed, which may vary widely as to size, form and activity. Such sources are most often prepared by dispensing one or more drops of a calibrated solution on to a suitable support. The preparation can be very difficult, as loss of activity by splashing, evaporation or sublimation must be avoided. Several different methods are used for the calibration of radioactive solutions, but most of them require the preparation of sources of as low as possible self-absorption. Such sources are, in general, prepared by quantitative deposition of drops of the solution on to very thin supports (Yaffe, 1962). This technique is most important for metrological laboratories and is discussed in some detail in this chapter. A survey of currently used source-preparation techniques may be found in Table 13 of NCRP (1885). 3.3.3.2. Source swoorts.
backine and cover foils
Many different source supports and mounts are used for thin sources, mostly plates or discs of suitable dimensions and suitable low-Z materials if low-energy-electron scattering is to be minimized. In general, the supports and mounts are to be electrically conducting, in order to avoid electrostatic-charge accumulation which could cause counting errors. For many simple measurements, aluminium, steel or platinum discs of 0.1.mm to l-mm thickness
Radioactivity
776
measurements:
principles
and a diameter appropriate to the counter (20 to measurements rather sophisticated supports may be
50
and practice
mm)
suffice.
For
very
accurate
et al., 1970), or the thinnest possible conducting plastic foils (for 4a measurements in gas-flow counters). Thin supporting foils are, in general, placed on thin aluminium or stainless-steel annuli with inner diameters of 16 to 28 mm and thicknesses between 0.1 to 0.5 mm. Plastic foils of not-too-low thickness (more than about 100 pg/cm2 or 0.001 mm can be bought from many commercial suppliers in the chemical industry; very thin foils, down to about 5 pg/cmZ must be prepared by the user (Maissel and Glang, 1970). A simple method of preparation is the pipetting of a suitably concentrated solution of a polymer plastic (such as cellulose, polyvinylchloride, polyvinyl polystyrene, alcohol, polyvinylchloridepolyvinylacetate copolymer (VYNS), dissolved in cyclohexanone or a similar solvent) on to a rotating glass plate. The latter may be a square of 10 cm x 10 cm and one millimeter thick, and it should rotate at about 500 to 5000 revolutions per minute, depending on the expected foil thickness. The glass plate must be prepared by cleaning with some watersoluble substance (preferably detergents) and then coated with a thin gold layer (by vacuum evaporation or other means) before use. The glass plate with the plastic foil on its gold-coated surface can again be coated with a suitable gold layer (or other conducting material (Lowenthal and Smith, 1964). Then the doubly-coated plastic film is cut into pieces of appropriate size, using, for example, a razor blade, and taken off the glass plate by cautiously dipping into water. The floating foil pieces can be caught on annular supports and and the thickness determined by weighing or measuring in any other suitable The conducting layers should have the bulk resistivity of the material used, which is way. usually gold, and the layers should be at least 10 pg/cm' or, better, 15 to 20 /lg/cmz thick. It is wise to use a plastic with a thin layer of conducting material that is resistant against the source solution, because otherwise the sources could deteriorate too rapidly. Many variations of this method for the preparation of thin foils are used successfully (Pate and Yaffe, 1955). Thin foils for source covering or sandwiching, needed especially for efficiency extrapolation (75.5.2.3),are prepared in the same way, but here the inner diameters of their annular supports must be greater than the outer diameters of the sources to be backed or covered. 3.3.3.3. Quantitative dror, deoosition The crucial step in the preparation of thin solid sources from radioactive solutions is the quantitative deposition of drops onto thin supports. The determination of the drop masses can be performed volumetrically, by using calibrated pipettes or burettes (J.S. Merritt, HN, 1973, p. 325; Y. Le Gallic, HN, 1973, p. 333; NCRP, 1985), or gravimetrically. The accuracy of the first method is only moderate, about 0.5 to 5%, but it suffices for many applications. For accurate measurements the mass of the deposited drop or drops must be obtained by weighing with a precision microbalance (73.3.2.2), which can yield, under favorable conditions, uncertainties as low as 0.01% (Merritt, lot. cit.). Two drop-weighing methods are commonly applied, namely the pycnometer method and the extrapolation method. The first, which is generally recommended as the most accurate, is based on the weighing of the vessel (pycnometer) containing the radioactive solution before and after dispensing the source drop. The mass of the latter is given by the difference of the two weighings. Different pycnometers have been used, but disposable small, low-mass, plastic ampoules with long tips (NCRP, 1985) proved to be the most suitable. In the extrapolation method the mass of the deposited source drop (from a micropipette kept about 5 mm above the foil) is weighed as a function of the time elapsed after deposition of the drop (for about 0.5 to 3 minutes). Extrapolation of the weighings to time zero eliminates to a certain extent the evaporation and yields the value of the mass dispensed. Due to effects (especially cooling of the drop) at the moment of deposition, the extrapolation method gives systematically 0.2 to 0.3 % too low results for the drop mass. But modern electro-balances with continuous indication of the mass could give a better extrapolation. 3.3.3.4.
Methods
for imurovine. source
Quality
as possible Metrological sources must, in general, be as thin and as homogeneous (throughout the well-defined source area). But simple drop deposition from a salt solution does not generally lead to the wanted uniform formation of small crystals in the source This can easily be seen by inspection with a magnifying lens or under a microscope, area. a test which should be performed on every individual high-quality source. Therefore, several different techniques are routinely used to improve the quality of drop sources, of which only the most important ones can be mentioned here. Wetting agents such as insulin or Catanac (Baerg et al., 1964; supplier's addresses are given in NCRP, 1985) can be deposited onto the supporting foil and dried before depositing the drop; seeding agents such as Ludox SM (Pate and Yaffe, 1955; NCRP, 1985) can be added to the deposited drop before drying; drops of solutions of suitable chemicals can be added to the deposited drops in order to induce precipitation and uniform crystallization. The method of precipitation may often be the only possible one for the preparation of stable sources, as for example, in the case of sublimating HgS sources (by precipitating with thioacetamine(TAA)or H,S, or in the case of low salt concentrations (Korenmann, 1966).
Radioactivity
Although testing, as be performed outside the can be done surface, or 3.3.4.
principles
and practice
most unsealed laboratory sources are legally not subject to safety and quality are sealed sources (73.3.2.5), every possible, reasonable testing should also on them. Especially important, in this case, is to check for contamination stated active source area (which can often occur because of splashing). This by defined-solid-angle counting using suitable diaphragms just above the source by auto-radiography.
Preoaration
3.3.4.1.
measurements:
Tvpes
of liauid
of source
and easeous
laboratorv
sources
needed
In addition to many types of solid sources, different liquid and gaseous sources must be prepared quantitatively, or measured in metrology laboratories. The preparation of the most frequently needed ones is discussed in what follows; in particular, "liquid sources" in the form of ampoules for gamma-ray or bremsstrahlung measurement (e.g. 32P), vials for liquid-scintillation counting, and "gaseous" sources, i.e. suitable ampoules filled with radioactive gases. Such source preparations have been discussed in NCRP (1985) in some detail. 3.3.4.2.
Ooeninp
filling.
emotvine. and sealine
of amooules
and vials
The handling of ampoules and vials, especially their filling and emptying, is probably one of the most frequent functions in activity-calibration laboratories. There are two reasons for that: first, most radioactive solutions of high quality are stored in ampoules or vials, and second, most of them can be measured easily, fast and with considerable accuracy in standard ampoules using standard ionization chambers (SIR; see 72.2.3) or similar standard devices with other detectors (NaI(Tl), Ge, etc.). The filling of new, well-cleaned ampoules must be performed gravimetrically, if high accuracy is required. They are first weighed empty and reweighed after filling from a pipette or burette. It is most advantageous to use some mechanical, precision positioning device for the movement of the ampoule towards the pipette or vice versa, in order to avoid splashing, etc., during filling. After reweighing the ampoules should be flame-sealed and the vials closed by a suitable stop or cap as soon as possible. They could be again weighed after sealing for control. Ampoules should be filled to a part of their capacity (about half), in order to keep the liquid well away from the hot top when sealing. The latter is best accomplished using commercial equipment which produces only negligible evaporation. The opening of the ampoules must also be carried out with the greatest care. After an outside wipe test and careful shaking and draining of the solution from the tip, a file mark at the narrowest diameter is drawn and the tip is cracked by contacting the file mark The emptying of the ampoules with a small bead of molten ("red-hot") glass or a hot wire. may be done in a similar way as the filling, using the same mechanical device or a The use of standard ampoules is mandatory for the SIR (72.2.3), but also of pycnometer. great advantage for all other purposes. 3.3.4.3.
Preparation
of sources
for liauid-scintillation
counting
Most radioactivity measurements in life sciences and many in other fields are made by of the light emitted due to liquid-scintillation counting (LSC), i.e. by measurement radiations from radionuclides in a scintillator solution (75.4.3). The basis of all LS solutions is an organic (aromatic) solvent (e.g. toluene, xylene, dioxane) with a primary and a secondary solute (wavesolute (scintillator; a few percent of PPO) . The main problem in length shifter; e.g. a few tzn:hs of a percent of POPOP). LSC is to introduce aqueous radioactive samples into the LS solution in such a way that stable and homogeneous solutions or dispersions (of sufficiently small particles) with a This can be done in different ways: essentially, high counting efficiency are formed. ideal solutions, "real" solutions and emulsions three kinds of LS sources can be prepared: Ideal (molecular) solutions are, of course, obtained, (Coursey and Moghissi, BIPM, 1980). if the solvent is itself labelled with the activity (eg. 3H-toluene), but also noble gases, (of halides, metals (Grignard), lipids, etc.) yield ideal and many organic compounds The mostly needed uniform mixture of the LS solution with an aqueous solutions. agents are radioactive sample is, however, only possible if other added, such as complexing agents, emulsifiers, etc. The resulting ternary "real" solutions solubilizers, neighborhood of relative concentration, and emulsions are only stable in a limited temperature, pH value, salt (carrier) content and chemical behaviour, etc. Therefore, it is often the most important experimental work to find these proper conditions for the a considerable part of all "applied" LSC measurements is individual cases. Nevertheless, - ethanol (up to 15%) - water made using "real" solutions, especially toluene-scintillator naphthalene - water mixtures and scintillator (less than about 1%) systems: dioxane mixtures with alkyl phosphate chelating (complexing) agents (e.g. HDEHP). The greatest part of LS counting in life sciences is probably carried out using (colloidal) emulsions. The counting samples are in this case ternary mixtures of the basic LS solution with a dispersing agent (emulsifier; surfactant or detergent; e.g. 20 to 30% of Triton-X100) and small drops) in the aqueous radioactive sample, the water forming micelles (microscopically The size distribution of these the scintillator which are stabilized by the emulsifier. micelles and how this can be influenced is not yet completely understood. Also the limited stability of the emulsions, which can even break up into several phases, makes their use
777
Radioactivity
778
for
metrological
purposes
measurements:
principles
and practice
difficult
Liquid-scintillation counting offers, in general, several advantages for metrological purposes, especially its versatility (more than 60 of the important radionuclides have already been measured by LSC and its possible high efficiency (4x-geometry). But it has also serious disadvantages because, in addition to the chemical and stability problems encountered in source preparation, the counting efficiency is often but poorly known. Due to quenching, i.e. absorption of the light produced by the radiations from the radioactive sample, which is caused by impurities (especially oxygen), by sample heterogeneity, colour quenching, etc., the counting efficiency of LS samples is never equal to the theoretically possible lOO%, especially for low-energy radiations as those from 3H, etc. Therefore, the determination of the counting efficiency is a most important part of accurate LS measurements, which are essentially comparative (relative) assays. Several methods have been proposed for the experimental determinations of the LSC efficiency; but most of them call for standards. Therefore, metrology laboratories should be able to of standards for LSC: internal standards (75.4. 3 ) prepared from supply a variety calibrated radioactive aqueous solutions for the individual LS measurement conditions, unquenched ("ideal" solution) standards for the determination of optimum measuring conditions and efficiency calibrations, and differently-quenched standards prepared from standard solutions, for the efficiency determination using the channel-ratio method or the external- standard method. All these standards must be prepared quantitatively, as must the sources from the original solutions; but the stability, homogeneity and accuracy of the standards should be the best available today. The preparation of metrological LS sources follows widely the guidelines discussed in the preceding chapters, but some special problems must be mastered. In order to avoid disturbing phosphorescence, the whole procedure of source preparation and subsequent storage (and the storage of the materials used) should, when necessary, take place under red light or in the dark. Also the strong evaporation of organic solutions causes problems, and may necessitate the application of extrapolation techniques (weighing at subsequent time intervals) after deposition, and extrapolation to the time zero). A proposed standard procedure for the preparation of LS sources, especially standards, is to pipette about 0.1 ml of the radioactive solution into a 100.ml bottle or Erlenmeyer flask, weigh it by the pycnometer method (73.3.3.3) or the extrapolation method, add about 50 ml of the scintillator solution and reweigh the filled bottle (if necessary again by the extrapolation technique). It may be important to shake the mixture very thoroughly (10 minutes mechanically) in order to get homogeneous "real" solutions, which can then be filled in the normal way into vials (83.3.2.2). Instead of this method which implies premixing of the scintillator and solubilizer and, finally, the radioactive solution, all the parts can be filled quantitatively into a container and mixed there. But one must make sure that the weighings exclude non-negligible losses of volatile organic solutions. A method of mixing after sealing was used by Garfinkel et al., (1965) in the calibration of the NBS tritiated-toluene radioactivity standards. 3.3.4.4.
Gaseous
sources
Some radioactive substances must, or can advantegeously, be measured as gases, e.g. In this case the compounds, etc. 3H, 14C02, *'Kr, 331'333Xe, Rn, some metallo-organic classical (vacuum) equipment for the handling of gases is needed for the preparation of Such a samples for the generally used measuring method, internal gas counting (75.4.4). vacuum line for radioactivity work involves not only the stainless-steel tubing, currently in use, but also accurate temperature and pressure-measuring devices, combustion ovens (eg. for H,O to H, or CH,), freezing traps, calibrated volumes for quantitative mixings, etc. An important problem is also the suitable admixture of a carrier gas to the active Most gaseous samples, especially in order to prevent wall adsorption, etc. component, But special standards, are filled into ampoules with easily breakable seals (Fig. 3-4). ampoules could be for measurement in ionization chambers, such as are used in SIR. "gaseous sources" are flow standards, needed to monitor gaseous special Very Other effluents from nuclear installations, etc., which are available commercially. gaseous standards needed for applications are environmental standards, but their preparatin and use is quite similar to the preparation of sources for high-accuracy internal gas counting. 3.3.5.
Special
3.3.5.1.
laboratory
General
sources
and special
and soecial
source-ureoaration
techniaues
techniaues
While sources of the types discussed in 73.3.3. and 73.3.4. are used in the vast special sources are sometimes needed for particular majority of radioactivity measurements, Their preparation will be described briefly in 873.3.5.2. 3 and 4. Other applications. electrolytical deposition on special procedures can only be enumerated here, namely: (Verdingh and Lauer, 1967; thick or thin (foil) backings (Talvitie, 1972), electrospraying 1971; G.C. Lowenthal and H.A. Wyllie, HN, p, 353, 1973), molecular plating, Verdingh, deposition from organic solutions, electrophoresis (Verdingh, 1971), use of isotope (mass) separators (Landgrebe, et al., 1970) or lasers (Murnick and Feld, 1979; Hurst and Payne,
Radioactivity measurements: principles and practice
779
1984), vacuum evaporation, sputtering, distillation, transfer by recoil, sedimentation, (Van Audenhove and Joyeux, 1972), surface adsorption, painting, mechanical processing precipitation, ion exchange, chromatography, solvent extraction, differential absorption, etc. And radioactive atoms introduced into molecules of organic surface-active substances, such as stearates, can be used to prepare sources on monomolecular-layer (MML) films of The preparation and use of such MML have recently been calcium and barium stearates. reviewed, with references, by Watanabe et al. (1987) and by Dobrilovic et al., 1986). 3.3.5.2. Snectrometrv sources and other verv thin sourcee For the spectrometry of a or fl particles or of low-energy 7 or x rays, very thin sources are required. Preparation on thin foils improves the energy resolution and reduces the disturbing effect of backscattering. In general, such sources do not need to be For many applications electrodeposition and vacuum evaporation prepared quantitatively. (volatilization from a hot filament) may be the most suitable techniques (Bambynek and Reher, 1967). Only in extreme circumstances, are more refined methods necessary (Reher et al., 1982). Of course, the difficult deposition of radionuclides in an electromagnetic or in general - used only for a laser separator yields the thinnest sources, but these are research work. The quality of thin sources is best described by their contribution to the FWHM (Full Width at Half @ximum) of measured spectral lines. However, it would be quite useless to try to reduce this contribution far below the limit that is set by the resolution of the For the best commercially available detectors, these limits are today detector system. 12 keV for 5.MeV o particles, 4 keV for electrons, 0.15 keV for approximately as follows: 5.9 keV x rays, 0.5 keV for 122-keV 7 rays, and 1.8 keV for 1.33.MeV 7 rays, or better (see Ch. 4). 3.3.5.3. Multi-gamma-ray
sources
Sources emitting 7 or x rays of one or more different energy values and emission probabilities in known ratios are often used for calibrating defined-solid-angle devices. For 7 or x radiations above about 30 keV, and also, to a certain extent, electrons, This can be defined-solid-angle counters must be calibrated for the energy range used. done by means of a set of x- and y-ray standards of single radionuclides with photon energies distributed over a useful range (e.g. rGIAm, "'Cd, 57Co, r3'Ce, "'Hg, 51Cr, rz7Cs, 54Mn, %b, %c, %o, '*Y). But a single measurement with a calibrated mixture source would be more practical. Such mixed sources are available commercially, but the relative emission probabilities change considerably with time and require frequent corrections. Single nuclides having a complex spectrum and a long half life are therefore preferable. Such calibrated sources are e.g. rszEu (0.1 to 1.4 MeV), r3'Ba (30 to 400 keV), '**Ta (58 to 1231 keV), etc. Although the emission probabilities for the different photon energies are well-known, corrections for correlated (coincidence) summing must always be applied, because the radiations are emitted practically simultaneously. Some mixtures of a few T-ray emitters are also recommended for calibration purposes, expecially a 125Sb-'5'Eu-'55Eumulti-T-ray and x-ray standard, which has 18 peaks between 25 and 1600 keV, has a useful life of more than 10 years, and needs only small coincidence-summing corrections. Samples of certain a-particle emitters are also useful as multi-y-ray and x-ray sources for energies between 20 and 500 keV. Accurate photon-emission probabilities can be determined, provided that the decay data are sufficiently well known, because a-particle activities are in general easy to measure. 3.3.5.4. Other special laboratorv sources There are many other types of source that may have to be prepared and occasionally measured by radionuclide-metrology laboratories. Such are the long-lived, rigid (metallic, if possible), low-activity standards for o particles and x rays, as, for example, 235U, natural uranium, and 239Pu. An even more useful group includes sources of moderately long life and intermediate activity, such as %o, rJ7Cs or 9c(Sr + Y). Sources of %o prepared by irradiation of samples of 59Co, the only stable cobalt isotope, in a nuclear reactor provide extremely useful laboratory standards for different purposes and for many years. Simulated or "mock" standards (that are not generally recommended) and radionuclide generators ("milking cows"; sometimes referred to as "isotope generators") effectively extend the periods of availability of short-lived radionuclide sources, while maintaining, usually for medical purposes, the advantage of their rapid decay. Simulated standards are mixtures of longer-lived radionuclides, or sometimes single radionuclides, emitting gamma rays of approximately the same spectral distribution as the one to be simulated. The most important example is that of mock iodine, i.e. the simulation Of r3r1 (T& = 8 d) by a mixture of 133Ba (T = 10 a) and r3'Cs (Tb = 30 a), maybe ti with a cadmium filter to absorb x rays. An isotope generator comprises a column containing
a longer-lived parent nuclide
780
Radioactivity
measurements:
principles
and practice
(e.g. -MO, 66 h) adsorbed on to some resin from which a short-lived daughter (in this exMore than one hundred such systems are known ample, ggmTc, 6 h) can be eluted as needed. (Lebonitz and Richards, 1974; Knapp and Butler, 1984), about ten are available commercially, and some play an important role in nuclear medicine. Special laboratory sourcesmust sometimes be prepared for special applications, such 7 rays (6.13 MeV from 238Pu/13C (a,n), Robert et as, for example, sources of high-energy x-ray sources (Knoll and Rogers, 1982, large-area or largeal., 1977) ) ultra-low-energy and Line-shaped or wire-like sources for the volume sources for contamination measurements, calibration of ,9-ray spectrometers. In order to complete this enumeration of special sources it is appropriate to mention for the labelled compounds (Welch, 1977), neutron sources (Cierjacks, 1983), and sources M&ssbauer effect (Gibb, 1976) for x-ray flourescence-spectroscopy systems (Dzubay, 1977), and for activation-analysis detectors and standards (Schneider, 1973). However, sources included in this group are, in general, prepared only by specialized laboratories. 3.4.
EVALUATION
OF RADIOACTIVITY
3.4.1. Characterization 3.4.1.1.
Results.
MEASUREMENTS
of the results
correction
of a radioactivitv
measurement
factors
Referring to a statement already made in a more general context (see 72.2.1), the result of a radioactivity measurement is to be described by the "best value" for the This "best value" is normally the activity and a realistic estimation of its reliability. No result should be arithmetical mean calculated from all partial results obtained. discarded without a cogent reason. Each individual result may be considered as being more or less affected by various of the disturbing influences for which corrections must be made, e.g. by multiplication Each method calls for a different set of such result by appropriate correction factors. correction factors the values of which vary from one experimental configuration to another. It is useful to write down this fact in a single analytical expression that should be If M denotes the with most pulse-counting methods. used throughout, where applicable, B+ and I+ those of background and interfering radiations, number of counts registered, during the measuring period, T, and R the respectively and both properly corrected, including dead-time losses, pile-up (random correcting factor for finite time resolution, summing) and accidental coincidences, we can write for N(t,), the number of disintegrations occurring during T and referred to the time t,, as
or
N(t,)
=
(MF-B+
N(t,)
=
(MR
-I+)GPQCDAHWESZ, B+- I+) F Z
The factors G, P, _........., following corrections:
Factor
(3-7)
(with their overall
product
equal
to F) represent
the
Effect
G
geometry
P
decay-scheme-dependent
factor
= 4rrsr/n,rf; correction
(e.g. r-ray-emission
source effects
Q
(anisotropy of emission, inhomogeneity, source geometry);
source, C
absorption, attenuation and of the detector;
D
detector
A
electronic
H
higher-order effects, fluorescence radiation;
W
"wrong
radiations",
E
finite ility,
energy discrimination including summing;
S
coincidence
Z
decay
Three
(3-6)
very
response pulse
during
useful
and
scattering
shaping,
between
including
(efficiency)
influence
secondary
scattering
energy-to-voltage
radiations,
(threshold
and absorption
the surfaces
of amplifier
e.g. 7 rays in p-ray
probability);
of the source
conversion;
time constants,
e.g.
in the
annihilation
and delays; or
induced-
and zero-detection
probab-
detectors; or window)
summing; the measurement
applications
and conversion
of an analytical
to the reference
expression,
such
time,
as Eq.
to
3-6,
can be
Radioactivity
measurements:
principles
and practice
the evaluation seen immediately in the definition of efficiencies, If Eq. 3-7 is inverted, ments, and the calculation of uncertainties. MR
781
of relative one obtains:
measure-
- B+ - I+ = N(t,)/F = N(t,)e = M
,
(3-8)
This equation shows quite clearly which is the definition of an overall efficiency, B. conditions, even, that efficiencies are not set a priori, but depend on the experimental For practical purposes it is, therefore, in general necessary possibly, on the decay rate. to separate the count-rate-dependent and the decay-scheme-dependent parts from the overall In any case, efficiency efficiency and to define efficiencies as instrumental constants. definitions should be fully explained. Equation 3-6 also helps one to understand the advantage of relative measurements. If the source to be measured can be compared with a very similar standard, so that c = cSt, all corrections cancel, and it follows that N(t,) = N(t,),,(MR - B+ - I+)/(MR - B+ -I+),t
(X-9)
= N(t,),,(M/M,,) If the source and the standard accordance with Eq. 3-6.
differ
in any
respect,
then
corrections
Finally, it is evident that an analytical equation is needed overall uncertainty from the component uncertainties, using the (Eq. 3-38). 3.4.1.2.
General
orinciules
for reliability
are
necessary
in
for the calculation of an error-propagation law
statements
A result of a measurement is of little use if it is not accompanied by a statement on In calculating the best value (or the mean) of a how reliable it can be considered to be. reliabilities have to be taken into account. number of individual results, their "Reliability" is not a generally accepted term with a clearly defined meaning, and the important question of how it should be expressed by a numerical value is treated in very in the abundant literature (Topping, 1962; ICRU, different and rather controversial ways 1968; Bevington, 1969; Ku, 1969; Dietrich, 1973; Wagner, 1977; Mfiller, 1979a; Romanowski, 1979; Ferro Milone and Giacomo, 1980; Miiller, 1984). were elaborated by a working group A few years ago, simple and clear recommendations of experts from eleven national laboratories and issued by the BIPM (1981a). These recommendations have been found useful and satisfactory in many applications, especially in international comparisons of activity measurements. They are as follows: The uncertainty in the result of a measurement generally consists of 1. several components which may be grouped into two categories according to the way in which their numerical value is estimated: A. Those which are evaluated repeated determinations; and B. those which
are evaluated
by
applying
statistical
methods
to a series
of
by other means
There is not always a simple correspondence between the classification into categories A or B and the previously used classification into "random" and uncertainties. "systematic "systematic" The term uncertainty" can be misleading and should be avoided. Any detailed report of the uncertainty should consist of a complete list of the components, specifying for each the method used to obtain its numerical value. 2. The components in category A are characterized by the estimated sl) and the number of variances, s:, (or the estimated standard deviations degrees of freedom, ui. Where appropriate, the covariances should be given. The components in category B should be characterized by quantities uf, 3. which may be considered as approximations to the corresponding variances, the existence of which is assumed. The quantities u: may be treated like variances and the quantities uJ like standard deviations. The combined uncertainty should be characterized by the numerical value 4. The obtained by applying the usual method for the combination of variances. should be expressed in the form of combined uncertainty and its components "standard deviations". applications, it is necessary to multiply the 5. If, for particular combined uncertainty by a factor to obtain an overall uncertainty, the multiplying factor used must always be stated.
782
Radioactivity measurements: principles and practice
Proposals similar to the above (3 and 4) regarding the estimates of category-B uncertainties (i.e. those not amenable to statistical analysis) were also made by Jaech (1973; see his "systematic-error"variance) and continue to be used (see ANSI, 1987, p. 23) at facilities, established by the then U.S. Atomic Energy Commission, for the processing nuclear materials. It cannot be denied that some arbitrariness always remains in the assignments of uncertainty, and that the conditions for a probabilistic treatment are never completely However, this is not really disturbing as long as the terms used are clearly fulfilled. defined and every reported numerical assignment is fully explained, in such a way that a reanalysis, under different hypotheses, would equally well be possible. In the case of activity measurements, the quantity being measured is itself subject to But even when a constant quantity is measured repeatedly, the results random fluctuations. obtained deviate from each other. The amount of this dispersion, which is normally expressed as a variance or standard deviation, is an inverse quantitative measure of the repeatability of measurements, provided they are taken by the same observer, using the same method and the same instruments, at the same location and under the same conditions of use, within a short period of time. However, when some or all of the above conditions change (in a specified manner) between individual measurements, one speaks of reproducibility (see ISO, 1984). The term accuracy is applied to any estimate of the closeness of the agreement between the result of a measurement and the true but unknown value of the measured quantity. On the other hand, the term precision (expressed as a variance or standard deviation, that include repeatability and reproducibility) is used for expressing the closeness of results among each other. These two terms, if explained in detail, are the most important for the characterization of a measurement. Precision should m be confused with accuracy. It is very clear and must be accepted that an overwhelming number of metrologists in many scientific disciplines have an inkling as to the meaning of the terms "preclusion" and "accuracy" as they relate respectively to "random" and "systematic" uncertainties. The Webster dictionary gives a definition of "systematic" as in "systematic bias". It is also clear that these terms overwhelmingly dominate the scientific Literature, often ambiguously, and will probably continue in use for decades hence (see, for example, INDC, It is therefore important to take cognizance of the present "state of the art" if 1985). one is to continue to enjoy the privilege of reading about the work of our colleagues, past, present and future. In the first place, it is of the utmost importance when giving an estimate of the uncertainty associated with the measurement of a physical quantity that, as has been stated above, the nature of the uncertainty be clearly stated and its method of estimation be fully explained so that it can be "unscrambled" and reassembled in any other way to suit the requirements of the reader and possible user of the datum. The three principal statistics for estimating random uncertainty are: the standard deviation or its square, the variance, of an individual measurement; the standard deviation of the mean (sometimes called "standard error") or its variance; and the confidence level of the mean given for a stated confidence limit, e.g. 68, 95, 99 percent or any other suitable Limits. The terms "error" and "uncertainty" are almost synonymous, but the latter may perhaps be preferable in most contexts: Unknown to the observer his result may actually be the "true" value, and therefore have zero error, but the uncertainty is never zero. So often in reading the scientific literature, a measurement of a quantity is quoted with an appended fU with no indication at all as to which estimate of the three statistics mentioned above has been used, nor with any indication as to whether an estimate of systematic uncertainty has been included. Quite often an average of several measurements will be given togerher with an estimated standard deviation, and one is left to speculate whether it is the actual standard deviation, or that of the mean which is n* times smaller (see Eq. 3-23 below). In assessing the magnitude of possible systematic uncertainty, an estimate by an The former will experienced experimenter may be quite different from that of a novice. know his equipment and its capabilities and may be able to estimate its maximum conceivable limits of systematic bias. As no such estimate is likely to be better than 10 percent, let alone 1 percent, it can be considered to be approximately equivalent to the 90 or 99 Some observers find that they can estimate such percent confidence-Level statistic. systematic uncertainty more readily at the 68.percent level of confidence (73.4.2.1; and Miiller, 1979a), but so be it. It is, however, essential that the level of the estimate and the manner of combining it, linearly or in quadrature, with any estimates of other always -be stated. systematic uncertainties and with the random uncertainties m Some uncertainties may start as "non-random" but gradually take on the nature of randomicity. Such might be the dead time of a detector system which may have been measured only once or twice at the initiation of the system, but many tens of times, after a few weeks.
783
Radioactivity measurements: principles and practice
3.4.1.3. Some basic statistical concewts and definitions * The result of a measurement can be regarded as a random quantity, x, which may be If x takes on only discrete values (e.g. 0,1,2,...) then the discrete or continuous. expectation value, E(x), is defined as E(X) = C xjP(xj)
3
(3-10)
j where P(x,) is the probability of finding x=x3, and the sum is extended over all possible values XJ. Similarly, if x is continuous, one has E(x) = s x f(x)dx
l
In OL
3.4.1.3 a
recent.
and
sxtensivs
3.4.2.3
paper
by
.J.
us*
w. Ma1er
,
(3-11)
1% made (1984a).
where the function f(x) is called the probability frequency whole range of existence of x.
The integral extends over the
The variance, o'(x), is defined as o'(x) = E([x-E(x)]') = E(x')-E*(x)
.
Its positive square root is called the standard deviation.
(3-12) The ordinary moment (of order
r) of a random variable, x, is defined by m,(x) = E(x=)
,
(3-13)
and the central moment (of order r) by r,(x) = E( [x-E(x)]=)
Hence
PI(x) = 0
and
/Am
(3-14)
= E([x-E(x) 1’)
= d(x) = m,(x) -m:(x). It should be noted that this relation is valid quite generally, irrespective of the The only assumption required is that the first two ordinary moments distribution of x. exist (i.e. are finite). independent of each other, whereby this If two random variables are not interdependence may be from very weak to very strong, they are said to be correlated. Formally, an observed correlation of the variables x and y can be described by the definition of their covariance, Cov(x,y), where Cov(x,y) = E([x-E(x)l[y-E(Y))) (3-15)
= E(xy)-E(x)E(y) Two special cases are worthy of note: if x = y, it follows that
Cov(x,y) = G(X),
and if x and y are independent, then
COV(X,Y) = 0.
It is often practical to form
the
Cov(x,y) P(x*Y) = ___ 0(x)0(y)
correlation coefficient, p(x,y), defined by
9
(3-16)
which lies always between the limits -1 and +l. If x1 and xz are two random variables such that x1' = a,x,+b, and x2'= a,x,+b,, where alI b lI a2 and b, are constants, then the following rules will be useful: E(x;+x;) = a,E(x,) + a,E(x,) + b, + b,
,
l
for expectation values:
l
for variances: 02(x;+x;) = a+2(x,) + 2.,%+(x,) + 2a,a, Cov(x,,x,)
(3-17)
,
(3-18)
Radioactivity
784
l
for covariances:
l
for correlation
measurements:
principles
Cov(xi, xi) = 8182 Gov(x,,x,) coefficients:
p(x;,x;)
and practice
(3-19)
>
= p(x,,x,)
For a1 = az = 1 and b, = b, = 0, one obtains
(3-20)
the important
relation
uZ(xl+xz) = 02(x,) + 02(x,) + 2Cov(x,,x,)
(3-21)
According to Eqs. 3-12 and 3-15, the terms on the right-hand side of Eq. 3-21 contain differences of expectation values, i.e. values that could only be known after taking infinite numbers of measurements. Because this is not possible, especially with radioactivity measurements, one has to use approximate values. Such an approximation is the sample mean of n measurements 4 1 x
1-
Further,
I
:xj j=l
n
(3-22)
it can be shown, and it also follows
from the first rule of Table
3-5. that
02(x) d(a)
=
(3-23) n
is n This important result indicates that the variance of the mean value of n measurements It is, however, measurement. only of an individual times smaller than the variance strictly true for large numbers of observations and should used with caution for n less than 5. If we define
the
sample variance 1 s2(x) = n-1 z
it can be shown
by n
jc_1(xJ-z)2
f - EZ
(3-24)
that E(s2) = o'(x)
%'
A generalized each multipled
(3-25)
form of Eq. 3-21 can be obtained by extending it to n random variables, by a constant factor, a,; in other words, xl' + xl is replaced by
z
=
+
alxl
+x2
+...+
a&
(3-26)
=
j=l whence n
d(z)
=
will be used This equation propagation of uncertainties. 3.4.2.
Statistical
3.4.2.1.
Probabilitv
evaluation
1 +?(XJ) j=l
in
+ 2 1 a& j>k
73.4.2.3
for
of radioactivitv
distributions:
the normal
COV(X,,Xk)
deriving
a
(3-27)
general
expression
for
the
measurements distribution
do not reproduce exactly the same values. An Repeated measurements, in general, infinite, or at least very large, number of repetitions would be needed in order to find the distribution function which gives the probability to obtain any particular value of the This function is called the parent distribution (of the parent populvariable considered. ation). Any finite number of measurements is taken as a sample of the parent distribution. This means that the characteristic parameters of the parent distribution (mean, variance and higher moments) can be estimated from finite samples and are, in mo.st cases, sufficiently good approximations.
It is often assumed ("Gaussian") distribution
that the results from repeated (see 82.3.5 and Fig. 2-3).
measurements
follow
a
normal
785
Radioactivity measurements: principles and practice
(x-P)2
1
P(x) =
-h
0(2*)
(3-28)
exp (- -), 202
The Gaussian for the probability frequency, where p and oz are its mean and variance.* It distribution is a two-parametric, continuous and symmetric (about the mean) function. is often used for the statistical evaluation of experimental data because of its relative simplicity, although the experimental data are sometimes not distributed completely normally [but are leptocurtic or platycurtic (Aitken, 1949; Romanowski, 1979)]. The normal distribution has many times been tabulated, mostly as a standardized normal distribution, 1
P(z) = (2*?
exp(-z2/2)
,
(3-29)
* This is, however, only true for IE(x)-XI << E(x) and large numbers of events. where
x-IJ -, 0
z=
(3-30)
or as its integral, the "Gaussian" error integral or error function, ~G(z) =
J" P(E) de a
,
(3-31)
with the lower limit a = 0 or -z or -m (see, for example, Abramowitz and stegun,
1965).
It should be noted that
P(z)dz = I
(3-32)
0 The best (unbiased) estimates of p and o2 of the parent distribution from a sample of n measurements, as indicated in Eqs. 3-22 and 3-24.
are calculated
Using the normal as the parent distribution, it is possible to calculate the probability of finding a result, x, within the interval from (r-o) to (r+o), namely 68.3%. The probability, P,, of x to be found between (p-w) and (r+co) can also be calculated by using the error function, Eq. 3-31. The results for the most frequently used confidence limits, c, [i.e. the probability that a result will lie within the confidence interval between For statistical correctness, for limited sample (/J-cu) to (r+co)l, are shown in Table 3-5. size, c should be replaced by Student's t value (o is the selected confidence level, and P?V u is the number of degrees of freedom), but this is only clearly different from c for low values of n, and far from the mean value (Aitken, 1949; Joiner, 1969).
Table
3-5
Confidence level for normal distribution, P,, as a function of the confidence interval. *co
0.674X
0.5000
1.645
0.9000
2.327
0.9800
1.0
0.6827
1.960
0.9500
2.576
0.9900
1.177**
0.7608
2.0
0.9545
2.807
0.9950
* 0.674
is called
the "probable
**2 x 1.177 = 2.355 = FWM
error”,
(full width
because
4.0
PO.6745
at half maximum,
= 0.5
see 73.3.5.2
786
Radioactivity
measurements:
principles
and practice
At this point it may be well to reemphasize that the standard deviation of an individual observation, x, about the mean value, oand that of the mean, TI, are parameters that apply only for a population, namely a %'ery large, if not infinite, number of observations. The estimators of these parameters for a small, or limited, sample are usually designated as sx, the estimated standard deviation, and sthe estimated standard deviation of the mean. The Student-t factor can be used to esti&te the interval (? ts-) within which the mean may lie at a given level of confidence (e.g. 95 or 99 percent), f'sr as few as two observations n (i.e. u = n - 1). In this case, for n = 2 and u = 1, t is, of course, very large, namely 63.657 at a confidence level of 99 percent. But for as few as six readings it has already dropped to 4.032, and then, as implied above, it rapidly approaches c in value as n increases. Finally it should be mentioned that an estimated standard deviation has also its uncertainty the relative value of which, $for the case of a normal population and due to limited sampling, is equal to 1/[2(n-1)] (see Cramer, 1946; Miiller, 1979a). Table
3-6 gives
the corresponding
Table X,Y: a,b:
variables constants (positive
Function
estimated
Variances
3-6
variances.
of some common
functions
or negative)
Variance
z = ax + by
G(z)
z = axy
sZ(z)/zZ = sZ(x)/xZ + sZ(y)/yZ + 2Cov(x,y)/xy
z =
ax/y
= a%s(x)
sZ(z)/zZ = sZ(x)/xZ + sZ(y)/yZ - 2Cov(x,y)/xy
z = axh
s(z)/2 = bs(x)/x
z = a&x
s(z)/2
z = a ln(bx)
+ b's'(y) + 2 abCov(x,y)
= bs(x)
s(z) = as(x)/x
Uncertainty components which cannot be estimated by applying statistical methods (i.e. the recommendations and discussion of non-random components of category B, to which or, at 73.4.1.2 apply) must be evaluated "by other means", i.e. by auxiliary measurements As is pointed out in the above-referenced recommendguessing". least, by "intelligent it is highly important that the result of a measurement be accompanied by a ations, detailed list of all the uncertainty components indicating their values and the way in It is up to the experimenter to use all his experience and which they have been obtained. imagination in order to track down unsuspected influences that might falsify his This may be attained by extensive variation of important parameters or by using results. All these procedures must be reported in different instruments and independent methods. full detail, if the result should not run the risk of losing its value. Experimenters often neglect covariances even if the measured quantities involved are This can lead to considerable errors in the uncertainties stated, not really independent. as has been illustrated by Mannhart (1981) in a simple example involving the use of three well-characterized gauge blocks by three different experimenters, A, B, and C, to derive, for the same length. We have taken the liberty of between them, two different variances but the help of only two of his with three gauge blocks, borrowing his illustration These two experimenters set out to measure a given length of xs, equal to 25 colleagues. mm, in different ways that yield quite different values for the variances if correlations The lengths of the three gauge blocks chosen for the purpose, are not taken into account. together with their estimated standard deviations and variances, were as follows: Length (mm)
Estimated std. devn. (pm)
Estimated variance (gms)
50
0.05
0.0025
15
0.03
0.0009
10
0.02
0.0004
Radioactivity measurements: principles and practice
787
3.4.2.2. The statistics of radioactive decay: the Poisson distribution All the statistical considerations discussed above apply to measurements of radioactivity, but, in this case, an additional feature must be taken into consideration, namely the statistical character of the radioactive decay itself (see 72.3.5). The quantity usually measured, a count rate, is not an invariable physical constant, but a stochastic quantity, the expectation value of which has to be determined. Even under ideal conditions (no "systematic" or other non-random errors) and after applying appropriate adjustment for radioactive decay, repeated count-rate measurements do not yield the same result, but are The probability distribution function that governs the distributed around a mean value. radioactive decay is the single-parameter, asymmetric, Poisson distribution, based on a decay probability equal to
1 - emXr, namely
P(x)
=
fix e-p X!
,
(3-33)
where x = 0, 1, 2... Its most important property is that its variance and mean are equal (see NCRP, 1985, TB.3.5), i.e. 02(x)
=
E(x)
=
(3-34)
/J
Thus, in the case of radioactivity measurements, a single result may already be regarded as an estimate of the mean of the parent Poisson distribution and of its variance. The corresponding relation for count rates, r, is
(r/t)‘,
s, = M&/t = (rt)yt =
(3-35)
where M is the accumulated number of counts in the measuring time, t. A consequence of Eq. 3-34 is that the estimate of the relative variance, s~M*=l/M, can be reduced to any small value by increasing t and, thus, the number of the counted events. For not too low numbers of counted events (say above M = 50, Hilaire, 1973) the Poisson distribution may well be approximated by the normal or "Gaussian" distribution. In this case, the latter, normally characterized by two parameters (JJand o) can be used with a single parameter, by means of the Poisson relation, p = 02, or M/t2 = s',. But before this approximation can be made, tests should be made to determine whether the Poisson distribution is appropriate. Otherwise, the two-parameter normal ("Gaussian") distribution must be used, which is often the case in low-level measurements (Hilaire, 1973). 3.4.2.3. Combined uncertaintv:
"error oronaaation"
Let us return to Eq. 3-27, where the variance of a linear function,
of the n random variables, xJ, is described. Let us further consider the more general case where z is replaced by some differentiable function f(x,,x,,...%) and see what happens to us(f) if each variable, xJ, varies by a small amount which is of the order of its statistical uncertainty. Any such function can be developed into a power series, in the neighbourhood of a given reference point, e.g. the point defined by the mean values, T. If each variable changes from T to si, + Axj, the beginning of a Taylor expansion may be written as 6f f(x,,x,,
,‘h) = fG,,x,,
,51”) + c” j=l
where terms of second and higher compared with the associated 4's.
Axj +
,
order in Axj can be neglected Thus one has
Af = f(xl,x,,...) - f(TI,,S;,....)=
(3-36)
6xj
n 6f 1 Axj j=l 6x,
if the Axj's are small
,
which has nearly the same form as Eq. 3-27. Therefore, we can now write propagation law for uncertainties, also called the error-propagation law, as
02(f) =
6f 2 c" &Xj) j=l (16x,
+
2 1 6f 6f j>k dx, 6x,
Apart from the partial derivatives of at least approximately, the only quantities products and power functions, the use of For the most frequently great advantage.
COV(X,,Xk)
(3-37)
the general
(3-38)
the function f which can always be calculated, needed are the corresponding sample values. For estimated relative variances, sz(x)/x2, is of encountered functions of one or two variables,
Radioactivity
788
measurements:
principles
and practice
The first experimenter measures x3 by comparing it with 1, + .& = 25 mm, and, ignoring any uncertainty arising from his own measurement, he computes the variance of xj to be var(x,) = var(P,) + var(P,) = 0.0013
(3-39)
pm2
The second experimenter measures xJ as the difference x2 - x1, where xz = 1, + I3 = 60 arising in his own measureand x1 = 1, - 1, = 35 mm, and, again ignoring uncertainties ments, calculates the variance of xg as mm,
var(x,) = var(x,) + var(x,) = 0.0063
pm2
,
using
var(x,) = var(ll) + var(P,) = 0.0034
pm'
,
and
var(x,) = var(P,) + var(P,) = 0.0029
pm’
(3-40)
(3-41)
would have given an Combining these last two results, in equations 3-41, in quadrature The reason for the discrepancy between the results overall variance equal to 0.0069 pd. of the two experiments lies in the fact that the second experimenter used the gauge blockI, to obtain both of the values x1 and x2, which causes he taken this into account, he would have obtained var(x,) = var(x,
a correlaion
that he neglected.
Had
- xz)
= var(x,) + (x2) - 2Cov(x,,x,) = 0.0029
+ 0.0034
= 0.0013
/Xl? (
Thus because Cov(x,,x,) = var(P,). the same as that by the second.
the uncertainty
2 x 0.0025
, (3-42)
obtained
by
the first
experimenter
is
experimenters should report with their results, not only variances, but Therefore, At least, the reported uncertalso covariances or correlations, where this is possible. This is only ainty components should be separated into uncorrelated and correlated ones. possible if the experiment is described in detail, especially with respect to measurements Cases similar to the above example are frequent in radiohaving certain parts in common. in measurements of decay constants and coincidence nuclide metrology, as, for example, If the experimental data are used for large-scale evaluations (e.g. of neutroncounting. capture cross sections), possible correlations between all data must be considered. Such evaluations are in general made using matrix ents are then assembled in a variance-covariance matrix with the individual variances of the measured variables as off-diagonal terms.
3.4.2.4.
Statistical
The uncertainty componcalculus. (usually called covariance matrix), in the diagonal and the covariance
testing
results of It is often useful and necessary to test the soundness of experimental radioactivity measurements by statistical procedures. A decision is then sought whether are compatible with theoretical predictions at a given level of the observed data Such tests may concern the randomicity of a set of repeated measurements, the probability. significance of a measured count rate above background, the assignment of two independently measured mean values to the same population ("Student's t test"), or the identification of two variances, differing in value, with the same population ("F test"). In each cause a characteristic "test parameter" is derived from the data and compared The underlying distributions are generally the with the theoretically expected value. Poisson or the normal (Gaussian) distribution, and the theoretical predictions for various If the value of the degrees of probability are reported in tables (see e.g. CRC, 1985). experimental parameter exceeds the expected value, the data must be rejected. in the so-called "analysis of variance" or of Both F and t tests are involved "covariance". If this interesting procedure is to be applied, the measurement scheme should laboratories) can be be designed so that component variances (e.g. within and between studied. (Also see Paule and Mandel, 1982). As important as being able to analyse results by statistical methods, is the need to to such analysis. design an experiment in such a way that the data are best suited experimental design are the Latin, Graeco-Latin and orthogonal Examples of such And an expert in the creation of such designs was W. J. Youden squares (Fisher, 1949). who coined the phrase that an experiment was a considered course of action aimed at Examples of his design are the Youden answering one or more carefully framed questions. three quantities against each other in every combination. diagram and his measuring describing such experimental designs have been reprinted by H. Eleven of his publications H. Ku (1969).
Radioactivity
measurements:
principles
and practice
789
In the statistical analysis of data, if the number of independent experimental data is test (Pearson, 1900) is often the limited, but not too small, the so-called chi-squared This test is a special application of the most suitable.
) nx
for u = n - 1 degrees
(3-43)
i=l
of freedom.
from the estimator The numerator in this equation differs only by the factor n/(n-1) is equal to X, the estimator of sz of the variance (I' , which for the Poisson distribution if the observed data follow a Poisson distribution, the value of the mean p. Therefore, L2 (= sz/X) should tend to unity as the number of observations, n, increases. Any large and deviation from unity is a measure of non-Poissonian, or, in the case of radioactivity (non-"Gaussian") behaviour. n large, non-normal is a rather complex function that allows the The Pearson chi-squared, x2, distribution where 0 < x < mn to be calculated as a probability of the values of x2 exceeding x, with the distribution. function, only, of the number of degrees of freedom associated Values of the probability for different values of x2 can then be computed for different degrees of freedom and tabulated (CRC, 1985), or plotted (Fig. 3-6).
5
10
15
20
25
Chi-squared , X2, for different probability levels, Fig. 3-6 dependence on the number of degrees of freedom, Y .
P,in
namely, the sum of In the same paper Pearson (1900), derived a simple statistic X2, the quotients of the squares of the residuals divided by the expectation value, that is distributed as chi-squared, i.e.
(0,
- Ei)*
x2 = 1 i where Oi is the ith assumed distribution classes.
(3-44) E,
and E, is the experimental observation, of the experimental data, and the sum
expectation value for the is over all i groups, or
Radioactivity measurements: principles and practice
790
As an example of the chi-squared test for the goodness of fit, we will explain its application to a series of measurements of the number of counts, xj, observed a large number of times from a long-lived radioactive source, during the same, and suitable, fixed intervals of time. If j = 1, 2, . . . ..M. and the frequency fj is the number of times that each number xj was observed, then n. the total number of intervals is
and N, the total number of counts registered, is
Let us now compare the frequency distribution fj of xJ of a Poisson distribution, -x $2 e E(f,) = nP, = Xj!
with the expected frequencies
(3-45)
of counts, N, and that has the same expectation value (mean), and the same total number CPj = 1. We then enter these values into the statistic X2 (Eq. 3-44) of the chi-squared distribution, to give
x2=
M [fj- E(fj)12 1 j=l E(fj)
(3-46)
Table 3-7 gives a simple numerical example of the application of the chi-squared test in which the calculations are explained step by step. Table 3-7 - Example of a x2 test 1 j
XI
fj
1
5
1
5
0.038
1.48
-0.48
2
6
0
0
0.063
2.46
-2.46
3
7
3
21
0.090
3.51
-0.51
4
8
4
32
0.113
4.41
-0.41
5
9
6
54
0.125
4.88
1.12
6
10
10
100
0.125
4.88
5.12
7
11
7
77
0.114
4.41
2.59
8
12
5
60
0.095
3.71
1.29
9
13
2
26
0.073
2.85
-0.85
10
14
1
14
0.052
2.03
-1.03
11
15
0
0
0.035
1.37
-1.37
n
=
N =
Xjfj
Pj(p=lO)
E(fj)=nPj
fj-E(fj)
39 389
j = index for classes
xj = number of counts for j-th class fj = frequency of intervals with Xj counts in a total of n intervals Pj = Poisson probability for observing Xj, given its mean p, estimated by X = N/n = 389/39=10 "
=M-2=9 -51
-5
E(fj) = n X
x2= x,!
M [fj 1 j=l
_
E(f,)l' = 12.47
E(fj) + P = 0.20 (see Table 3-6)
Radioactivity measurements: principles and practice
The range of xj should be between 5 and 20. If it is much to pool the data in a more convenient number of intervals.
791
larger, it is preferable
Further, the number of degrees of freedom, u, the only parameter of the X2 distribution, must be determined. It is equal to the number of classes, M, minus the number of restrictions placed upon the empirical data, here equal to two, due to the estimation of the mean and the common value of the total number of counts. Thus v = M - 2. Finally, the "experimental" test parameter X: can be compared with "theoretical" values xi,r (Fig. 3-6), and the hypothesis (e.g. Poisson behaviour) is rejected with probability P, if X$ > X:,,. Alternatively, the probability P that the hypothesis can be accepted may be derived from Fig. 3-6 by noting the value of P at the point where X$ = Xg p. P can also be regarded as the probability that Xf will exceed its theoretical value in a repeated measurement. In practice, a hypothesis is usually accepted, if 0.1 < P < 0.9, and rejected strongly for 0.02 > P > 0.98. 3.4.2.5. Further statistical problems in radionuclide metrolopv 3.4.2.5.1.
Consequences of the Poisson distribution and its distortions
As radioactive decay is governed by the Poisson law, all properties of the latter In particular the sole (Haight, 1967) can also be applied to study radioactivity. parameter of the Poisson distribution, the mean count rate ii, can be measured by several methods different from the usual counting of the number of disintegrations in a given time interval. For example, the fluctuations of the output current of an ionization chamber can be used to measure the current itself (variance = mean), thus avoiding problems from high direct currents (Oda et al., 1976; Lux and Baranyai. 1982). Also the measurement of the mean time interval, 2, between pulses is equivalent to the measurement of the mean decay rate (B = l/6). Other relations involving the Poisson distribution that could conceivably be used to measure decay rates are those between adjacent probabilities such as, for examor the different moments about the mean M, = ii, M, = ii, M, = ii +3ii2, ple, nP, S = FP"_iB or about the origin, ma = ii + ii2 (Miiller, 1978). But, in addition to the Poisson frequency distribution, other distributions can or must also be used for the description of radioactivity phenomena. This is expecially the case for the Poisson interval distribution, that is, the distribution in size of the intervals between successive events. This follows from the probability-frequency distribution, based on the probability of no event occurring in the time interval from zero to t, combined with the probability of one event occurring in the time interval between t and t + dt. This combined probability, dP,, equal to the product of the two separate probabilities, is -zit iidt = [(Tit)'e /O!] Kdt dP, = P,,,,ii =Tie -ntdt
.
Radioactivity
792
measurements:
principles
and practice
To understand this, consider an experiment in which a detector is used to record the counts, Na+b for a time f,+b from a source "a" plus background, and then to record the for a time 4; that is, with the source removed, and probably an background count, N,, inactive dummy source in place of the active source in order to reproduce the scattering of environmental radiation into the detector by the source. And let ta+b + tb = T. Suppose 2 s,, si are the estimated variances of the source and background count rates, ra and r,,, and Thus st is let si be the estimated variance of the source "a" derived from Na+b and N,. the unknown "true" variance of L-,, of source "a", and s"d = s=il+ + szb which is equal to B So that, in general, si must be greater than s,, and especially so when Na+b/t'.+b + N,/t’,. r, and rb are of comparable magnitude. Thus the background radiation will tend to broaden the frequency distribution of the net count rate. In general it is, however not important to distinguish between s, and sd, particularly bearing in mind the large uncertainty associated with the standard deviation, referred to in ~3.4.2.1. Therefore, in order to avoid unnecessary confusion we will only consider s,. If the total measuring time, T = f.+b + tb, is limited, measurements of low levels of activity, then we may ask how subdivided in order to minimize the variance, sf of the net sample answer, consider the summation of the component variances of sza as sza
=
=
as it may well be in that time may best be count rate, ra ? For an given by
sza+b + SZb
(3-48)
N a+b -*-
Nb (3-49)
t:+b
tzb
By differentiation 2s, ds,
=
N a+b Nb - 2 dt,, - 2 dt,
and, by above
setting
question
ds, = 0
and
dta+b + dt, = dT =O,
is then obtained ta+b -=-
(Knoll, ra+rb
(3-50)
t3b
t:+b
as T is
constant,
the answer
to the
1979) as
r, (3-51)
(
tb
Tb )
This relation is also derived in NCRP (1985, p. 306), and its use is there illustrated by means ofa nomogram devised byR.Loevinger and M.Berman,from which an optimum division of counting times between source and background can be chosen in order to give a desired level of uncertainty in a minimum total time of counting. If it is possible to vary certain parameters of the counting experiment, such as the kind of detector, the source configuration, the impurity rate, and the pulse-height discrimination, one may want to measure r, to within a given relative uncertainty, u, equal to It then = sz - (N,+J/t' a+G)
NJ/t'b
(l/T)[r,+, (1 + tb/t.+b)
= (l/T) [ra+&+(@,+b)‘) =
(l/T)[rF+,
r,(l
&+b)/tbl
+ rb(l+(rs+b/&
Radioactivity
measurements:
principles
and practice
793
sample treatment (impurity reduction, etc.), and selectivity, volume ( etc.), radiation A similar, but more complex figure of merit can also be defined for spectrometric price. methods (Knoll, 1979). It should also be mentioned that background subtraction present particularly complex problems (see 74.11.4.1.1).
in spectral
analysis
may often
Another statistical concept concerning background is the "minimum detectable activity" For many applications simple which is defined in different ways in the literature. definitions are sufficient, as, for example, the minimum detectable activity is one that give.s rise to a count rate of three times the background standard deviation (ICRU, For low-level measurements and some 1972b); or to one tenth of the background count rate. 1983; refined statistical definitions are needed (Sumerling, applications more other Currie, 1984). The statistical investigations above are valid for any digital pulse-counting system. But they are also valid, in a somewhat modified version, for analogue systems, especially These are connected, for current-measuring devices such as ordinary ionization chambers. to a current-measuring instrument, and the via an integrating RC filter, in general, statistical fluctuations of the measured current can be described by the root-mean-square (rms) deviation, which is equivalent to the standard deviation in digital measurements. Thus analogue and digital measurements are statistically equivalent (Weise, 1971), but each of them has advantages for particular applications. 3.4.3.
Corrections
3.4.3.1.
for svstematic
Dhvsical
effects
General
The accurate measurement of radioactivity is always a complex procedure. In general, applied to the directly measured data. This is especially many corrections have to be But the same, although mostly true for direct (sometimes called absolute) measurements. if the unknown and the much smaller, corrections must be applied in relative measurements, The individual corrections can be very different reference source are not exactly alike. counting, coincidence counting and for the various methods, especially for single-channel Therefore, only the general aspects of the different corrections peak-area measurements. referred to the simplest will be discussed in this report, and it is, where possible, The subdivision into physical and instrumental analytical method described in 73.4.1.1. because they may involve overlapping corrections cannot always be completely consistent, effects. 3.4.3.2.
Backpround
and interfering
radiations
the presence of a radioactive source. Every counting system yields counts without is normally measured under exactly the same conditions as for the This "natural background" In general, source of interest, using an inactive but otherwise identical dummy source. any interfering radiations, e.g. from impurities, are added to the natural background and For singlethe sum, the "extraneous counts", is treated as a second radiation source. it is simply subtracted from such as defined-solid-angle counting, channel measurements, For coincidence measurements and spectrometry, the definition and the source count rate. The possibly different coincidence treatment of the backgrounds can be very difficult. (and the behaviour of the background and the sample, and the peaks in the backgrounds background below the peaks in spectrometry) cause serious problems (Jorch and Campbell, (See later in this section.) 1977; Miiller, 1983). environmental radiation (especially The components of the natural background are: of the r3'U and 232Th series), radiation from zzzRn, 'OK, e5Kr, and from the radionuclides rays (minimum-ionization muons, high-energy and cosmic from the detector material, Different measures must be taken to reduce nucleons, and wide photon-electron showers). these different background components. In general, also any kind of electronic noise and but one always tries to set the discriminpick-up is included in the natural background, For some systems this could be a ation level high enough to eliminate any noise influence. The root-mean-square noise is, in such delicate problem (e.g. proportional gas counters). This and the cases, best described by the equivalent number of electrons and their energy. discriminator-threshold adjustment can then be controlled with a low-energy-radiation source, e.g. 3'Ar or 55Fe. the effect of which must be subtracted together with the The interfering radiations, Nearby accelerators and neutron natural background stem from several different sources. sources (up to several hundreds of meters away), or sample changers can cause direct disturbing radiation, and both, as well as the sample itself, can induce activation in the and subsequent radiation (e.g. detector (e.g. "Na or lzsI in NaI(T1) and its environment, Especially important can be radioactive contamination of the sample, reactions). (n,% and also possible contamination both initial and any introduced during sample preparation, With care and modern high-resolution spectrometry these effects can be of the detector. corrected for satisfactorily. The backgrounds
of individual
counting
systems
vary
strongly,
depending
upon
the kind
Radioactivity
794
measurements:
principles
and practice
and size of detector, and the shielding. Therefore, only very approximate general figures Some very special detectors, such as a thin layer can be given. of ZnS(Ag) on a thin plastic disc, when unshielded, show backgrounds in the energy range from 0.1 to 6 MeV of from only one to a few counts per minute; ordinary, small, gaseous counting tubes can have background counts of several tens to several hundreds of counts per minute; NaI(T1) and other scintillators a few counts to several thousands of counts per minute depending on the measuring conditions (a 3" x 3" Na(T1) detector, shielded by 5 cm of lead, could register about 10 s-l above 10 keV, and semiconductors about an order of magnitude greater, per unit volume). Proper shielding reduces these backgrounds by one to two orders of magnitude and special procedures, especially anticoincidence shielding, again by a similar factor. Several measures must, or can, be taken to reduce backgrounds. First, the electrical installation must be designed adequately. One single efficient (5 to 10 ohms) ground connection without loops is absolutely essential, and the insertion of an efficient wide-frequency-band filter at the output of the main power supply is strongly recommended. Furthermore, the electrical shielding of the whole equipment should be complete, Also shielding against other atomic or nuclear radiations is, in general, essential. Usually the detector and the counting chamber are placed inside a lead enclosure (e.g. Fig.5-2). The optimum size of this enclosure and the thickness of the lead shielding depend on the use of the detector. Larger enclosures show smaller wall-scattering effects, but smaller ones are cheaper. The thickness of the lead does not, in general, need to be greater than 4 to 8 cm (99-percent reduction of 2-MeV gamma rays at 8 cm), because greater thickness contributes only little. The lead shield could be supplemented by the addition of some neutron-absorbing material, e.g. boron-loaded concrete or plastic, at its outside. And at the inner surface, the shielding could be improved by a lining of lower-Z materials, e.g. 0.8 mm of cadmium and 0.5 mm of copper or steel, in order to improve the absorption of low-energy x rays. For further background reduction anticoincidence and coincidence procedures must be applied. The most common is anticoincidence shielding, in which the detector is surrounded by guard counters operating with electronic circuits that reject counts that are in coincidence with guard-ring counts. The procedure can reduce the background by 2 or 3 orders of magnitude. Further reduction by 1 or 2 orders is possible by selective coincidence counting (of radiations that are coincident due to the decay considered). Finally, pulse-shape discrimination (PSD) can be rather widely used for the elimination of extraneous counts (ICRU, 1972). This method is based on the differences between the rise times of pulses from different detectors or radiations and discards pulses with "wrong" rise times. The statistical problems with backgrounds are discussed in aJ3.4.2, and background Variable backgrounds, e.g. when measuring problems in spectrometry, partially, in 74.11. more detailed treatment. near accelerators, need a 3.4.3.3.
Effects
influencirw
the efficiency
The efficiency of a counting measurement or system can be defined as the number of (corrected for background and instrumental effects) per number of detected counts Consequently every interaction of the disintegrations in the source (see, also, 73.4.1.1). radiation occurring between its origin in the source and its detection as an electrical This is indicated pulse at the output of the detector system can influence the efficiency. for the defined-solid-angle counting by the correction factors in Eq. 3-6, and is similarly valid for every counting method. The largest correction is, in general, the geometry factor, the ratio of the full The latter is the solid angle solid angle, 4~ sr, to the effective solid angle, neit. subtended by the area of the detector at the point of the source from which the radiation defined for strongly absorbable radiations (nucleons, is emitted. It is, in general, electrons and low-energy x rays) by a circular diaphragm in front of the detector and for gamma rays by the detector dimensions. Mostly, the geometry factor can be calculated very Practical problems are accurately from the measured dimensions of the counting chamber. sometimes encountered because of source dimensions, source positioning and source-activity For the most frequently used geometry, namely a circular diaphragm, with a distribution. diameter of Za, and an axial source, at a distance z from the diaphragm, and for an arimutsimple analytical half angle 0 (Fig. 3-7a), the following ha1 angle 4 and a subtended expression holds
neff
8eff =
=
dn
/ 2n
SJ 0
= 2n(l =
O,ff sin
0
- co* 0,,,)
2s(l - z/(22 + ar)b)
zz na=/z=
(3-57)
Radioactivity measurements: principles and practice
No analytical expressions are known, except for special cases such as a = z, for axially-extended and non-axially-extended sources, but very accurate approximations are available for these cases (Jaffey, 1954).
r'
1-1
,top detector
f
I ’
I . ‘\bottom
I detector
Fig. 3-7 Defined-solid-angle counting; a) usual arrangement, b) doublecounter system, c) possible disturbance by scattering, d) baffles for reducing c). Complex corrections must, in general, be applied for absorption and scattering effects individual between source and detector. These can be subdivided into parts: self-absorption and scattering (especially backscattering) in the source; absorption in the media between source and detector (e.g. p-ray absorbers in y-ray measurements); scattering at the walls of the counting chamber (including the diaphragm); and scattering and Self-absorption in the source is of great importance absorption in and at the detector. for strongly absorbed radiations and can modify the peak forma recorded (Tq4.11 and 5.3.5.4). Backscattering in the source and at the source support can also be of crucial importance. For instance, for beta particles in 2a geometry the backscattering coefficient (the ratio of the backscatteredto incident radiation) varies between about 0.3 and 0.6 for saturation-thick backings of atomic number 7. between 10 and 80, respectively. For o particles the strong low-angle backscattering makes 2a measurements relatively inaccurate. Absorption in media between source and detector can, in general, be kept negligibly small (e.g. by evacuation, replacement of air by H, or He, or use of calculable absorbers), and scattering at the chamber walls can be minimized by proper construction and choice of materials. For CI particles, for example, the energy of the particles scattered from the walls into the detector can be kept so low, by the choice of low-2 material, that the scattered radiation is not contained in the full-energy peak (Fig. 3-8). Similarily, the height of 4ra counters for coincidence systems should be kept as low as possible, in order to minimize l-ray self-coincidences due to Compton scattering. Also the circular diaphragms defining the geometry can be constructed to minimize transmission and scattering (inner height about equal to the range of the measured radiation). The absorption and scattering in and at the detector, expecially the backscattering at its surface, are taken into consideration by the detector-response function. This describes quantitatively the spectrum at the detector output as a function of the incident spectrum. As this is a very complex function, it is usually approximated by a single parameter, the detector efficiency, defined in 115.?.1.5. An important correction, to which adequate attention is often not given, is that for the energy discrimination. In every piece of counting equipment there is either a deliberately incorporated or unintended threshold circuit, or discrimination level, which prevents pulses below a certain amplitude from being transmitted. This can influence the detector efficiency considerably (and under certain conditions can even make the detector ineffective). In general, the discrimination threshold can easily be set high enough to eliminate all instrumental noise, and possible physicalandinstrumental spurious pulses (see Campion, 1976). But it may sometimes be difficult to correct for small genuine pulses that are lost, especially at high count rates with considerable pile-up. Therefore, it is very useful to observe the direct detector output and to use additional low-energy radiation sources, such as "Ax- or "Fe, for the calibration of the discrimination threshold. Several other effects can alter the efficiency of radioactivity measurements strongly. Rather large corrections may be necessary for nuclides decaying in a complex way, especially corrections for the detection of other than the investigated radiations. For non-coincident radiations the individual efficiencies must be added, but for coincident radiations, terms proportional to(1 - *,)(z must be considered. For coincidence measurements (see q5.5),
795
796
Radioactivity
measurements:
principles
_ .~.~ +- ~--+
-0.1
I
and practice
‘4-M,S(Be)
I I
30"
60
90
120
150
Elastic scattering of alpha particles into an angle 0 ; ratio Fig. 3-8 of the energy after scattering, E(B), and the initial energy, Eo. the correction for the counting of “unwanted” radiations (e.g. gamma rays in the beta chanAlso angular correlaLions can influence the outcome of coincidnel) may become a problem. ence measurements. 3.4.3.4. Secondary radiations. second- and hipher-order effects Radioactive decay and the subsequent absorption of the emitted radiations are much more complex than described by the simple (first-order) decay or absorption schemes. Low-intensity secondary radiations and effects often interfere with, and may sometimes dominate, the detection process. This especially can be important for external bremsstrahlung, internal conversion and annihilation radia?rion. Electromagnetic bremsstrahlung, also named continuous Rantgen radiation, is always produced when charged particles (especially electrons) are accelerated or decelerated. It is always present, when radiation of any kind is absorbed, because absorption finally involves the deceleration of electrons. Consequently, every gamma-ray spectrum has a low-energy excess (with a spectrum proportional to approximately due to l/E) bremsstrahlung. This external bremsstrahlung is produced in the field of external nuclei, in contrast to internal bremsstrahlung which originates in the field of the nucleus producing the primary effect (electron capture, etc.). The intensity of the external bremsstrahlung is about 10-Z to 10m3 times that of the primary effect (beta-ray absorption, etc.), and is proportional to the 2' of the absorber material, while the intensity of the internal bremsstrahlung is still one to two orders of magnitude smaller and independent of the surrounding matter. Nevertheless, in many cases, bremsstrahlung may be the only measurable radiation (A. Spernol et al., HN, 1973, p, 169). Pure beta-ray emitters with high end-point energy, e.g. 32P, can be conveniently measured by means of the bremsstrahlung that they generate, especially if the beta particles are completely screened. Under certain conditions, this applies also to low-energy beta-ray emitters, such as tritium (see Curtis, 1972). The most frequently-assayed type of radioactive decay, that can only be detected and measured via secondary radiations, is electron capture by the nucleus (EC). Here the undetectable captured electron leaves a vacancy in the electron shell of its origin, and the central nuclear charge is reduced by one unit. The resulting rearrangement of the whole atomic electron cloud, which happens within 1O-12 to 1O-'3 s, leads to the emission of a cascade of detectable x and Auger radiation (see 72.4.5). Similar effects accompany every radioactive decay involving charged-particle emission, but here the secondary radiations are usually negligible compared with the main decay products, although the energies can be rather high; note, for example, that the binding energy of K electrons in high-Z atoms is of the order of 100 keV. Somewhat smaller energies are transferred to the recoiling residual daughter nuclei of the decaying parent atoms. But recoiling daughter nuclei from a-particle decay can cause more serious trouble, such as satellite peaks, ejection of some source substance with the recoil, and possible implantation into the detector. Another secondary radiation which can be more easily detected than the original radiation is the radiation following the annihilation of positrons. Annihilation photons are mainly produced when a positron at the end of its path, at rest, captures an electron and annihilates by emission of two 511.keV photons in opposite directions. Because a few percent of the annihilations also occur in flight (AiF) the 180° angular correlation between the two annihilation quanta, is, however, never perfect. The proportion of annihilation in flight to that at rest is greater the higher the atomic number of the can also cause material in which it occurs. Annihilation in flight some problelr,s in
Radioactivity measurements: principles and practice
797
Thus in the calibration of a %r-sZRb generator Hoppes et al. the assay of ,9'emitters. (1987) report a five-percent discrepancy between the results obtained using solid-state and liquid-scintillation detectors, which they ascribe possibly to uncertainties in the large corrections for annihilation-in-flight losses. Many other secondary and higher-order effects can influence radioactivity measurements, but they are, in general, negligibly small. Examples include one- and three-quanta annihilation, internal ionization and, or, excitation (with EC, IC and beta decay), and double and multiple processes such as double-beta decay, double Compton scattering, exotic decay (72.4.2; Rose and Jones, 1984) and environmental effects (B. Crasemann,HN, 1973, p. 33; Harbottle and Maddock, 1979). 3.4.3.5. Radioactive-decav
correction
Every radioactivity measurement is referred to a certain time, the reference time, in order to allow corrections to be made for radioactive decay. In this context the term "correction" may not be entirely correct, but it is in universaluse. The radioactive-decay law is a law of nature, as immutable as that of our own aging to which we may adjust but for which no correction is yet in sight. But because of radioactive decay, it is necessary, especially when measuring a short-lived activity, to adjust or normalize by calculation to a specific point in time, usually described as the "reference time". Most often, either the starting time (t,) or the midpoint time (t,) of the counting interval is chosen as the reference time. If the counting time is short compared with the half life, the source activity can be regarded as constant during the counting time, and no "correction" for decay during the measurement needs to be applied. For the calculation of the activity at any reference time (t,) the simple exponential formula must be used, i.e. ntr = where n
and n L
tr
nt, exp [-0.69315(t,-t,)/Tti] ,
(3-58)
are the count rates at, respectively, t, and
t,.
If the counting time is not negligibly short compared with the half life, TS, the This is a difficult problem, decay during the measurement must be taken into account. because in general the background (usually assumed to be constant) and count-rate-dependent Often background and dead-time losses must be combined with the decay calculation. In this case the midpoint of the counting interval (t,) dead-time losses can be neglected. is most advantageously taken as the reference time, and a simple decay computation can be If the counting interval is 8, the measured count rate n in the interval 8, must be made. multiplied by the factor D (Eq.3-6) to obtain the count rate at the reference time t,, i.e. %,
=
?iD @/2 exp(-Xt)dt _I-e/2
=
ne
=
Z(O.69315 S/T,)&xp(O,69315S/2T$
- exp(-0.69315 0/2TQ].
(3-59)
The factor D has relatively little effect; even for 6 = Th, it is only 0.981. Exact formulae for the combined "correction" for decay and for extending and Formulae for the combined non-extending dead-time losses are given by Miiller (1983). correction for decay and background (for negligible dead-time loss), have been proposed by many authors and discussed, e.g., by Kalantar (1983) and in NCRP (1985). Both approximate and exact formulae for combined corrections for decay, dead-time loss background have been derived by Axton and Ryves (1963), for extending and for nonextending dead times. Approximations must be adapted to the conditions considered. Of these, the relation that is used most frequently is and
"0 = [n'/(l - n'r)
--xt, / (1 - e-XB) B] e
,
(3-60)
for the reference time t, at the beginning of the counting interval of duration 8, n' the measured count rate, T the dead time, x the decay constant of the nuclide measured, and B the background count rate. Still more complex is the combined correction for decay, background and dead time in These problems are reviewed by A.P. Baerg in NCRP (1985, 73.2.5) coincidence counting. references (also see 75.5 in this Report). Difficulties also arise with many relevant This problem is always present in measurements with particle from variable backgrounds. accelerators.
4.
DETECTORS
4.1. INTRODUCTION radioactivity such as atomic and The previous pages deal with the peripherals of nuclear theory, the stochastic nature of radioactivity and the laws of radioactive decay, exposure to it), and so radiation and its interaction with matter (including man and his The rest of this manual will deal with the measurement of radioactivity in its on. various modes of decay, with the measurement of the various parameters of nuclear decay, and with the instruments and measuring systems required to effect such measurements. in their interactions Radiations, of different nature and different energies, can, with matter, produce both intranuclear and extranuclear (atomic) effects. Thus alpha particles or gamma rays of sufficient energy can produce nuclear transmutations, and they of light in the visible can also, in common with all radiations (including photons region), remove extranuclear electrons from atoms to create positively charged ions. Neutrons can interact elastically with the nuclei of atoms to produce energetic recoil nuclei, and energetic nuclear recoils also occur as a results of alpha-particle decay. provide Free electrons and positive ions or positive holes the modus operandi for all methods of electrical detection of radiation in gases, liquids and solids. The higher mobilities of electrons govern the speed of counting successive radiation events in such detectors, and the energy required to create one electron-ion or electron-hole pair in the substance of the detector determines the resolution between events of closely the same energy. The higher the mobility, the faster can events be counted; the greater the number of pairs from a given expenditure of energy, the better the resolution. The measurement of radioactivity is not limited to measuring the radiations emitted by the atoms of radioactive elements. The number of radioactive atoms can themselves be measured and related to activity by means of the radioactive decay law. Such measurements, however, usually involve rather specialized methods such as, for example, mass spectrometry, accelerator mass spectrometry, and selective laser excitation of individual species of atom. None is yet widely used in the measurement of radioactivity. 4.2. REFERENCES Nearly all of the methods, and their principles, to be considered in this section have been treated in far greater detail in other recent texts. That to which reference has been most frequently made in this Report, in order to avoid unnecessary elaboration, is the National Council on Radiation Protection and Measurements Report No. 58 (NCRP, 1985) A Handbook of Radioactivity Measurements Procedures published originally in 1978 and as a revision in 1985. This second edition contains decay-scheme data, for some 270 biomedically important radionuclides, from the evaluated-data and reference nuclearstructura files of the Oak Ridge and Brookhaven National Laboratories, from which, also, the 13 examples shown in Table 2-4 have been provided. NCRP Report 58 also lists around 750 references covering many aspects of radionuclide metrology not covered in the present Report, which is concerned more with the establishment of new radionuclide metrological laboratories. But in such an enterprise the proceedings of the First International Sumner School on Radionuclide Metrology held in Herceg Novi, Yugoslavia, in 1972, and published as a special issue of Nuclear Instruments and Methods in 1973 (HN,1973), could be of the greatest value. These proceedings contain 56 papers by outstanding experts in the field that cover practically every aspect of radioactivity measurement as practiced today, with the exception of the methods of selective sampling, anticoincidence counting, and the counting of the numbers of radioactive atoms instead of their decay rates, In these proceedings there are some 1,500 references (some of which, however, are bound to be redundant), going back as far as 1908 in the case of Campbelling (q.v.). Following the Herceg Novi Summer School and to perpetuate its aims, members of the organizing committee, with strong support from Y. Le Gallic and B. Grinberg, of WI, and the national and international laboratories active in the field, founded the International Committee for Radionuclide Metrology (ICRM). As a sequel to Herceg Novi, ICRM sponsored a seminar on Applied Radionuclide Metrology that was held in Geel, Belgium, on May 16 and 17, 1983, the proceedings of which ware published in a special issue of the International Journal of Applied Radiation and Isotopes in August 1983. These proceedings provide a vary valuable source of information on the developments in the field of radionuclide metrology that had occurred in the decade following Herceg Novi. 4.3.
The different kinds of radiation have been described in 72.4. The types of radiation arising from spontaneous atomic disintegrations are generally alpha, beta, gamma and x radiations, extranuclear electrons, neutrinos, neutrons and protons, and fission products, Measurements of radioactivity normally involve the first five of these. The detection of
799
800
Radioactivity
measurements:
principles
and practice
of ionization, neutrons and protons is also their loss of energy in matter by the process Radioactivity is an atomic other nuclei. either directly or indirectly by the recoils of and the total energy available in a radiophenomenon, involving the whole atom (72.3.21, equation, to the difference in active decay is always related, by the Einstein mass-energy Decay rates can be measurably of the daughter atom. mass of the parent atom and that altered, for example, by altering atoms or their compounds.
the state of ionization
or chemical
composition
of some
Charged corpuscular and energetic electromagnetic radiations dissipate energy in their passage through matter by ionization either directly by producing positive ions and electrons (usually free but sometimes bound to electronegative atoms), or indirectly through recoils or, in the case of photons with energies in nuclear recoils, Compton-electron excess of 1.022 MeV, by the creation of electron-positron pairs. When radiation is absorbed, an amount of heat equivalent to the energy absorbed is When free electrons, or electrons in the outer shells of atoms, return to lower produced. atomic energy levels, electromagnetic radiation is emitted either as x rays or as photons in the visible or ultra-violet range of frequencies. Radiation can therefore be detected calorimetrically as well as by measuring electrical currents or light generated in gases, liquids or solids. Energetic particles travelling in a transparent medium with velocities exceeding the velocity of light in that medium, also emit visible radiation, known as Eerenkov radiation Detectors based on the observation of Cerenkov after its discoverer. radiation have physics of nuclear reactions and the been developed, but find application mainly in the search for new elementary particles using high-energy accelerators. Accelerated or decelerated electrons also emit radiation known as bremsstrahlung. Such are the x rays that were found, by RGntgen, to be emitted when cathode rays were decelerated in solid targets. Bremsstrahlung finds some, but rather few and unimportant, applications in the measurement of radioactivity. The properties of all the foregoing types of radiation and their interaction processes rather fully in the previous sections of this report, in with matter have been discussed Knoll (1979), Mann, et al., (1980), NCRP (1985), and in many other texts. The earliest detectors of radiation were the photographic plate, crystals of zinc The grains of a photographic emulsion became sulphide and the gold-leaf electroscope. A crystal of zinc sulphide, a solid scintillator, emitted a developable on irradiation. flash of light in the process of stopping an energetic alpha particle. The gold-leaf gas-ionization chamber, the voltage on the leaves dropping electroscope was the prototype rate that was correlated with the rate of production of positive-ion-electron pairs at a The photographic plate still finds use in the detection of nuclear-particle in the gas. autoradiography but is not otherwise significantly used in measurements of tracks and in Liquid- and solid-scintillation detectors and ionization detectors, both radioactivity. are very widely used in the measurement of activity and of the gaseous and solid-state, 1980, or NCRP 1985). energies of the radiations emitted. (See Knoll, 1979, Mann et al., In order to characterize a radioactive species (radionuclide) completely one must number, the activity and decay constant, the nature of its specify its atomic mass, atomic and electric moments of it radiation or radiations, spin, parity and the nuclear magnetic level of the state of its progeny to which decay occurs, and also of the excited or ground difference in mass between parent and daughter atoms (or total energy available for the and transition probabilities of all its possible the transition; or Q value), the energies conversion electrons, such as alpha particles, x and gamma rays, and Auger and radiations and a spectral distribution and mean energy in the case of beta particles and bremsstrahlung. The instruments and processes involved in such characterizations include non-energyof various kinds of radiation and discriminating and energy-discriminating detectors nuclear photographic emulsions and accurate timing devices, macro- and micro-calorimeters, and beta-ray spectrometers, mass radiation-track recording plastic films, alpha-particle spectrometers, mass (or "isotope") separators, and a host of nucleonic instruments such as amplifiers and multichannel analyzers. cathode-ray oscilloscopes, satisfied to know their For most purposes the user of radioactive materials is specific activities or activity concentrations and purity, their decay constants and the Rarely, however, would a of their radiations, including the energy of each. nature secondary standardizing laboratory be called upon to measure or verify more than the calibrated activity and purity, and the former would usually be measured with equipment regional laboratories; and the latter using activity standards supplied by national or could often involve half-life and radiation-energy measurements. Purity (chemical and radionuclidic) should be the responsibility, however, of a reputable supplier, and nuclear specialized laboratories and published in nuclear-data data are usually produced by tables.
Radioactivity
4.4. DETECTION 4.4.1.
OF RADIATION:
measurements:
principles
and practice
801
PRINCIPLES
Ionization
was The photographic plate, in use in 1896 time for the recording of x radiographs, More sensitive the detector at hand to Henri Becquerel when he discovered radioactivity. detectors in the form of simple ionization chambers were used by Pierre and Marie Curie and The Curies used a parallel-plate air by Ernest Rutherford in their early experiments. condenser connected to an electrometer to measure the relative activities per atom of various chemicals and rocks spread in the form of a layer of powder on the lower horizontal Rutherford in his early work used the simple plate of the parallel-plate condenser. invented in 1777 by Abraham Bennet (Phil. Trans. Roy Sot. 77, 26) gold-leaf electroscope, The gold-leaf for the purpose of investigating the properties of static electric charges. in the early electroscope, in its use as an ionization chamber, found elegant expression 1930's as a measuring instrument of very adequate precision in the form of a quartz-fibre Much of the pioneering work at the electroscope designed by Charles and Thomas Lauritsen. Radiation Laboratory in Berkeley in identifying new radioactive species was carried out that has access to Any laboratory using the Lauritsen electroscope (see Fig. 4-l). calibrated standards and also has a good balance and plastic pycnometers could distribute in the range of 1.5 to 3.0%, relative radioactivity standards, with random uncertainties using the quite inexpensive Lauritsen electroscope as its comparator (Mann et al., 1980). Quartz-fibre electrometers of greater precision were developed in the late 1940's by Hugh Carmichael at the Chalk River Laboratories of the present Atomic Energy of Canada Limited.
View of a Lauritsen electroscope used for internal measureFig. 4-l ments of sources emitting a or fl particles or external photon sources (after Hunter and Mann, Nat. Res. Council of Canada Report CRM-409, 1948). radiation traverses a volume of gas it produces If electromagnetic or corpuscular In the process of ionization ionization and excitation of the gas atoms and molecules. together with free electrons. In an atomic and molecular positive ions are formed electronegative gas such as oxygen the electrons may attach to neutral gas molecules to form negative ions. radiation field is confined in an enclosure If the volume of gas in a constant containing two electrodes between which an electrical potential difference is maintained, then positive ions will move towards the cathode and negative ions and electrons towards the ionization current, flows across the gas and current, the anode, and an electric Such a device is known as an ionization chamber and the through the external circuit. value of the ionization current observed in the external circuit is a measure of the number of gaseous ion pairs created inside the chamber and therefore also of the amount of the The configuration of the chamber can vary particular radiation that is traversing it. considerably to suit the experimental requirements, but is more often than not either the former consisting of outer cylindrical and inner axial cylindrical or rectangular, electrodes, and the latter of parallel plates or grids. Positive-negative ion pairs formed in a gas will, unless drawn apart, recombine. On introducing a small voltage difference between the electrodes of the ionization chamber the ion pairs will be separated and start drifting to the respective electrodes, but at low On increasing the voltage, and therefore the still voltage recombination occurs. occurs until a maximum current, the velocities of the ions, less and less recombination saturation current, is achieved (See Fig. 4-2).
Radioactivity
802
measurements:
principles
and practice
z e
2 --_---I
E ._ 5
I
Plateau region
.; 0
Applied voltage
Saturation Fig. 4-2 chamber. 4.4.1.1.
Pulse-ionization
curve as obtained
with a typical
ionization
mode
If the ionization chamber is provided with an external RC circuit similar to that ions of electrons towards the anode and positive shown in Fig. 4-3, then the movement the high resistance R, towards the cathode will induce a pulse of voltage V, across where V, is a function of time t. The shapes of these pulses are illustrated in Fig. 4-4. The electron mobilities are some lo3 times greater than those of the positive ions so that the initial sharp negative slope shown is due to the movement of the electrons away from the cathode, and the slower return of the pulse tail is due to the inductive effect of the The larger R, the smaller is the slower movement of the positive ions towards the cathode. current flowing in the external circuit. 0
Td
T
t 00
i
IX
I
I
t*
I
I
I
=
Principle of a parallel-plate ionization chamber. A single ion pair is assumed to have been formed at time t = 0 (after
Fig. 4-3
Mann
et
al.,
1980).
Typical pulse shapes obtained with a parallel-plate pulse Fig. 4-4 ionization chamber, as a function of time, t. The dashed line is for a single ion pair, the solid lines for a number n of ion pairs, where RC>> RlCl > RxC2 . The ionization chamber is thus able to generate a steady current output in a constant radiation field, or to operate in a pulse mode to detect separate ionizing events. For the purpose of understanding the operation of the ionization chamber as a proportional or Geiger-Miiller counter it is convenient to consider such a chamber having a cylindrical configuration operating in the pulse mode. In the direct-current mode, resistance R (as shown in Fig. 4-3) would be zero (capacitance would merely represent that of the chamber and residual capacitances), and a current-measuring device would be placed across AB. In the pulse mode, R would be large and a cathode-ray oscilloscope or (as in the case of the calibration of samples of ZZ2Rn) a pulse-recording nucleonic circuit would complete AB.
Radioactivity measurements: principles and practice
The questions considered above have been discussed in somewhat more detail in Mann et al. (1980). 4.4.1.2. Gas multinlication If. after achieving saturation, the voltage applied to the ionization chamber is increased still further, we reach a condition where the electrons accelerated towards the anode achieve velocities between collisions with neutral molecules, and therefore energies, sufficient to ionize these molecules and to create more ion pairs, and multiplication of the ion pairs, over and above those created by the incident radiation, occurs. The onset of such multiplication will occur at lower voltages in a cylindrical ionization chamber than in a parallel-plate chamber containing a comparable mass of a given gas because of the very much greater electric-field strength in the neighborhood of a rod or wire anode of relatively small radius. As a result of this multiplication of ion pairs the current flowing in the external circuit again increases with increase in applied voltage. In addition to the direct-current mode of operation, the ionization will also give rise to current or voltage pulses in the external circuit. Thus consider the situation in which a single 01 particle of, say, energy equal to 5 MeV dissipates all its energy in the gas of the ionization chamber. The average energy, W, expended by a, ,9 or -r radiation in creating one ion pair when traversing the gas a gas-ionization chamber is a quantity that has been measured for a variety of gases for different radiation energies (ICRU, 1979a; Niatel et al., 1985). For such gases, W lies in the range of from 25 eV to 35 eV per ion pair, so that a 5-MeV a particle that expends all of its energy in the gas will create of the order of 1.5 x lo5 ion pairs in the chamber. The application of the principles of gas multiplication to the development of detectors capable of recording single radioactive events can best be considered in terms of a cylindrical ionization chamber with an anode of wire having a small cross-sectional radius. A voltage is applied between the outer cylindrical cathode and the wire anode by means of a circuit similar to that shown in Fig. 4-2 and the chamber is filled with a pure electropositive gas so that any primary ionizing event occurring in the chamber will give rise to positive ions and free electrons without the formation of negative ions. We "ill suppose that N ion pairs are formed within the gas filling of the chamber when a single ionizing event occurs within it, and will consider the number of electrons and positive ions that will be collected at the electrodes for different values of the applied voltage V. For zero voltage V applied to the chamber, the N electrons and N positive ions will either recombine in the track of ionization or move randomly until they are neutralized within the chamber. If the primary ionizing event occurs when a voltage is applied to the electrodes that is less than that necessary to give the saturation current in the steady state, then a fraction of the ion pairs will be collected and a voltage pulse V, would be detectable across AB. When the voltage V is greater than that which would promote a saturation current from a constant source of radiation, then essentially all the N ion pairs from a single primary event would be collected and a voltage pulse similar to those shown in Fig. 4-4 for the two shorter time constants, R,C, and R,C,, would be detectable across AB. This functional relationship between the number of collected ion pairs and the applied voltage is illustrated in regions I and II of Fig. 4-5, for two cases in which ionizing events forming respectively 10 and lo4 ion pairs have been hypothetical primary assumed. In Fig. 4-5 region I is that region of applied voltage where recombination occurs, and region II is that of saturation where essentially all of the initially formed ion pairs are collected. 4.4.1.3. Voltare nulses from sinele radiative events The boundary between regions II and III in Fig. 4-5 represents the onset of gas multiplication which has already been discussed rather generally for the case of the direct current arising from a constant source of radiation, for either a parallel-plate or cylindrical geometry. In more detail, however, one must remember that the electric field, E, is constant between parallel electrodes, but is inversely proportional to the radius, r, from the axis in the case of the cylindrical geometry. The field gradient, the rate of change of E with r is therefore proportional to l/t. Thus E becomes very large as r becomes very small. In other words the electric-field intensity in a cylindrical detector with a fine-wire anode can become very large close to the wire anode. Thus secondary ion pairs, formed by collision, will be mostly generated in the immediate vicinity of the anode wire. 4.4.1.4. The nronortional region In a cylindrical detector with a wire anode, multiplication will begin on entering region III from region II, with increasing applied voltage V, and it will further increase
803
Radioactivity measurements: principles and practice
804
Applied voltage,V
Number of electrons collected vs applied voltage in a gasFig. 4-5 ionization detector. (I) recombination, (II) saturationl (III) proportional, (IV) Geiger region. The lower curve is for Nl = 10, the upper curve for N2 = lo4 ion pairs formed in a primary event. The dashed ordinate L indicates the onset of limited proportionality (see text). (After Mann et al., 1980). with increasing voltage as the electric field becomes sufficient to impart enough to free electrons at greater values of the radius r to cause secondary ionization.
energy
In the lower-voltage part of region III the numbers of electrons and positive ions to the number of ion pairs, N, formed collected, n, at any given voltage V is proportional in the primary ionizing event. Thus n = MN where M is known as the multiplication factor, and region III is known as the proportional region. Pulse detectors operating in counters, this region are called proportional The higher-voltage part of region III is known as the region of limited proportionality because the number of ion pairs collected is no longer proportional to the number of ion pairs produced in the primary ionizing If we consider two primary ionizing events the one resulting in N, and the other event. in N, ion pairs, where N, is about 10 and N, about lo", then it can be seen that above a certain applied voltage L (Fig. 4-5), n1 and n2, the numbers of collected ion pairs corresponding to N, and N,, tend to equality. At a voltage A (Fig. 4-5), the ratio nz to n1 is closer to 10 than to lo4 for N, and N, equal to 10 and 1,000, respectively. The gas multiplication of region III contrast with no gas amplification in region where the multiplication of proportionality change in applied voltage, V.
amplification, in is sometimes called gas Region II is also, of course, a region II. factor M is unity and remains constant with
Because the amplitude of the output pulse is proportional to the number of ion pairs formed by a primary ionizing event in the saturation or proportional regions of a gasenergy operating in the pulse mode, such detectors can be used for ionization detector completely in the sensitive region of spectrometry provided that the radiation is stopped The output-pulse amplitude is slightly modified, however, if the primary the detector. ionizing track is not parallel to the wire or electron-collecting plate of the detector. The secondary electrons may be collected at the anode in the order of 1 /bs, but the thousand times longer to reach the cathode. If the positive ions take of the order of a ionizing track is oriented at a considerable angle to the cathode then there may primary collection of the positive ions that are also be a considerable lapse of time between the The induced potential at the anode due to cathode and further away. formed close to the the positive ions moving away from it will therefore be smeared out in time and the To overcome this in the case of a particles in distorted. electron pulse correspondingly wire grid intermediate a parallel-plate chamber, Otto Frisch placed a fairly transparent anode in such a manner that all the a-particle in voltage and between the cathode and SOUL-ce on the cathode ended on the cathode side of the grid. In this tracks from a manner the electrons reached the anode in a very short time to give a short voltage pulse the grid from the inductive effect of the receding and the anode was also shielded by Good a-particle energy spectra were then obtained. positive ions. This device, known as the Frisch-grid pulse-ionization chamber, is now only of passing interest because a-particle spectrometry can be more conveniently carried out using surface-barrier for a particles detectors silicon detectors and solid-state operation of silicon detectors for electrons. The the gridded lithium-drifted is discussed more fully in Knoll (1979) and Mann et al. (1980). pulse-ionization chamber The cylindrical pulse-ionization chamber is, as mentioned above, used for the detection and assay of radon in air, but in that application it is essential to remove the electronegative oxygen from the air. 4.4.1.5.
The Geieer
region
1n the proportional region the chain multiplication process in which one electron can produce large numbers of ion pairs is known as a Townsend avalanche. A primary ionizing
Radioactivity
measurements:
principles
and practice
805
length along event will normally produce a cluster of such avalanches whose magnitude and This the anode wire will be determined by the size and disposition of the primary event. cluster of avalanches is also generally limited to a short length of the wire for low that the primary event does not values of the applied voltage in region III, provided extend for much of the length of the cylindrical chamber, and the cluster will spread along the wire with increasing applied voltage. As the applied voltage is increased up to the threshold of, and into, the region of field increases in the proximity of the anode wire limited proportionality, the electric Campion (1968) has also shown, using and the Townsend avalanches increase in magnitude. them, that the number of photons emitted by an electron-multiplier phototube to observe deexcitation of the atoms and molecules in the ionized plasma near the anode wire also the ion sheath, or plasma, increases with increasing voltage (i.e., with the size of from the cathode photons, in turn, release photoelectrons around the anode wire). These and anode of the wall, and these photoelectrons again traverse the gas between cathode avalanches, and secondary pulses ("after ionization chamber to cause further Townsend pulses") at the anode wire. Some four or five such photon pulses of diminishing amplitude were detected by the phototube in a time that "as of approximately the same duration (2 to 3 +z) as the duration of the electronpositive-ion pulse illustrated in Fig.4.4. is increased through the Concomitant with these developments, as the applied voltage region of limited proportionality, is the creation near the anode wire of a positive space charge that will wipe out the high electric field near the wire and terminate the process of gas multiplication. As the positive ions move away from the anode the high-intensity region will be restored. lower-voltage Thus in the true proportional region (in region III of Fig. 4-5 on the side of L) the Townsend avalanches are relatively small and photon emission is not so great as to destroy the proportionality between the primary ionizing event and output pulse. As the applied voltage is increased through the region of limited proportionality more and more photons are emitted from the Townsend avalanches near the anode wire, with more photoelectrons emitted practically simultaneously from the cathode (c = 3 x 1O1' cm s-l), and The the Townsend avalanches begin to spread along the whole length of the anode wire. but the more slowly moving positive ions form a electrons are quickly collected, positive-ion sheath around the anode wire and the induced pulse on the anode terminates as When the applied the positive ion sheath moves out towards the cathode and is collected. voltage is so high that the electron-ion sheath envelopes the whole length of the wire, This region is the ionization chamber is said to be operating in the Geiger region. When operating in the Geiger region, at a given illustrated by region IV in Fig. 4-5. applied limits, primary more.
chamber are, within statistical voltage, the output pulses from the gas-ionization all equal in amplitude, irrespective of the number of electron-ion pairs in the ionizing event whether it be one electron-ion pair or many orders of magnitude
On raising the applied voltage above that corresponding to the upper limit of region IV, the ionization chamber will begin to develop multiple pulses, not necessarily related to any applied voltage, a ionizing event occurring within it, and, on further raising the continuous electrical discharge with the emission of light can occur. For complementary 4.5. GAS-IONIZATION COUNTERS
details
DETECTORS:
see Mann
et al.
IONIZATION
(1980)
CHAMBERS.
PROPORTIONAL
AND GEIGER-MijLLER
radionuclide metrology. Gas-ionization detectors have been the "work horses" of They can be divided into two broad types of instrument, namely those with steady-current and outputs. those with pulse In the former there is a great diversity of instruments, while in the latter there are grid-shielded pulse-ionization chambers, and proportional, GeigerMuller and spark counters. These last the spark counters find no application in routine radionuclide metrology and are used mainly for high-energy-particle detection. And pulse-ionization chambers, as mentioned in 74.4.1.4, have been largely replaced in metrological applications by solid-state ionization devices. 4.5.1.
Ionization
chambers.
As mentioned earlier, the gold-leaf electroscope was one of the first ionization instruments to be used for quantitative measurements of radioactivity. This instrument was the precursor of a great many other instruments such as the Lauritsen electroscope, the Carmichael electrometers, pocket dosimeters, free-air chambers, cavity chambers, reentrant chambers (on which the present radionuclide calibrators or "dose" calibrators used in the assays of photon-emitting radiopharmaceuticals are mostly based), and also pressurized ionization chambers, and internal ionization chambers into which radioactive gases such as can be introduced for assay. tritium r:in the form of [3H]-HzO) or 14C (as [%-CO,) Many of these chambers and their applications have been discussed extensively and in detail in NCRP (1985, 77 3.11, 4.4, and 6.4.3.2.3). In particular the evaluation and use of the calibration "K factors" (activity per saturation current) for different photon-emitting nuclides is discussed in those sections.
806
Radioactivity
measurements:
principles
and practice
Almost every application of a gas-ionization chamber to radionuclide metrology is as a relative-calibration instrument. In other words, the chamber must be calibrated in terms of a radioactivity standard sample and the K factor measured for a given radionuclide. The only exception is the activity calibration of a photon-emitting nuclide using a cavity ionization chamber of known volume, that is generally air-filled. This method is described in NCRP (1985, 83.11.2). But its use requires a knowledge of the emission probabilities per decay for all photons emitted by the radionuclide in question, and the difficulties in constructing and maintaining such a chamber places it more in the purview of a national laboratory. Gas-ionization chambers are operated in a region of applied voltage such that the value of the ionization current is saturated (region II in Fig. 4-5). In this region of saturation current the exclusion of electronegative gases is not necessary, so that Lauritsen and Carmichael electrometers, and gas-ionization chambers at atmospheric pressure, are normally filled with air. However, in national and international laboratories the calibrations of activity, for many photon-emitting radionuclides. are normally maintained, or checked, using reentrant ionization chambers containing argon or nitrogen at a pressure of about 20 atmospheres (= 2 MPa) (see 74.4.3 and Figs. 74 and 75a in NCRP, 1985). Direct activity calibrations of radionuclides which emit, say, beta particles and gamma rays are obtained using a fundamental, or direct, method such as @-y-coincidence counting. If the radionuclide is short-lived (e.g. 1311, with 8.02.day half life) the calibration is preserved, or maintained, by measuring the saturation current when a known volume of a solution having an activity A of the radionuclide, usually contained in a flame-sealed glass ampoule, is placed in the reentrant finger of a pressurized-argon ionization chamber. Saturation ionization currents range from 10.' to lo-l3 A and must be measured by one of several methods available (NCRP, 1985, 74.4.6). If R is the measured readout due to the saturation ionization current, I, then the calibration "K factor" is defined as K = A/R. or response, R, (The readout is normally proportional to the saturation current I.) The "K factor" is inversely proportional to R and is in the nature of a reciprocal efficiency. As long as the current response of an ionization chamber is stable over long periods of time, then any other solution of that radionuclide with activity A’ can be calibrated by measuring the saturation current obtained on placing an eaual volume of solution, in a comuletelu similar ampoule, in the fame position within the reentrant finger of the ionization chamber, and measuring the new response R’. The activity A' of this second solution of the same radionuclide is then equal to AR’/R, or KR'. For assurance of reproducibility over extended periods of time, the stability of measuring its of an ionization chamber is usually checked (or monitored) by response to a long-lived reference source (or sources) at the same times that R and R’ responses Such long-lived reference sources may consist of sealed sources of "Co or are measured. with its 7. la7Cs, but are most frequently well-sealed metal capsules of z26Ra inequilibrium in terms of a radium-226 reference for convenience, ray-emitting daughters. Continuing, source, then if the responses to the long-lived source are RRa (at the time of measuring R) source or for and R;, (at the later time of measuring R', either for the old radionuclide are the respective (but not a new batch of the same radionuclide), and if AR,, and 46 necessarily known) activities at the earlier and later times, a "K factor", KRa, can be And defined for the reference source such that KRa is equal to A&RR. or to A ka/Rka (i.e. the ratio of ionization currents), should be equal R&JR,,, the ratio of responses making the two measurements on the to As',/&,, the ratio of activities at the times of reference source. function of the decay But the decrease in the ratio A&/A,, is a simple, calculable, If *=Ra, in equilibrium with its r-ray-emitting constant of the reference nuclide. If the is the reference material, then its decay amounts to 0.05% per annum. daughters, ratio Ak,/A,,, then good is found to decrease in like proportion to the ratio R;,/RR, stability and reproducibility of the ionization-chamber system can be presumed. of calibrations of short-lived radioactivity Another approach to the maintenance standards by means of an ionization chamber is to define a "relative K factor", KR, equal where R and R are still the observed responses (ionization currents) for the to AR&R, of interest (of activity long-lived reference source and for the short-lived radionuclide subsequent date it is desired to calibrate one or more new If at any A), respectively. only necessary to obtain samples of the radionuclide of interest (e.g. lJII), then it is calibration sample and to the old, long-lived, and R.& to the new the responses R’ In this when placed in the same geometry in the same ionization chamber. reference source to be calibrated means the same context, the same geometry with respect to the new sample volume and density of solution in an exactly similar glass ampoule. The activity (or activity interest is then given by A’
concentration)
A' of the new
sources
of the radionuclide
= K,R’/R,,
Apart from any calculable radioactive decay the value of R/R’ will be equal decay, will reflect some departure from unity, other than for radioactive
of
(4-l) to unity. A"Y instability or
Radioactivity
measurements:
principles
and practice
ionization-chamber system (inclusive of geometry or source characteristics) change in the investigated. In effect therefore, the activity calibratshould be and, if significant, in terms of ions of shorter-lived radionuclides, such as '"'I or even %o, are preserved the application of this method in the ionization chamber and the reference source. In the ionization chamber could be uncertainties can be tolerated, cases where larger "chirper" which, in pocket dosimeter or even a pocket replaced by an electroscope, device. conjunction with a timer, can be used as a radiation emission-rate-response 4.5.1.1.
Quality
4.5.1.1.1.
control
In national
usinp
an ionization
chamber
laboratories
long-lived reference source Not only can an ionization chamber in conjunction with a standards from previously made calibrations, but such a be used to prepare new batches of to check new direct ("absolute") used in national standardizing laboratories system is Thus standardizations against previous direct standardizations of the same radionuclide. batches of s°Co solution standards might have been prepared by a national standardizing both 1970 and 1980. In the laboratory using the method of coincidence counting in, say, amount of the solution can be flame-sealed in a standard glass first calibration a 3-ml ionization chamber in terms of a ampoule and its "relative K factor", Ks: measured in an encapsulated, sz6Ra reference source, or in terms of two or three such s2sRa well-sealed, Likewise in 1980, K, can again be measured for the new batch of "Co standards sources. that has been prepared by coincidence counting, using 3 ml of the new standard in a similar glass ampoule in the same ionization chamber and in terms of the same szaRa reference sources.
If the ratio of the 1980 to 1970 values of KR is in the same proportion as the 1980 to measured by coincidence counting, then there is 1970 values of activity concentration that have there is consistency amongst all the dilutions and measurements assurance that been made in preparing the two batches of standards. laboratories is normal use in standardizing the ionization chamber in The pressurized-argon ionization chamber (see NCRP, 1985, 74.4), in which the mass of the gas clearly remain constant. Open-air filling the chamber should (in a robust chamber) Such chambers have chambers have, in the past, also been used in national laboratories. but their response must be corrected for small given long-term satisfactory performance, changes in temperature and atmospheric pressure. The procedures
described
above
for the preservation
of a direct
calibration
(sometimes
"absolute" miscalled an calibration) for the calibration of successive batches of relative activity standards (sometimes called "secondary" or "tertiary" standards), can be applied in terms of a long-lived reference source, constant source-to-detector geometry, radiation rate-of-response (e.g. an ionization-current-measuring) and any detector that gives an output signal that is a linear function of the amount of radiation detected. 4.5.1.1.2.
International
quality
control
In the late 1960's discussions took place at the Bureau International des Poids et Mesures (BIPM) and at the International Atomic Energy Agency (IAEA) with a view to establishing international reference systems, based on ionization-chamber measurements, for the quality control of national-laboratory activity standards for both consistency within and between national laboratories. Details of the method as it was finally adopted IAEA and BIPM are given in papers by Houtermans (1970) and Rytz (1983). The latter by publication gives a detailed description and valuable discussion of the SIR programme. Soon after the death of Hans Houtermans, the IAEA international quality-assurance program was brought to a close, but that at BIPM, known as the Systeme International de Reference (SIR) program that was started in 1972 by A. Rytz (1983), continues to give the most valuable service to the national radionuclide-metrology laboratories. From the periodic data sheets issued for each radionuclide, national laboratories can learn if their calibrations agree with those of other laboratories in the international community, and, further, any major discrepancies between laboratories that become evident in the activity calibrations of any given radionuclide can indicate the need for a special distribution of split solutions, having the same activity concentration, for international intercomparitive measurements under the aegis of BIPM. The basis of the SIR program, as described by Houtermans in 1968 (Houtermans, 1970), is the measurement of equivalent activity (see below) of a photon-emitting radionuclide in reentrant ionization chamber in terms of a long-lived reference source (also see ;5.4.6.5). The reference sources adopted by IAEA and BIPM consisted of szsRa in equilibrium with its y-ray-emitting daughters contained in well-sealed metal (usually platinum-iridium) capsules.
case or, (or,
the
The quantity on the right-hand side of Eq. 4-l h as the dimensions of activity; in the of a solution standard this would be activity concentration multiplied by the volume preferably, mass of solution. This quantity is known as the eauivalent activity, A,, where sz6Ra is used as the long-lived monitor, as the radium eauivalent activity) of radionuclidic source in the ionization chamber. As Houtermans (1970) pointed out
Radioactivity
808
meaSUrement8:
principles
and practice
"the essential quantity is A,, i.e. the activity of the nuclide, which gives the same instrument response as the long-lived standard when measured under standard conditions, Of course, care must be taken to keep all conditions such as ampoule dimensions, absorption in the liquid, etc., "constant". (also see 75.4.6.5.) 4.5.2.
Prouortional
and GeiPer-Miiller counters
and Geiger-Miiller counters Proportional are gas-ionization detectors operating, respectively, in the proportional and Geiger regions (Fig. 4-5). Their cathodes are often cylindrical, but can have different shapes to suit different requirements, and their anodes, often of stainless steel, usually consist of a fine straight or looped wire of the order of 0.02 mm to 0.1 mm in diameter. The gas filling, contained within the cathode and anode insulators, usually consists of a pure electropositive gas such as argon, to which has been added up to ten percent of a multiatomic gas such as methane in proportional counters and ethyl alcohol or a halogen in the case of Geiger-Miiller counters. The function of the multiatomic gas is to absorb photons and to dissipate the energy from excited molecular levels rather than as photoelectrons. This inhibits after-pulsing in the case of proportional counters and, as "quenchers", the initiation of continuous discharge in the case of Geiger-Mtiller counters. In the Geiger region, however, alcohol molecules also expedite the spread of the positive-ion sheath along the anode wire,because the photons arising in the initial Townsend avalanche while being highly absorbed by the alcohol molecules also have enough energy to ionize a significant fraction of the alcohol molecules, thus creating a positive-ion sheath, and space charge, that helps to quench the initial discharge. Because of the creation of this positive-ion sheath the output pulses from a Geiger-Miiller counter are, apart from statistical fluctuations, all of the same size irrespective of whether the detected ionizing event in the counter consists of one ion pair or many orders of magnitude more. The ions of the main electropositive gas filling can also be neutralized on their way to the cathode, exciting molecular levels in the multiatomic gas additive, in both the proportional and Geiger regions. Also, in the Geiger region, the alcohol and halogen ions tend to dissociate as they are neutralized at the cathode instead of emitting further photoelectrons. Thus it is that a Geiger-Miiller counter with an alcohol quenching additive has a limited life, whereas the halogen atoms can recombine into molecules. Geiger-Miiller counters can also operate when filled only with a pure electropositive gas but it is then necessary to incorporate electronic quenching of the applied voltage, in the external circuit, to give reduced voltage for a time that is somewhat longer than that Proportional counters used in reach the cathode. required for the positive-ion sheath to dating are also operated with a gas filling of only carbon dioxide, but this radiocarbon must be highly purified. An argon (90%) and methane (10%) mixture is the gas filling most commonly used in gas-proportional counters, but for more penetrating radiation the higher atomic-number noble gases, krypton and xenon, may be used. D.R. Carson and R.R. Wilson in their 1948 paper on Particle and Quantum discussion of the modus operandi of gas-filled a detailed and comprehensive
Counters, give detectors.
1n typical proportional counters with a distance of a centimeter, or so, between anode collected in microseconds and the positive ions in and cathode, the electrons can be moderate But at after the detection of an ionizing event in the counter. milliseconds applied voltages, because of the limited size of the Townsend avalanche and the absence of (see large positive-ion space charges, the counter is able, with a short time constant Fig. 4-4), to record a subsequent ionizing event in the order of one microsecond. space charge there is a large positive-ion In a Geiger-Miiller counter, however, created by the positive-ion sheath that stretches along the whole length of the anode wire. longer to This can give an output pulse of several volts, but it takes correspondingly where a further ionizing event in the counter can be clear the space charge to a point In a counter of typical dimensions this inoperative time can amount to as much recorded. as 500 milliseconds. counter is the detector of choice. Therefore, for high count rates, the proportional record successive "fast" external circuitry, ionizing events It can, with special counter at rates of the order of lo6 per second. occurring in the 4.5.3.
Special
aoolications
of pas-ionization
detectors
Direct-current-reading reentrant ionization chambers operating in the saturationcurrent region normally constitute the detection systems of the so-called "dose" calibratused in the assays of radiopharmaceuticals. The output ors or radionuclide calibrators, circuitry to give a direct reading current in these instruments is digitalized by special or multiples of the becquerel, of the radiopharmaceutical or in submultiples of the curie, the chamber. other radioactive preparation placed in the reentrant cavity of and Geiger-Miiller, counters can be made in different configurations for Proportional, Many are cylindrical in design and may have special thin alumindifferent applications. Other counters ium or beryllium windows to enable low-energy radiations to be recorded. mounted to fill an aperture in the cathode may be "windowless" with the radioactive source
Radioactivity
measurements:
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809
One very widely used "windowless" design is that in which two of the counter. identical windowless counters are joined so as to form an air-tight seal around an cr- or p-particle Source mounted between them, in such a way that each counter subtends a solid Such a configuratangle of effectively 2n steradians at the source on either side of it. Either half of such a 4n counter can be used with a source ion constitutes a 4rr counter. on a solid backing to count in 2rr geometry. Examples of both types of counter are illustrSuch ated in Knoll (1979), Mann, et al. (1980), NCRP (1985) and many other publications. used almost exclusively in counters have been operated in the Geiger region but are now the proportional region in order to measure high count rates. The counting gas, usually argon (90%)/methane (lo%), is ordinarily flushed through the counters from a tank of the Specially designed 4a counters operate at pressures up to 75 atm compressed counting gas. purpose of detecting j3 particles, conversion electrons and x rays with (7.6 MPa) for the These are described by A. P. Baerg in NCRP (1985) and in the publicathigh efficiency. ions by him and his colleagues that are referenced in that report. These counters are also used extensively in the method of efficiency-extrapolation coincidence counting, also described in papers by Baerg and his colleagues that are also referenced in NCRP (1985), and later in this Report. wall
Proportional counters of cylindrical geometry are also used for internal gas counting. In this method a radioactive gas such as 3H in carrier hydrogen or 14C02 in carrier carbon gas, is admitted into dioxide, mixed with a suitable proportional-counting the counters (See 75.4.4, and also for activity measurements. NCRP, 1985, and publications referred to therein.) Because the detection and energy characterization of gamma rays depends very largely on their interaction with electrons in the Compton and photoelectric processes, it is desirable to use ionization-chamber gas fillings with high electron densities. With this end in view, work has been in progress since about 1970 on the use of noble gases in condensed These provide the only known condensed nonconductor in which form, both liquid and solid. the ion pairs created by ionizing radiation can be collected as in gas-filled ionization chambers. Of particular interest was xenon with its high atomic number. Knoll (1979) describes, with references, the stage of development, at that time, of such detectors, and presents an interesting table of some of the pertinent properties of liquid argon and xenon The cryogenic requirements for this method could clearly and of liquid and solid argon. constitute a limitation for many laboratories. 4.6. LIGHT-EMITTING.
ELECTRON-EMITTING
AND
SOLID-STATE
DETECTORS
For the reasons stated in the immediately preceding paragraph it is of interest to use detectors that have both high electron density and large stopping powers (i.e. those in the loss of energy of the radiation per unit length of path travelled is which M/h, devoted to the development of radiationFor this reason much research has been large). Of those in current use there are two detecting materials in the liquid and solid states. excited by radiation namely liquids and solids that emit light when broad categories, and the group of semiconducting crystals in which radiation can create (luminescence), and and positive holes that are collected, respectively, at the anodes mobile electrons cathodes attached to the crystals, as an ionization current. Although there has, in the past, been no Luminescence can be prompt or delayed. is now generally termed fluorescgeneral agreement in the literature, prompt luminescence and delayed luminescence is termed phos"x-ray fluorescence", ence, analogously to There is a fundamental difference between the functioning of organic and phorescence. light emission derives from the deexcitation of inorganic scintillators in that the of excited molecular energy levels of organic molecules, whereas most of the deexcitation Lattice vibrations inorganic crystals is from energy levels of the whole crystal lattice. and deexcitation from one level to another is assumed to quantized, are assumed to be bring about the emission of a quantum of elastic-wave energy known as a phonon (Hughes and Pooley, 1.975). A phosphorescent pulse decays exponentially. Because of the difference between the organic and inorganic responses a phosphorescent pulse decays in times that are of the times shorter in organic crystals than phosphorescent pulses in order of a thousand The time decay constant (the time to decay to l/e of the initial inorganic crystals. The rise time amplitude) is of the order of 10 ns for the former and 10 JLS for the latter. of such a pulse to maximum amplitude in either type of crystal is of the order of one nanosecond. 4.6.1.
Organic
Scintillators
of Organic scintillators are mostlv polycrystalline substances (i.e. consisting is stopped or scattered in such a If a, p or 7 radiation randomly oriented crystals). crystal, energy is deposited in its substance by the a or B rays, or by secondary electrons molecular levels of the constituent produced by the 7 rays and this energy can excite organic molecules that reemit the energy in the form of photons in the visible or ultraH. Kallmann in 1947 was the first to use crystals of violet regions of the spectrum. naphthalene to detect ionizing radiation by the scintillation process, and he was followed by P.R. Bell in 1948 who used crystals of anthracene for the same purpose. Because
the
reemission
of the energy
deposited
by
the radiation
event
is through
the
81 0
Radioactivity
measurements:
principles
and practice
can act as scintillators when deexcitation of single molecules, anthracene and naphthalene dissolved in organic fluids or in solid-plastic solution. The former is an example of the widely used method of liquid-scintillation counting in which the radiation energy is dissipated in the solvent and transferred to the dissolved molecules of the scintillator. added substance known as a wavelength shifter is often used to absorb Also another higher-energy (high-frequency) radiation from the prime scintillator and to reemit it at lower frequency in a suitable range of wavelength to match the sensitivity of an electron-multiplier-phototube detector. In plastic solution the energy is again dissipated in the solid material and transferred to the molecules of the scintillator. Many organic More detailed discussion of this method is given in fluors are now available. Birks (1964), Knoll (1979) and NCRP (1985). 4.6.2.
Semiconductors
and thermoluminescence
Semiconductors are crystalline materials with resistances intermediate between those and insulators. of conductors Their resistivities are also logarithmic functions of (1971) comments that the resistivity (specific electrical temperature. C. Kittel resistance) of a pure metal can be of the order of 10“' ohm cm at low temperature and that of a good insulator may be as high as 1022 ohm cm. He quotes a remark by E.M. McMillan that this range of 10z2 in resistivity may be the largest of any common physical property of solids. The properties of semiconductors are best described in terms of the band theory of insulators solids, developed from Bloch's (1928) collective electron model for crystalline 1948-49). In this theory it is assumed that in a crystal the valence (see Garlick, electrons, that bind the atoms together in the lattice, occupy electron-energy levels in a valence band, while free electrons that can move freely through the lattice occupy higher-energy levels in a conduction band. Between these two bands, as illustrated Electrons in the valence band can, in Fig. 4-6, is a forbidden region devoid of electrons. acquire enough energy from ionizing radiation, thermal agitation, or phonon however, interactions to be excited from energy levels in the valence band into energy levels in the conduction band, through the forbidden region where no electron states are allowed. Such a forbidden region is called a band gap or energy gap, the increment in energy of which is This energy can vary from less than 1 eV for semiconductors to more than 5 designated E,. eV for insulators. The excitation of an electron from the valence band to the conduction band is completely analogous to the process whereby radiant (including thermal) energy can excite extranuclear electrons in lower-energy atomic shells to higher-energy shells, or to complete freedom (ionization), through the forbidden regions between the atomic electron It is also analogous to the process postulated in the Dirac theory by which a shells. negatively charged electron in a universal "sea" of negative-energy states is excited through an energy gap equal to somewhat greater than 2mocz to occupy a positive-energy level, and the vacancy or "hole" left in the "sea" of otherwise completely filled negative-energy states has all the attributes of a positively charged electron. In the band theory, if the valence band is completely filled and the conduction band is empty the crystal will behave as an insulator. On the other hand, in a conductor, such as a metal, the valence band is filled and the conduction band is partially filled, so that on application of an electric field to the conductor the electrons are free to move and a current flows. In contrast to insulators and conductors, a semiconductor at ambient temperatures around 300 K may have the valence band almost completely filled and the conduction band almost completely empty except for the few electrons that are always being excited by thermal agitation into the conduction band. In the simplest case exemplified in Fig. 4-6 the concentration of electrons elevated by thermal agitation into the conduction band (and therefore the conductivity) is governed by the Boltzmann distribution law and is proportional to exp(-E,/kr), where E, is the energy gap between the valence and conduction At room temperatures kT is equal to about 0.025 eV bands, and k is the Boltzmann constant. while E, ranges from 0.2 eV for indium antimonide to 6 eV for diamond (in graphite E, = 0). In a high-purity crystal the simple representation of Fig.4.6 holds, but impurities and crystal defects contribute extra allowed electron states at a variety of energy levels in the forbidden region. Conduction
Donor
level
Electron
Hole
band
traps
traps
Acceptor level
Valence band
Band-gap energy-level Fig. 4-6 (after Mann et al., 1980).
diagram
for an
inorganic
crystal
Radioactivity measurements: principles and practice
811
But for a high-impurity crystal at 300 K with a low value of E,, electrons can be excited by thermal energy available in the lattice into the conduction band and, on application of an electric field, a small leakage current will flow in the crystal. Moreover, for every electron raised to the conduction band, a vacancy or "hole" is created in the valence band in the form of a missing valence electron. This hole can also act as a positive-charge carrier by virtue of accepting a valence electron from a neighbouring lattice bond which creates a hole in that bond that can accept another nearby valence electron, and so on. This movement of electrons in one direction is equivalent to a positive hole moving in the opposite direction. Under the influence of an applied electric will move to the anode and holes in the valence field electrons in the conduction band Kittel (1971) has made the following cogent comment: "If the band towards the cathode. band is filled except for an electron missing from the state E, we say that there is a hole in the state E. The physical properties of the hole follow from those of the totality of electrons in the band. This sentence is the key to the understanding of holes." With decreasing temperature E,/kT becomes larger, and its negative exponential becomes rapidly smaller. Thus, as the temperature decreases the numbers of electrons being excited into the conduction band rapidly decreases and semiconductors tend to become insulators at extremely low temperatures. The resistivities of high-purity semiconductors are proportional to p_exp(w/kT), where p. is the limiting resistivity at very high temperatures, and w is an excitation energy. Thus the resistivities of semiconductors decrease with increasing temperature whereas the temperature coefficients of metals at ambient temperatures are predominantly positive. suppose that a semiconducting crystal, at a reduced temperature such that the conduction band is devoid of free electrons, is exposed to ionizing radiation the energy of which would normally be considerably greater than E, (Fig.4-6). The radiation is scattered around the crystal lattice to which it imparts energy directly by ionization and by such secondary processes as Compton scattering, phonon scattering and the photoelectric effect. Free electrons are therefore excited to the conduction band and those with residual energy will move through the lattice and rapidly dissipate such energy in further interactions with the atoms of the lattice creating more free electrons in the conduction band. Every electron excited to the conduction band will leave a hole in the valence band, and the numbers of free electrons and holes created will be proportional, within statistical fluctuations, to the amount of energy imparted to the crystal by the ionizing radiation. Moreover, if a voltage is applied across the crystal the electrons will be collected at the anode and the holes at the cathode, and a current flows in the external circuit. In this respect therefore, the semiconducting crystal is operating as a solid-state ionization "chamber"; also single ionizing events will give single current pulses in the external circuit. Unfortunately, however, even the purest crystals are rarely free from small traces of impurities or from defects in their structure, and such impurities create electron and hole absorption-and-emission energy levels intermediate between the energy levels of the valence and conduction bands. Such impurity and defect energy levels are called electron traps and hole traps, and can exist, respectively, as little as a few hundredths of an electron volt either above or below the valence and conduction bands. As electrons can now be excited, with relatively little thermal energy, into such traps from the valence band (leaving holes in that band), or from such traps into the conduction band, even very pure crystals will give rise to leakage currents that militate against the use of such semiconductors as high-efficiency absorbers of radiation energy. But fortunately three methods have been developed to reduce the leakage current in such crystals to a minimum, namely by creating a semiconductor rectifying diode, by purification or by compensation. These three methods will be discussed later (84.6.3.3). In the early days of solid-state physics, the purest crystals were designated as intrinsic but with the introduction of the method of compensation the term "intrinsic" was extended to include both very pure material and also that in which compensation had reduced the number of uncompensated charge carriers to less than about 1O'O cme3. But very pure material is now mostly referred to as high-purity, or HP, and that in which the charge carriers have been reduced by compensation as compensated or drifted. 4.6.2.1. Semiconductor imuurities and douing Diamond, germanium and silicon crystals with tetrahedral bonds.
all are quadrivalent
and form
face-centered-cubic
If there are present in any of these crystals small numbers of pentavalent impurity atoms, such as atoms of phosphorus, they will substitute in various lattice locations. But in satisfying the valence requirements of the surrounding quadrivalent atoms, each phosphorus atom will find itself with a loosely bound electron which requires less energy to set it free. Such atoms are called donor atoms and, if solely of one kind, will exist in an elevated energy level about 0.01 eV below the conduction band as illustrated in Fig. 4-6. Such an impurity is termed an n-type impurity because it can contribute negative electrons readily to the conduction band.
Radioactivity
812
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principles
and practice
If, on the other hand, the impurity atoms are trivalent (e.g. boron), they will also replace the quadrivalent atoms at many lattice locations, but the lattice structure calls for a quadrivalent atom. Thus the one trivalent atom in the otherwise quadrivalent tetrahedral lattice in closest proximity around it will be quite ready to accept the missing electron that the lattice would otherwise normally accommodate. This location with its non-negligible probability of accepting a loosely-bound extra electron is called a" acceptor site. The energy levels of such acceptor sites are of the order of 0.01 eV above the valence at ambient temperatures, band. Therefore, kT being equal to about 0.025 eV, electrons in the highest-energy levels of the valence band can readily be excited by thermal agitation to the acceptor-energy level (Fig.4.6). With the great number of electrons available in the upper-energy levels of the valence band, most of the acceptor sites will be filled by thermally excited electrons from the valence band. Impurities that create acceptor sites in a crystal lattice are called p-type impurities because the vacancies, or "holes", created at lattice sites throughout the crystal can The natural impurities that occur in most crystals of act as positive-charge carriers. germanium and silicon are such as to render them p-type. Selected impurities can also be diffused into high-purity crystals of germanium and silicon at elevated temperature a process know" as doping. If thin films of aluminium or gold are evaporated on to opposite faces of such a ptype crystal to form electrodes to which a voltage is applied, there will be a leakage current due to electrons moving from vacated site to adjoining vacant site in the valence band, from cathode to anode, across the crystal. Such a current in p-type material is, as mentioned earlier, equivalent to positive charge being transported across the lattice by the movement of positive holes from anode to cathode where they are neutralized by electrons from the external circuit. In n-type material,free electrons that have been elevated to the conduction band from donor sites move freely (apart from collisions that may generate phonons and, or, heat) through the crystal lattice from cathode to anode under the influence of the applied electric field. The drift velocities of electrons and holes in semiconductors are more nearly in which the drift velocities of electrons can be equal than in gas-ionization detectors, of the order of lo3 times greater than those of the positive ions. Thus in germanium and silicon detectors, having applied electric fields of 250 V.cm-l at a temperature of 300 K: the drift velocities in germanium are of the order of lo6 cm se1 and 5 x lo5 cm s-l, for the electrons in the conduction band and holes in the valence band; in respectively, silicon the respective figures are of the order of 5 x lo5 cm s-l (electrons) and lo5 cm s-l (holes). I" majority material
material the holes are the dominant carriers of charge and are called p-type carriers, and electrons in the conduction band are minority carriers. I" n-type electrons are majority carriers and holes the minority carriers.
4.6.2.2.
Traps. recombination and luminescent centers, and thermallv-stimulated exoelectrons
thermoluminescence.
in semiconducting crystals create traps for electrons and Impurities and defects The behaviour of some semiconductors such as diamond and thermoluminescent holes. materials can only be understood, eve" if imperfectly, by assuming that electrons and around the crystal lattice, encounter such defects where they holes, in their movements Such electron and hole traps occur can remain trapped for various intervals of time. within the energy gap, E,, between the valence and conduction bands, and some of them can occur at a relatively large fraction of E, from either band. One of the earliest semiconducting materials to be experimented with as a detector of ionizing radiation was diamond. Such radiation created electron-hole pairs in the crystal and, under the influence of a" applied electric field, a flow of charge could be detected Diamond was in fact found to operate satisfactorily as in an external electrical circuit. except that with continued use its output signal a detector of ionizing radiation, due to the build-up of space charge caused by the decreased in magnitude apparently trapping of electrons in its lattice. This space charge could however be removed by heating the crystal so that the traps could be emptied by the thermal excitation of the electrons into the conduction band, whence they could return to the valence band. Such thermal deexcitation underlies the phenomenon of thermoluminescence described overall below. Many semiconducting crystals, combined with a variety of dopants, have electron traps some 0.04 to 0.05eV (corresponding to a value of kT at about 500 K) below the lower limit of the conduction band (Fig. 4-6). Ionizing radiation interacting with the crystal can deposit sufficient energy in it to excite electrons from the valence band into these even when the energy is insufficient to excite an electron into the electron traps, conduction band. Free electrons in the conduction band, if not removed by a" applied return promptly to the valence band with the emission of electric field, will normally radiant energy.
Radioactivity
measurements:
principles
and practice
813
However, in many doped materials the trapped electrons have no way of escaping unless fortuitously excited by further incident radiation into the conduction band, whence they They can also be elevated to the condution band by heating deexcite to the valence band. to above about 500 K, from which they return to the valence band with the emission of This is usually accomplished by raising the temperature of the semiconductor at a light. rate of about 1 K 5-l by means of which procedure a "glow curve" of light intensity vs. This observation corresponds to more and more temperature (i.e., also time) is obtained. energetic photons being emitted as the increasing value of the energy kT reaches traps that are at deeper and deeper energies below the lower energy limit of the conduction band. This phenomenon is known as thermoluminescence. in semiconducting crystals is fundamental to the The concept of electron traps their photoconductive and thermoluminescent properties. When a understanding of the conducting or thermosemiconducting crystal is irradiated with high-energy photons, luminescent response persists for varying lengths of time after the source of radiation is removed. In some thermoluminescent crystals the incident radiation energy is stored for years. Such is the principle underlying the well-known thermoluminescent dosimeter (TLD) and the use of thermoluminescence in dating ancient pieces of pottery. In some cases that have indicated that thermoluminescent discordant results have been observed deexcitation may occur by the emission of phonons (thermal quenching) rather than photons; also long decay lifetimes, ranging up to one-hundred million years for calcite, have been For a discussion of these properties, an article by M.J. Aitken in Oberhofer and quoted. Scharmann (1981) may be consulted. Thermoluminescent dosimeters made from a variety of materials can be used for photon, neutron and charged-particle dosimetry (see Christensen et al., 1982). A few typical materials (and their dopants) are lithium fluoride (P, Mg, Cu and Ti), calcium sulphate (Dy and Tm), calcium fluoride (Mn, Dy and undoped CaF,), and magnesium silicate (Tb). Typical maximum emission wavelengths of the radiation and fading times are also given in the above review by Christensen et al. The fundamental role of electron traps in phosphorescence and thermoluminescence has been discussed very fully by Randall and Wilkins (1945). Briefly, they consider the case of a trapped electron at an energy level E below the conduction band, that must absorb at least an amount of energy E before it can escape from the trap. As the electrons in the traps have a Maxwellian distribution of thermal energies the probability, p, of an electron escaping at temperature T is given by p = &E/kT
)
(4-2)
where s is a constant (with the dimension frequency). If the trap is in the nature of a potential well, then these authors point out that the constant s should be the product of the frequency with which an electron strikes the side of the well and of the reflection coefficient (also see Mott and Gurney, 1964). Randall and Wilkins quote a value for s of the order of lOa s-l in phosphors that had been studied. It had also been observed experimentally, as mentioned above, that if certain crystals were exposed to radiation at room temperature for a given time and were then heated so that their temperature increased uniformly with time, light was emitted during the heating process. This effect was referred to as glov and the plot of intensity of light emission as a function of temperature attained gave the glow curve. Such a glow curve could moreover consist of a whole series of glow peaks, indicating the existence of electron traps at different discrete energy depths E. Randall and Wilkins then proceeded from the above equation by assuming that n was the number of electrons in traps at a given energy depth E and temperature T at time t, so that dn/dt = -r~se-~'~~ provided warming,
(4-3)
that there was negligible retrapping. then they derived the expression E = T,
where
,
f(s,p)
[l
+ f(s,p)]
<< 1, and To is the temperature
k log s
If
P,
equal
to
dT/dt,
is
the
,
of maximum
rate
of
(4-4) glow
Using this equation with some further assumptions and experimental data, able to calculate that a temperature of maximum glow equal to 340 K corresponded depth equal to 0.67 eV at the rate of warming normally used.
they were to a trap
More recent experiments show that different crystals used in thermoluminescent dosimetry may exhibit many glow peaks with very different lifetimes. Thus Pohlit (1973) has shown that lithium fluoride has five strong glow peaks at temperatures ranging from 332 K to 427 K with corresponding trap depths between 1.41 eV and 3.62 eV and half lives at 298 K ranging respectively from 2 minutes to lo4 hours. Two weak glow peaks were also observed at higher temperatures. The energy of 3.62 eV corresponds to kT for a temperature of about 4 x 10" K. This trap level is however drained by electrons having velocities at the higher end of the Maxwell distribution as described above, following Randall and Wilkins (Lx. cit.).
Radioactivity measurements: principles and practice
814
The foregoing very brief outline is intended only to indicate why it "as necessary to postulate the existence of electron traps in semiconducting crystals. There are also corresponding defects that act as hole traps. And some traps can also act as recombination or luminescent centres. Thus an electron elevated to the conduction band, from either the valence band or from a trap, is free to move around the crystal (in the absence of an electric field) until it encounters a hole, that is either moving freely in the crystal or is located in a recombination or luminescent centre. In the process of recombination either a phonon or a photon is emitted. The mechanisms of the atomic processes involved in these centres is not always completely understood. Moreover another interaction can occur because of the Coulomb attraction existing between a free electron and a free hole; when they meet in the crystal they can form a stable bound state, somewhat analogously to the formation of positronium. Such a bound state is called an exciton. An exciton can decay into a free hole and free electron, or by the electron falling into a lower-energy hole state with the emission of a photon or phonons. Another mode of escape is also possible for a trapped electron that receives sufficient energy to elevate it into the conduction band, with enough residual energy to overcome the surface work function, and traverse the interface. Such energy can be imparted in diverse ways such as mechanical deformation of the crystal or by heating it, provided that the electron is also close to the crystal surface. This phenomenon "as first described in 1902 in the Philosophical Magazine by J. C. McLennan in an article entitled On a kind of radioactivity imparted to certain salts by cathode rays. The title itself implies that McLennan noted the delayed emission. According to Becker (1973; chapter 3) this phenomenon of electron emission had been known by a number of different terms, of which the following (and their abbreviations) were still then extant: Exoelectron emission (EE) for "cold" or spontaneous emission; optically stimulated exoelectron emission (OSEE); and thermally stimulated exoelectron emission (TSEE). The last of these, TSEE, is of interest because of its potential for radiation dosimetry, by detecting electrons instead of photons (see Becker, 1973, and Kriegseis et Electron detectors that are used include current-reading or pulse-counting al., 1985). and closely-packed channeltron multipliers gas-ionization devices, electron multipliers, Many suitable semiconducting media are also described by (74.6.6 and Becker, 1973). Becker, and detailed information is given about the use of thin Be0 films by Kriegseis et al. Beryllium oxide can, for example, be thinly coated on to graphite discs which can then be heated rapidly with a halogen lamp, and dose readout can be accomplished within 30 s using microprocessor-controlled equipment. The low mean energy of about 0.2 to 0.3 eV of TSEE from thin films of Be0 necessitates the use of electron multipliers with the Be0 in Such dosimeters have a dose response that vacuum, or of sensitive proportional counters. is almost independent of photon or electron irradiation energy, and that covers a linear dose range from 10 pGy to 10 Gy. Systems using ionization chambers and counters, with the semiconductor in many configurations (including deposition upon the internal surface of a Auger-like cylindrical-counter cathode) are described and referenced by Becker (1973). the surface acquiring sufficient transitions are also possible, with electrons close to energy to escape, when other electrons in the crystal deexcite to lower-energy states. Becker and Kriegseis et al., may be consulted for further information and for very many references. 4.6.3. Semiconductor detectors From the foregoing sections it may be seen that it should be possible to use an ionic crystal as a solid-state ionization detector, closely analogous to its gaseous forerunner. Ionizing radiation incident upon the crystal creates electron-hole pairs, each free electron and free hole moving through the crystal under the influence of an externally applied electric field, the electrons to the anode where they are collected, and the holes As in a gaseous ionization chamber any leakage to the cathode where they are neutralized. current must be reduced to a minimum for satisfactory operation. 4.6.3.1. Resolution The average energy to create one electron-hole pair at 77 K is about 3.8 eV for This is inclusive of energy dissipated in competing silicon and 3.0 eV for germanium. processes, and is considerably less than the average energies ranging between 25 eV and 35 eV in producing an electron-ion pair in gaseous ionization detectors. The ability to resolve ionizing events of proximate energy, which is proportional to the number of charge carriers formed and collected per ionizing event, is therefore considerably greater in solid-state than in gas-filled detectors. 4.6.3.2. LeakaPe currents Leakage currents occur for different reasons in gaseous-ionization and solid-state detectors. In the former they are limited to poor insulation of the high-voltage electrode including surface leakage across the insulator; in the latter they can arise from surface derives from the close proximity in energy the principal problem leakage, but (approximately of the order of 0.01 eV) to the valence and conduction bands of the donor and acceptor levels created by impurity atoms. Surface-leakage currents can be reduced by
Radioactivity
measurements:
principles
and practice
815
the inherent leakage and, as has been previously mentioned, etching the crystal surfaces, acceptor and donor impurities can be reduced to satisfactory levels briefly by caused by or by compensation. two basic methods, namely by high purification 4.6.3.3
Purification
and comoensation
Because the acceptor and donor levels can be easily populated and depopulated at room temperature (kT - 0.03 eV) from the valence or into the conduction bands, respectively, an If NA and N, are the impure ionic crystal always has an abundance of charge carriers. then NA + N, is the cubic centimetre, numbers of acceptor and donor atoms present per carriers and it is essential that this be reduced to less than number of potential charge levels. Up about 10" cmm3 in order that leakage currents may be at acceptable operational it has been found possible to purify only germanium crystals to such an to the present, Such crystals have been called intrinsic, but there has been acceptable level of purity. some tendency also to apply the term to crystals in which the total charge-carrier density It is has been reduced by the method of compensation, without removing the impurity atoms. therefore preferable to refer to high-purity germanium detectors (HPGe), when such are the detectors being described. is applicable to silicon and germanium The second method, that of compensation, but that still have too high a density of impurity charge crystals of good purity, It is based on a method described by Pell (1960) in which he drifted positive carriers. most residual impurity atoms lithium ions into p-type crystals of silicon and germanium In this method a layer of lithium in pure crystals of silicon and germanium being p-type. is deposited on to a face of the crystal maintained at a temperature of about 4OO'C in an After a short time the lithium will have diffused several tenths of a evacuated enclosure. is then millimetre into the crystal, to which an electric field of from 500 to 1000 volts applied, at temperatures ranging from 0°C to lOO'C, for times ranging from several days to The positive potential is applied to the a month, depending on the size of the crystal. lithium-coated face and the negative to the p-type crystal, at locations depending on the crystal shape. through Under the influence of the electric field, lithium ions drift interstitially the crystal lattice forming neutral (zero-charge) loosely-bound chemical complexes with the If one plots lithium the lithium boundary advances. impurity acceptor atoms as concentrations, N,,, against depth of drift, d, as in Fig. 4-7, then at some short distance Complexed acceptor atoms in the lattice behind the interface N,, will be equal to NA. (phonon) excited valence structure, such as calcium, no longer readily accept a thermally electron from a silicon or germanium atom and will therefore have a much lower probability hole in that region of the of contributing to the creation of a free, charge-carrying,
c
Lithium concentration YS depth, d in e p-type crystal, Fig. 4-7 1980). before, end b) after drifting (after Mann et al.,
a)
After the lithium has been drifted through the desired volume of the crystal, the temperature is lowered and the distribution of lithium is allowed to equilibrate by further "self-adjusting" diffusion, without an externally-applied electric field (see Fig. 4-7). In this condition, in any region of the crystal where NLi > NA the resulting positive space charge will tend to move excess lithium ions out of the region, and into regions where Excess lithium ions will be squeezed back into a relatively thin layer on the NL, < NA. face (n+) at which the drifting was initiated, and at the other boundary there will be a residual layer of uncompensated p-type material. With the latter coated with an evaporated layer of gold, both bounding surfaces serve as the electrodes for the compensated region; the linear drift distance, d, can be of the order of about 2 cm. Both the n+ layer and the p layer will contain negative and positive charge carriers, respectively, which between them will cause a small drop of potential acros.s the "intrinsic" or compensated region. Although the lithium compensating atoms are interstitial, they are nevertheless referred to as acceptors and the bounding layer of lithium atoms designated n', denoting a substantial excess of donors. In its use as a detector of ionizing radiation an external source of potential is applied in opposition to the space-charge potential, i.e. a reverse
Radioactivity
816
measurements:
principles
and practice
bias, with the positive pole of the external source connected to the n+ layer and the negative pole to the p layer. In this configuration the lithium-drifted detector acts as a rectifying junction, and no current will flow across the highly resistive compensated electrical breakdown occurs. But, if the external polarity is interchanged, region until free electrons supplied by the n+ layer (in the conduction band) and free holes from the p layer (in the valence band) will flow unimpeded. The mobilities of the electrons and holes pairs in a gas, about the same are, unlike electron-ion order of magnitude. In diamond, silicon and germanium, respectively, at 300 K the mobilities are 1,800, 1,600 and 3,800 cm2 V-' 5-l for electrons, and 1,200, 400 and 1,800 cm' VW' 5-l for holes (Kittel, 1971). At 77 K the electron and hole mobilities for high-purity and compensated germanium are of the order of 4 x lo4 cm' V-' 5-l and lo4 cm' V-' s-l, respectively. However, when an energetic photon deposits energy in the depleted region, producing Compton electrons or a high-energy photoelectron, their energy will be dissipated in further interactions with lattice atoms, creating many free electrons and free holes that will be collected respectively at the anode (n+ layer) and cathode (p layer). The operation of a lithium-compensated germanium, Ge(Li), detector is illustrated in Fig. 4-8 which could equally well represent the functioning of a high-purity germanium detector; nowadays the latter is more generally available and the most frequently used.
n+Layer
p-Layer
i /--lntrmsic
reQion----_ti
Electron~hole Ge-2.96 St-3
1
pairs
&/pair 76
elrlpsir :
Illustration of a p-i-n planar semjconductor detector, showing a typical photon interaction with the detector, and the movement of electrons and holes (after Mann et al., 1980).
Fig. 4-8
4.6.3.4.
The ~-n
iunction
Many ionic crystals with various dopants, both natural and added in carefully controlled melts, exhibit the phenomenon of semiconduction and delayed phosphorescence. In radiation physics germanium and silicon are the best-known detectors, and cadmium telluride that has recently become available is also of interest in that it is relatively dense and can operate at ambient temperatures. Then there are many devices displaying delayed phosphorescence used as thermoluminescent dosimeters (see, for example, P. Braunlich, 1979, and M. Oberdorfer and A. Scharmann, 1981.) In carefully controlled growing of crystals, by adding different dopants to the melt at different stages, or by subsequent diffusion, both n- and p-type crystals of silicon and in a single germanium can be produced and in which n- and p-type regions are present crystal, or even a combination such as a pnpn sequence in a four-layer diode. Two further designations that are used to specify the type of crystal are ?r and u, meaning respectively slightly p and slightly n. Thus a high-purity germanium detector that was still slightly p-type, and which had an nf layer of lithium on one surface and a diffused p-type layer on the other serving as contacts for the external circuit, could be designated as a p-n' junction. Contacts and p- or n-type layers can also be created by bombarding a surface of the crystal with an accelerated beam of positive ions. Typical p-type (acceptor) impurities that can be incorporated into crystals of silicon or germanium are oxygen, phosphorus, calcium, arsenic and antimony. Some n- type (donor) impurities that can be incorporated into these crystals are lithium, boron, aluminum, gallium and indium. Two of the earliest semiconducting devices used to detect and quantify ionizing radiation were the p-n junction and the surface-barrier detector. Both are fundamentally the same as the lithium-drifted detectors, differing primarily in the thickness and nature of the charge-free region which is not compensated but deuleted of charge carriers. To form a p-n junction one can take a thin disc of a highly doped p-type crystal of silicon and germanium and expose one face of it to phosphorus vapor. On heating the crystal wafer phosphorus atoms diffuse into it forming a heavily doped n+ region about 10-3-mm deep. Thin films of aluminum or gold can be evaporated on to both surfaces of the wafer to form so-called ohmic (i.e. non-rectifying) electrical contacts. This is the p-n The contacts might equally well be achieved by lightly junction, or p-n+ in this instance. implanted ions; it is important that whatever material is used should not diffuse into the substance of the material thereby creating a rectifying junction so that the current is no
Radioactivity
longer
mea.surements: principles
the same for a given voltage
applied
in either
and practice
817
direction.
In considering the functioning of a semiconducting crystal it is important to remember that the territory of a free electron created in the n region is the whole crystal. It is also convenient to remember that a donor atom in the lattice constitutes a charge-neutral site with a loosely bound electron which, when excited into the conduction band, leaves a In like manner an acceptor atom is one positively charged site in the lattice structure. that constitutes a charge-neutral site in the lattice that however "needs" an electron. When it binds one loosely to itself it becomes a negatively charged site in the lattice. As phosphorus donor atoms begin to diffuse into the p-type crystal, electrons, populating the conduction band from the donor (n+-type) energy level, will move across the advancing phosphorus interface into the p region and combine with free holes. This in distribution, will populate more acceptor sites in the turn, by virtue of the Boltzmann acceptor energy level with electrons, which sites become negatively charged fixed sites in There is thus established across the nf-p interface a space-charge potential the lattice. donor sites on the n+ side and a corresponding caused b) a surplus of fixed positive surplus of negative acceptor sites on the p side. This condition is illustrated in Figs. 9(e) and 9(f). The space charge thus created across the p-n+ junction opposes the movement of further electrons into the p region or of holes into the n+ region, and thus constitutes a rectifyin such devices as the Zener diode and the field-effect ing diode, that finds expression It also tends to drive electrons back into the n+ region and holes into the p transistor. region and thus creates a region at the junction that is devoid of charge carriers and is called the deuletion repion. If a reverse bias is now applied to the p-n+ junction by means of an external circuit, as shown in Figure 9(g), it will act to reinforce the space-charge field and electrons will be used to combine with more holes in the p region and Some electrons donated to the conduction band by the donor atoms will be removed. The equilibrium will therefore shift to an increase in the numbers of positive donor sites in the n+ region and negative acceptor sites in the p region, and a consequent increase in the depth of the depletion region; i.e. an increase of the volume on either side of the interface that is depleted of charge carriers. In semiconductor parlance, electrons from the n+ layer and holes from the p region will diffuse across the junction to create more negatively charged acceptor sites on the p side of the junction and more positively charged donor sites in the n+ side. The size of the depletion region is thereby increased. The depths of the depletion region can vary from very thin up to about 20 mm depending on the value of the reverse bias. voltage is increased no current will flow until a break-down occurs and the current increases.
As the rapidly
If the polarity of the externally applied voltage is, however, reversed to give a forward bias no current will flow until the externally applied potential exceeds that created by the space charge at the junction. At this point electrons injected into the conduction band from the external circuit will be driven across the junction, and a current This is the basis of the semiconductor diode or transistor. will flow around the circuit. In semiconductor parlance, electrons and holes will be driven into the depletion region, neutralizing the positively ionized donor sites on the n+ side and the negatively ionized acceptor sites on the p side of the junction. 4.6.3.5.
The surface-barrier
detector
This is essentially another form of p-n junction with a very thin entrance window to facilitate the detection of low-energy photons and charged particles. If a wafer of an n-type silicon or germanium crystal is exposed to air for a few days a thin oxide layer is formed. Oxygen is electronegative and therefore an acceptor, so a p-n junction is formed. Contacts to the crystal are established by evaporating a very thin layer of gold on the front oxidized surface and an aluminum layer on to the back. 4.6.3.6
Semiconductor
detector
configurations
DifEerent configurations of Ge(Li) and HPGe cylindrical annular and semi-annular detectors are shown in Fig. 4-9. These various configurations, and their particular advantages are discussed fully in rather NCRP, 1985. The reversed-electrode n-type HPGe configuration shown in Fig. 4-10 has a boron ion-implanted p-type electrode of the order of only 0.3-pm thick. One of its characteristics is also worthy of note, that is its reduced sensitivity to the effect of radiation damage caused by fast neutrons that results principally in the production of hole traps. This is due to the fact that, in such a cylindrical geometry, increments in volume, dV. with radius r from the axis are proportional to rdr. It is therefore clear that more of the substance of the detector is closer to the outside than to the inside. Thus holes moving towards an outer electrode will on average have a shorter distance to go and therefore less chance of being trapped.
Radioactivity
818
measurements:
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and practice
Non-quantitative diagram of a p-n junction; a) depletion Fig. 4-9 in an unbiased junction of 8 acceptors, region; b) distribution, 8 donors, a electrons, and o holes; c) concentration of electrons
and holes; d) concentration of acceptors and donors; e) dipole layer produced by the net charge distribution; f) electrostatic potential distribution corresponding to e); g) distribution of acceptors, donors, electrons and holes in a reverse-biased p-n junction (after Mann
et al.,
1980)
__ n . typ.
F: HPGa
500 pm .+
n-type contact
100-200
mpm
n-typ.
pm COntlCt
b4;:::t K-twe core
-.._---___J
coaxial
HPGa
true co.xI.I
Ge,LI,
Different configurations of cylindrical high-purity germanium and lithium-compensated germanium detectors (after NCRP, 1985).
Fig. 4-10 4.6.3.7.
Other
semiconductor
developments
So far, it has sufficed to discuss the operation of the semi-conducting class of radiation detectors only in terms of crystals of silicon and germanium. It is desirable to keep or operate both types of detector in a cryostat near the temperature of liquid nitrogen. But in many cases, as in space, nuclear medicine or for environmental monitoring it is convenient to have such detectors that can be operated at ambient temperatures. For such operation it is necessary to use a semiconductor that has so large a band gap that negligible numbers of electrons can be thermally excited into the conduction band. To achieve this it is necessary for E, to be greater than about 1.4 eV (NCRP, 1985). Three such substances under development are HgI, (Es = 2.13 eV), CdTe (Es = 1.47 eV) and GaAs (E, = 1.43 eV). For further information and references NCRP, 1985 may be consulted. 4.6.4.
Inorganic-crvstal
scintillators
Activated crystalline sodium iodide, cesium iodide and calcium fluoride are amongst the oldest scintillators in use, with thallium-activated sodium iodide being probably the best known. Pure sodium-iodide crystals scintillate very efficiently at 77 K with very fast response, but their responses at ambient temperatures are greatly diminished. Sodium iodide is very deliquescent and has to be sealed in an aluminium can with a transparent window. Cesium iodide is less deliquescent and is of value because of its higher density, and calcium fluoride is nonhygroscopic. Silver-activated zinc-sulphide crystals were shown by W. Crookes in 1903 to scintillate when bombarded by alpha particles, and they have been used as alpha-particle detectors ever since, usually as thin films on thin plastic discs or glass discs or bell jars (e.g. for the assay of radon and its daughters). But it was not until 1947 and 1948
Radioactivity measurements:
principles
and practice
819
H.Kallmann and P.R.Bell next showed, respectively, that single crystals of naphthat thalene and anthracene could be used as scintillators to detect ionizing radiation. In 1948, R. Hofstadter also found that thallium-activated sodium-iodide crystals scintillated when exposed to ionizing radiation. Furthermore, as the density of sodium iodide was about three times that of anthracene it was better suited to the detection of gamma radiation. Today, thallium-activated sodium iodide is probably the scintillator that is most widely used for photon detector. Pure sodium-iodide crystals are also very efficient photon detectors at 77 K, but are about ten times less efficient at room temperature. Their useful thickness is also limited to about 1.3 cm because they strongly absorb their own fluorescence radiation in a narrow band of wavelength at about 300 nm. The principle of operation of NaI and of NaI(T1) as dissimilar to that of a semiconductor, in that it is presumed scintillators is not wholly that the photon irradiation creates energetic Compton recoil electrons, photo-electrons or electron-positron pairs that in their progress around the crystal suffer inelastic collisions in the crystal lattice thereby raising electrons to the conduction band, leaving The energetic electrons in their progress around the crystal holes in the valence band. can create more electron-hole pairs and also impart energy to the crystal lattice, this In fact, energy being then dissipated as quantised lattice vibrations (phonons) or heat. 90 percent or more of the absorbed energy is emitted in this form rather than as light. The holes left in the valence band can now act as ionizers of luminescence centres, by means of which electrons in the conduction band can deexcite. when they encounter them, with the emission of fluorescent radiation. The introduction of an activator, such as thallium, creates many more luminescent centres in the forbidden region between the valence and conduction bands, thus facilitating This is achieved in practice by the deexcitation of electrons in smaller decrements. adding thallium to the NaI melt, at a concentration of about 0.2 percent of thallium by mass, prior to growing the crystal. The thallium atoms form chloride complexes within the If a series of crystals with crystal lattice and these act as luminescence centres. different concentrations of thallium is examined, it is found that, as the concentration of thallium increases, so does the intensity of the NaI fluorescence (a band centered around 300 run) decrease and that of NaI(T1) (a broad band centred around 430 run) increase. An increase in wavelength of the fluorescence corresponds to differences in energy level between the activator sites (luminescence centres) within the forbidden region between the This fact also explains why NaI(T1) is, unlike NaI, valence and conduction bands. transparent to its own luminescence. Crystals of NaI(T1) emit a wide band of fluorescent Light ranging in wavelength between about 330 run and 550 nm, with a maximum at about 430 nm. The lower wavelength, 330 run corresponds to an energy of about 3.8 eV, and that of 550 run to about 2.3 eV. In this connection, it is useful to remember that the 589-m wavelength of the well-known D lines of sodium, is equivalent to an energy of 2.106 eV. NaI(T1) detectors are available in a wide variety of shapes and sizes, the latter from thin discs 1 or 2 cm in diameter up to cylindrical well detectors 20 cm in diameter There are also cylindrical geometries where the cylinder and 10 cm or more in depth. length is greater than its diameter, and they are available with "pin" wells, or widerWell-type or hollow- cylinder NaI(T1) detectors are diameter wells, or no wells at all. also used for scattered (Compton) photon elimination and for cosmic-ray or environmental background reduction. NaI(T1) crystals can also now be heated and moulded into a variety of shapes and extruded, for example, into long rods for use in airport x-ray security systems (see NCRP, 1985). Within the last ten years two high-atomic-number scintillators have been developed, namely bismuth germanate, Bi,Ge,O,,, often referred to as BGO, and cadmium tungstate, These have about double the density of sodium iodide, and about four times its CdWO,. linear absorption coefficient at 150 keV (see NCRP, 1985, for references). 4.6.5, Electron-multiolier
uhototubes
As gaseous-, liquid- and solid-scintillation detectors came into more and more general use it became necessary to devise a means of converting their extremely weak fluorescent responses into electrical pulses that could be amplified to a level that would permit of the output data being stored, processed and analyzed. Fortunately, two physical phenomena ware available that, when combined, served to provide an answer to the problem. The first was the photoelectric effect that is at least as old as the quantum theory, in association with the names of Planck and Einstein. The second was that of secondary-electron emission. The first of these effects was used to make a photoemissive -? cell more usually known as a photocell, that was described by Elster and GeiteL in 1910. Then in the Late teens of the century, secondary-electron emission was suggested by J. Slepian as a means of amplifying small currents of electrons. Next, in the 1930's multistage electron multipliers were developed commercially, presumably to meet the needs of the "talking movie." These consisted of a semi-transparent photocathode followed by a number of stages of electron-emission multipliers.
Radioactivity
820
measurements:
principles
and practice
and to the present time, the development of the 1940's, late Beginning in electron-multiplier phototubes has been pushed ahead to meet amongst other requirements those of the great variety of scintillation detectors that has been developed. A typical with a NaI(Tl)-crystal detector is ten-stage electron-multiplier phototube, in combination The individual electrodes of the accelerating system are called illustrated in Fig. 4-10. in a "Venetian-blind" configuration, and are also dynodes, and they are often arranged focussing of the secondary electrons electrostatic shaped, in order to give satisfactory from one dynode on to the next. The yields of emitted secondary electrons from a dynode surface are functions of the energies of the incident electrons (i.e. the inter-dynode accelerating voltage) and of the Depending on this nature, between four and six secondary nature of the dynode surface. electrons could be typically emitted for primary electron energies of a few hundred The corresponding gains for a ten-dynode tube would be 4" electron volts (Knoll, 1979). for, say, a single and 61°, i.e. lo6 and 6 x 107. The output pulse from the phototube photoelectron incident upon the first dynode will be sufficiently large for further amplifThe operation and statistics of electron-multiplier phototubes is ication and processing. probability in the case of discussed well by Knoll (1979), and their zero-detection liquid-scintillation counting will be further discussed in Chapter 5. Further details and references are to be found under Secondary emission of electrons, and Photomultiplier tubes in the Encyclopaedic Dictionary of Physics Electron multipliers, that electron-multiplier phototubes in the (Pergamon Press, 1962), which also notes This physically correct term seems to be in general use in "preferred IRE terminology". with the terminology of this the literature of exoelectron physics and is concordant report. 4.6.6.
Channel
electron
multiuliers
Channel electron multipliers (CEM) are similar to electron-multiplier phototubes in electron emission to provide the principle in that they use many stages of secondary They consist, however, of glass or ceramic tubes coated on the inside amplified output. surface with a high-resistance semiconducting layer, along the length of which a suitable difference in voltage is maintained by means of electrodes deposited on each end of the The device is contained and operated in an channel, as shown in Fig. 4-11 (Kurz, 1979). A somewhat similar principle had been suggested by McGee and his evacuated vessel. This consisted of an colleagues in 1960 (see McGee, 1960) for use as an image intensifier. array of metal tubes cut into short lengths, with ends at 55' to the tube axes to give and reassembled to form a matrix of short dynodes. No correct electrostatic focusing, operating results are, however, given.
4
Illustration of the various processes contributing to the Fig. 4-11 _ output from an electron-multiplier phototube by the InteractIon oI gamma-rays from a point source with a NaI(T1) scintillator detect?1 (after Heath,
1964, and Mann
er a1.,1980).
Radioactivity
measurements:
principles
and practice
821
As with the electron-multiplier phototube, the linear CEM can give spurious counts due to positive ions being accelerated in a direction opposite to the electrons and giving rise to secondary-electron emission from the next lower dynode. These positive ions usually arise from ionization of the residual gas between the last dynodes where the number of electrons per pulse is very large. In the case of the phototube the solution is usually to achieve and maintain the lowest possible gas pressure, but in the case of the GEM is to add a fairly large curvature to the channel so that the positive ions strike the walls travelling only a very short distance (see Fig. 4.12, also Kurz, 1979, for references). The CEM is, as its name implies, an electron multiplier, but it can be used to detect both positive ions or photons provided that the incident radiation has sufficient energy to liberate at least one secondary electron as it enters the opening of the CEM (Fig. 4.12). Some CEM have a funnel-shaped opening for improved collection.
mcomlng wmary
/
eiectron
’
--mwlg
wmary
electron
Cutaway views of channel electron multipliers (Cm's); left: Fig. 4-12 straight channel; right: curved channel. These channel multipliers are not yet widely used as detectors of radioactive-decay application in mass spectrometry, instrumentation in products, but find fairly extensive They space, and as detectors of spallation products in high-energy accelerator physics. are therefore probably of no more than academic interest at the present time to a burgeoning regional radioactivity metrological laboratory. 4.7. EERENKOV
RADIATION
DETECTORS
If a charged particle is propagated in a transparent medium, by energetic beta decay or as an energetic Compton recoil, with an initial speed in the medium that is greater than the speed of light in that medium, then it is observed to emit visible radiation in the Many will have range, in the case of its discoverer, Cerenkov radiation (Cerenkov, 1937). observed this bluish radiation surrounding the fuel assembly of a swimming-pool reactor. shock waves that are It is, in fact, produced somewhat analogously to the supersonic As the high-velocity created when a flying object breaks the so-called sound barrier. particle traverses the transparent medium it leaves in its trail a wake of electrically polarized atoms that emit electromagnetic radiation as they depolarize. The refractive index of water, n, is equal to 1.33 at ambient temperatures, so that If a high-energy charged particle the speed of light in water is equal to about 3c/4. traverses water with a speed equal to a fraction p of the speed of light then the tLrenkov radiation can only be emitted as a coherent wavefront in a cone of half angle ti where cos B = l/PI-L. For a particle that has a speed approaching that of light the value of B tends to unity and the angle 0 approaches a maximum value equal to cos-1 (l/n). Conversely, as the angle 0 approaches zero, fl tends to l/n, and c/n represents the threshold speed for the production of Cerenkov radiation in that medium. Eerenkov radiation has rather limited uses in radionuclide metrology but has usually applications in high-energy physics. It is detected by means of and electron-multiplier using liquid-scintillation-counting techniques phototubes, equipment. Colour quenching is a problem common to both methods of detection, but t?erenkov radiation is, from its very nature, not subject to chemical or ionization quenching. Gelsema et al. (1975) have enhanced the efficiency of the Cerenkov effect for the detection thereby of energetic photons by adding high-2 salts, such as sodium iodide to water, increasing the probability of observing high-energy Compton-electron recoils. The Eerenkov radiation produced by high-energy principally in the higher-frequency range of the visible for electrons
having
For further may be consulted
energies
information
between
275 keV and 2 MeV
and references,
Jelley
electrons spectrum, (Ross,
(1958),
in water is emitted between 250 and 600 nm
1970).
Franfois
(1973)
and NCRP,
1985
Radioactivity
a22
measurements:
principles
and practice
4.8. CALORIMETRY To the extent that radiation energy can be absorbed by matter, so can the quantity of radiation be measured in terms of the amount of heat generated in the process. In the case of a radioactive source, this is usually achieved by confining the source within an enclosure that is thick enough to absorb all the radiation (or much of it for relative measurements), and by measuring the rise in temperature of the enclosure as a function of time, or by balancing the rise in temperature against that due to a known source of power (often electrical power) contained in a second similar enclosure, maintained under identical conditions. The enclosure is often called a -1 thermel and its temperature is usually measured by means of thermistors or thermocouples. In the case of the well-known Bunsen ice calorimeter, the temperature is constant and the balancing source of power is provided by the latent heat of melting ice in a given interval of time. There are three broad classes of calorimeter, namely adiabatic with practically no loss of heat to its surroundings and its increase in temperature is measured, isothermal in the equilibrium condition of which the heat loss to the surroundings is equal to that generated by the source, and twin-cur, in the equilibrium condition of which the power generated by the source in one thermel is balanced against a known source of power in a second as-identical-as-possible thermel in similar surroundings as the first. Calorimetry, utilizing both calorimeters and very sensitive microcalorimeters, has been used since 1903 for the measurement of radioactivity. (For references between 1903 In recent years the uses of calorimetry have been largely and 1958, see Mann 1962.) limited to the assay of special nuclear materials such as 241Am and the isotopes of In this application the calorimeter designed by Jordan and Blanke plutonium (ANSI, 1975). (1959; also Jordan, 1967) and the Bunsen ice calorimeter (Ditmars, 1976) have been those of In the last paper, Ditmars describes his use of the Bunsen ice calorimeter to choice. measure the power of two sources comprising mostly z38Pu of nominally 0.23 W and 1.4W. The sensitivity of the Jordan-Blanke calorimeter is such that the magnitude of the half life of 'H, using a 2-kCi source, can be clearly discerned from the recorded power-vs-time graph in a period of from 2 to 4 hours. The preparation of standards of 63Ni was also carried out at the National Bureau of Standards in 1968 using a twin-cup microcalorimeter (Barnes, et al., 1971). Otherwise this method currently finds few applications to radionuclide metrology. For further extensive references NCRP (1985) may be consulted. A very
remarkable
development in cryo-microcalorimetry has recently been achieved by and their colleagues (see Moseley et al., 1984, and McCammon et al., 1985) using etching techniques developed by Downey (1980). Their calorimeter consists of a very small and thin doped silicon wafer (0.5 x 0.5 mm x 80 pm; Moseley et al., 1985) At these temperatures all with an ion-implanted transistor operating at less than 0.3 K. small. carriers are trapped and, by the Debye T3 law, the heat capacity becomes vanishingly Their calorimeter is therefore sensitive to a single "Mn x ray, for which they have obtained photopeaks with resolutions of 35 eV or less.
D.MCC~INIIO~and S.H. Moseley
4.9. COUNTING
RADIOACTIVE
ATOMS
Much more sensitive methods of measuring the activities of radioactive substances have of measuring the numbers of been developed in the last decade, based on the principle radioactive atoms in a sample before they decay instead of counting the numbers of atoms The earlier method was that of accelerator mass suectrometry, and decaying in unit time. the latter, based on the method of selective laser photoionization, is also known as resonance-ionization spectrometry. In the tandem Van de Graaff method (Bennett et al., 1978) negative ions are injected into the accelerator operating at about 10 MV. They pass through an electron-strippng foil in the high-potential electrode, and are accelerated Both before and after the ions through another 10 MV as they return to ground potential. undergo charge-to-mass selection in the manner illustrated in Fig. 4-13, they are finally In the case of 14C dating the sensitivities are identified by range and energy detectors. such that measurements can be carried out with samples of milligrams rather than grams, but The methods of accelerator-mass-spectrometry dating are possibly at some reduced accuracy. such as "Be not, however, limited to 14C, but may be applied to long-lived radionuclides and others produced by by cosmic radiation. Neither of these methods measures activity directly; the former method of high-energy mass spectrometry requires an appropriate standard of activity to calibrate the system, and the latter requires a knowledge of the value of the radioactive decay constant in order to calculate the activity of the sample. However in contrast with the direct method, the sensitivities may be as much as lo3 times greater but their accuracies are not yet as high. 4.9.1.
Accelerator
mass
suectrometrp
This method is based on the use of a cyclotron, or a system of deflecting magnets and Historically, probably filters with a tandem Van de Graaff accelerator as an ion source. the earliest published use of the cyclotron as a mass spectrometer was given in papers by in which they described the separation of 'He from 'He and Alvarez and Cornog (1939), the discovery of tritium using the 60.inch Berkeley cyclotron. The cyclotron itself has a
Radioactivity measurements: principles and practice
023
mass resolution that is considerably greater than that of a mass spectrometer, and the background of unwanted atomic ions with the same charge-to-mass ratio can be reduced by differential linear energy absorption in range filters and particle-identifier detectors. They also operate in the case of 14C to remove the otherwise overwhelming background contributed by residual atmospheric 14N. (Also see Bennett et al., 1968, and Fig . 4-13.)
principle of 14C-atom counting with the tandem-accelerator Fig. 4-13 mass spectrometer. 4.9.2. Selective laser ohotoionization Following the development of lasers operating at a variety of frequencies it became possible to photoionize selected individual atoms of an isotope of a given nuclide by means of a two-step photoionization process. This method of measurement selects any one atomic species from the rest of a sample by excitation of the atoms of choice, using laser radiation of an appropriate frequency, to an intermediate energy level (below the ionization potential), whence it can again by excited by laser radiation into the ionization band. For this second excitation the same laser frequency can be used, when appropriate. Such ions can then be electrostatically accelerated into a detector and counted. The development and applications of this method have been described in an excellent review by V.S. Letokhov and C.B. Moore (1977) entitled "Laser Isotope Separation". This has a wealth of useful technical detail (146 pages and 367 references). In their Preface the authors make the comment that the "laser enrichment of uranium Fromises to be the first major chemical applications of lasers in industry" and this forecast is given considerable substance by reference, later in their review, to the work of Tuccio et al. (1974) and Snavely et al. (1975), at the Lawrence Livermore Laboratory. These last authors subjected a collimated beam of zJsU and 23aU atoms to the radiation of a tunable dye laser that, at a wavelength of 591.54 nm excited the 235U atoms. Simultaneously the beam was irradiated with radiation from a mercury lamp in the wavelength range of 210 to 310 nm, which ionized the excited 235U atoms. These latter were then separated from the beam of neutral atms by a transverse electric field. In the work reported by Snavely et al., a Z35U+-yield rate of 20 mg h-' was obtained. G.S Hurst and his co-workers (1979, 1980) have developed many experimental systems and procedures for the application of this method. In the latter publication (1980), schemes are tabulated for photoionizing all known elements except helium and neon. An interesting and informative review of the development of high-energy mass spectrometry, with many references, has been written by Muller (1979), and some more recent reviews, with references, are contained in Currie (1982). An also interesting, but initially disappointing, attempt has been made by Hutchinson et al. (1987) to apply the method of resonance-ionization spectrometry to environmental samples by measuring trace uranium concentrations in soil. They concluded that, although the concentration of 238U could not be measured by this method, the ratio of 235U/238 U spikes (in about equal parts) could be measured with an accuracy of about 16%. 4.10. OTHER RADIATION DETECTORS More than 600 pages of the total of over more than 800 pages of Knoll (1979) are devoted to radiation detectors and to the subject of detector electronics and pulse processing. Furthermore, Knoll gives references to publications describing investigations carried out with many different kinds of detectors and giving details concerning their operational characteristics. There are also many other available references that describe different types of detectors ranging from solid-state detectors of small size (weighing fractions of a gram and used for in viva intracavitary detection) to the detector system, weighing 2 x lo3 kg, at the European Center for Nuclear Research (CERN), in Geneva, that is designed to detect and identify the particle showers produced by the collisions of very energetic protons and antiprotons. (This latter, with its ancillary equipment, is operated by technicians wearing contruction-workers' hats!)
824
Radioactivity
measurements:
principles
and practice
Very few detectors at either end of this scale will be used for routine radionuclide metrology, but for often very specialized and esoteric applications that are far beyond the limited scope of this Report. But for those who have an interest, academic or otherwise, reference could, for example, be made to England (1976), Kamitsubo et al. (1982) or Barth and Neuhofer (1983). Many further references will be found therein. 4.11.
RADIATION
ENERGY
General
remarks:
4.11.1.
4.11.1.1.
Enerev
SPECTROMETRY Detectors
nroblems
of choice
and the need
for enerev measurements
A rough energy spectrum is often sufficient for the spectroscopic identification of radionuclides and possible impurities. If a more definitive answer is sought, a precise spectrum must be registered and analyzed (spectrometry) by which activities can be measured or compared via peak-area evaluation; decay-scheme parameters may be determined, as well as detection limits or cut-off energies for counting devices. It is advisable to use standard geometries for such measurements, such as 76-mm x 76.mm (3" x 3") NaI(T1) scintillation detectors and sources at 25- or lo-cm distance, or 25-m& Si surface-barrier detectors. The source-detector distance for the latter should be at least 2 cm in order to avoid significant coincidence-summing effects. 4.11.1.2.
Characterization
of spectra
The energy of particles or photons emitted by a radioactive source is distributed in a way more or less characteristic for the source substance. The observed energy spectrum, i.e. the number of particles or photons per unit energy interval as a function of energy, is often modified by the material and geometry of the detector and by the source configuration, depending on the nature and energy of the radiation. As was explained in 72.4, energy continuous, and a distinction is made spectra,
spectra between
may be discrete ("line" spectra) differential spectra n(E) and integrzt
N(E) = s&E E
as functions of E’ (see Fig. 2-S). A single spectral "line" is broadened by the detection process and by interactions in the source itself and becomes a "peak" with a definite width. Peak shapes can often be fitted to normal ("Gaussian") distributions (see Fig. 2-3 and Eq. 3-28) and have their characteristic width (FWHM, FWTM, etc.) at one half or one-tenth of the maximum. The smaller the width, the higher is the resolution. The latter is often expressed by the quotient of FWHM by peak energy. In a photon spectrum the peak positions correspond exactly to the peak energies, provided the peak is symmetrical. However, the tail from another peak or from Compton scattering or "scattered radiation" may render a peak asymmetric, so that the maximum ordinate no longer corresponds to the real peak position. In This applies also, of course, to secondary peaks (escape, etc.), an o-particle spectrum, the peak position does not correspond to the full energy, whereas puse (i.e. free of conversion or Auger electrons) B-ray spectra have no peaks and extend as far as the full disintegration energy. Further peak-to-total, 4.11.1.3.
detectors may characterization of sources and peak-to-valley and peak-to-Compton ratios (see Fig.
Spectral
be expressed by 3-9 and q4.11.5).
the
distortions
The radiations emitted by the atoms of a source undergo a series of interactions on their way to, and inside, the detector by which the shape of the spectrum gets distorted in more or less important ways, depending on the nature and energy of the radiation, the source properties, and the construction of the detector, including its electronic system. its support and any surrounding matter cause absorption (self- and The source itself, foil-absorption) and scattering. Further scattering occurs in the detector material and its envelope. Counting statistics and detector response can be an important cause of distortions: pulses created by particles or photons may add randomly (pile-up) or by coincidence (sum peaks) or secondary radiations and peaks are produced (see 74.11.1.4). 4.11.1.4.
Secondary
radiations
and peaks
All the effects mentioned in y4.11.1.3 are unwanted but often unavoidable. Therefore, they must be recognized as such and taken into account. Bremsstrahlung (bremsen = to brake), originating from the stopping of charged particles, can be regarded as part of the background, and annihilation of positrons yields pairs of photons each of energy equal to 511 keV, and consequent single or double escape peaks. (These occur when one or both of the annihilation photons escape without interacting with the detector forming peaks mOc2 (0.511 MeV) and Zm,,c' (1.02 MeV), respectively, below the photopeak. With positron emitters, annihilation in flight, between source and detector, can cause errors (73.4.3.4) but this is not, of course, a factor in liquid-scintillation counting.) Internal conversion and the photoelectric effect ("external conversion") give rise to electrons and
Radioactivity
measurements:
principles
and practice
Backscattering of Q or 0 particles, x or 7 rays avalanches of x rays and Auger electrons. can modify a spectrum considerably and confuse its interpretation (see Fig. 4-15). Satellite peaks and higher-order effects may have similar consequences.
200
0
BOO
500
400
Fig. 4-14 Characteristic parameters of a spectrum: E,= Energy at maximum count rate, FWHM = Full width at half maximum, FWWl = Full width at one-tenth maximum, Nmax/Nmio = Peak-to-valley ratio, N,,,/NCE = Peakto-compton ratio, Np/Nt = Peak-to-total ratio = photofraction.
0.05 Fig. 4-15 Energy energies, Ey 4.11
.1.5. Instrumental
01
0.2 03
0.5
1
2
of Compton edge and backscatter , of incident radiation.
345 peak for different
considerations
The experimenter will choose the detector and associated electronic system according to the nature and energy range of the radiation to be measured. Low-noise preamplifiers are recommended in many cases and data processing with pulse shaping must be adapted to the detector on the one hand and to further data processing on the other. Complete systems are available commercially but may not be sufficiently flexible for the task at hand. Pulse-shape discrimination can often be used to distinguish between different kinds of radiation, e.g. 1 rays and neutrons. A multichannel analyzer of at least 1,000 channels is almost indispensable for all kinds of spectrometric work, whereas advanced systems such as anticompton and pair spectrometers, magnetic or curved-crystal spectrometers are not really needed in everyday radionuclide metrology. Spectrum stabilizers (based, for example, on electronically maintaining a high-energy peak in the same analyzer channel) are also available. 4.11.2.
AlDha-Darticle
4.11.2.1.
Suitable
sDectra
ener.ev-resuonsive
detectors
and their Drouerties
Many different types of detector, such as the following, can be used for the detection of 01 particles: Pulse-ionization chambers, gas proportional counters with thin windows or internal source, scintillation detectors (liquid scintillation, pure or activated NaI,
a25
Radioactivity
a26
measurements:
principles
and practice
activated CsI and ZnS, and plastic), and semiconductor detectors surface-barrier detectors, and diffused junction diodes).
(Si(Li),
Ge(Li),
HPGe,
Si
However, when a detailed energy spectrum is required, surface-barrier detectors and diffused junction diodes are superior to other types in most respects. We will therefore concentrate the discussion mainly on these two types and on their properties and merits. For further study the following references may be useful: Glover (1984), and Sze (1984). 4.11.2.2.
Silicon
surface-barrier
and ion-imolanted
detectors
The sensitivity of silicon surface-barrier (SiSB) detectors (74.6.3.5) to (I particles is much greater than it is to ,9 particles or 7 rays. Similar thin-layer detectors, both n+ and p', can now also be obtained by ion-implantation of appropriate dopants. Their responses are fully linear and the resolution is excellent (FWHM of 14 to 20 keV are current; 11 keV is obtainable with selected detectors, but usually for only a few months). The energy needed to produce one electron-hole pair is 3.62 eV at room temperature. The pulse height does not vary with count rate, and the pulses have a fast rise time of 10 ns The gold-layer entrance window may be as thin as 10 nm, corresponding to an or less. particles of 5 MeV. energy loss of 10 to 20 keV for a The sensitive volume (depletion Their small size makes them depth) ranges from 2 pm to 5 mm, depending on bias voltage. easy to use, but they are sensitive to light and relatively fragile. Irradiation by 10" (I particles per cm2 is likely to impair the detector irreversibly. Silicon surface-barrier detectors should be used in vacuum (5 10 Pa) in order to The gold surface must not be touched. However, prevent damage by surface-current leakage. Al-coated surface detectors have recently been developed that are not damaged by careful cleaning of the surface. Diffused-junction-diode detectors may be used where ruggedness is essential. The but the depletion region has been obtained in a operation is the same, in principle, different way and the dead layer is thicker. The surface may be wiped and the cost, in general, is less. The background pulse rate of fresh SiSB detectors is very low and negligible in the Therefore, sources of 208~209~210Po,a beginning, but may increase due to contamination. notorious "creeper", should not be measured without a cover foil. The energy range for a-particle spectra extends from 3 to 9 MeV, but mainly from 4.5 to 7 MeV. The pulse heights are in general large compared with electronic noise, the latter being due to "shot noise" from the detector-leakage current and from the preamplifier and amplifier circuits. The numbers of counts per channel in the peak is often several thousand times larger than that in the low-energy tail. Therefore, for detectors are very powerful tools the measurement of surface-barrier a-particle-emitting impurities and isotopic admixtures. Silicon surface-barrier detectors are produced in a large variety of configuration and specifications by many manufacturing companies, whose catalogues should be consulted. 4.11.2.3.
Other
a-uarticle
soectrometers
Such comprise gas proportional counters, scintillation detectors and Frisch-grid Owing to the energy of 28.2 eV necessary for producing an ion pulse-ionization chambers. pair in argon, FWHM values for 5-MeV a particles using proportional counters are about 100 considerably higher than those of about 15 keV that can be obtained with keV, which are With scintillation detectors efficiencies of 5 to 100 % (e.g. surface-barrier detectors. with CsI(T1)) can be obtained. Frisch-grid ionization chambers have an efficiency of up to Sources of a diameter up to 80 mm can be 40% and fairly high resolution (FWHM t 25 keV). The background rate is very low and the detector is easy to decontaminate. used. It is insensitive to j3 and 7 rays and is nearly indestructible. A proportional counting-gas mixture of high-purity Ar/CH, (in the ratio 9 to 1) is normally used, and the chamber must be vacuum tight, so as to be able to evacuate it rapidly to 10e3Pa, before filling. It is claimed to provide a good introduction to practical a-particle spectrometry (Glover, 1984). 4.11.2.4.
Shaoes
of a-uarticle
snectra
Alpha particles from radioactive substances always have sharply defined energy values corresponding to the mass-energy difference between parent and daughter atoms (see q2.4.2. On traversing the electron cloud that surrounds the parent atom, an (II and 2.5.2.). particle loses small amounts of energy which results in a slight broadening of the otherwise nearly infinitely sharp line. However, this natural line width is too small to because of the be observed, even with the highest-performance magnetic spectrometers, unavoidable self-absorption and back scattering. In surface-barrier detectors, additional broadening is produced by statistical incomplete charge collection and variations of energy loss in the phenomena (scattering, Geometrical effects are important and may necessitate a compromise between dead layer). source-detector distance, count rate and solid angle.
Radioactivity measurements: principles and practice
PO-215
6.4
6.6
6.8
7.0
7.2
24
PC.-214
76
7.8
8.0
8.2
8.4
8.6
8.8
Typical alpha-particle spectra measured with a conventional Fig. 4-16 surface-barrier-detector system with an overall FWHM of 12 to 15 keV. Numerical data are given in Table 2-6. Table 4-1 - Recommended energy and intensity values for selected a-particle emitters (see Fig. 4-16)
1, (%)
El2 (kev) 235"
4 599 4 556 4 502 4 414 4 400 4 365 4 344 4 325 4 218
(1) (2) (1) (2)
5.0 4.2 1.7 2.1 55 17 1.5 4.4 5.7
234u
4 774.8 4 722.6 4 603
(9) (9) (2)
72.3 27.4 0.3
239PU
5 156.70 5 143.9 5 105.1
(14) (8) (8)
73.3 15.1 11.5
222RKl
5 489.52
(30)
99.92
244Clll
5 804.82 5 762.70
5) 5)
76.4 23.6
252Cf
6 118.1 6 075.7
5) 5)
84.5 15.5
21bPo
6 778.3
( 5)
=lOO
215P0
7 368.2
(8)
=lOO
214Po
7 686.90
(6)
=lOO
213Po
8 376.3
(26)
=lOO
212P0
8 784.92
(12)
=lOO
(2) (2) (2) (4)
027
Radioactivity measurements: principles and practice
a28
A few typical spectra obtained with silicon surface-barrier detectors are show" in The corresponding energy and abundance values are presented in Table 4-1, in Fig. 4-16. Most spectra are complex and, for emitters with eve" the order of increasing energy. neutron and proton numbers, the line "intensities" decrease rapidly with decreasing energy. For even-odd or odd-even nuclides, this is not ordinarily the case, and the highest-energy It should also be noted that the particles often have very low emission probabilities. peaks stemming from the same nuclide have all the same shape. The thinner the source the However, there is always a more or less pronounced more "Gaussian" are the peak shapes. This is important in low-energy tail for which a hyperbola may be a good approximation. analysing complex u-particle spectra of isotopic mixtures. 4.11.2.5. Calibration enereies Direct a-particle-energy measurements are reserved to specialized laboratories and high-precision equipment, and have been carried out for nearly 30 different a-particle The large majority of energy values have been measured with respect to these emitters. high-precision standards which thus constitute the basis of a consistent system of recommended values (Rytz, 1979). Some of those are reproduced in Table 4-2. Table 4-2 Calibration energies for a-particles (in keV)
DECAY CHAINS
SINGLE EMITTERS 3 182.71 4 013 3 954
(3)" (3) (8)
238"
4 197 4 150
(5) (5)
235"
4 4 4 4
599 400 374 368
(2) (2) (4) (3)
4 687.7 4 621.2
(15) (15)
234U
4 774.8 4 722.6
(9) (9)
231P,
5 5 5 4
(1) (1) (I) (1)
230Th
239Pu
059 028 014 952
5 156.70 (14) 5 143.9 (2) 5 105.1 (2)
2IOPo
5 304.38
24IAlll
5 485.60 (12) 5 442.90 (13)
238PlJ
5 499.07 (20) 5 456.3 (2) 5 721.00
(8) (10)
244Clll
5 804.82 5 762.70
(5) (5)
*42cm
6 112.77 6 069.42
(8) (12)
253E*
6 632.57 6 591.4
236PLl
5 767.66
(7)
228Th
5 423.20 5 340.31
(22) (15)
224R,
5 685.42 5 448.7
(15) (12)
212Bi
6 089.94 6 050.83
(4) (4)
2%OR"
6 288.13
(10)
216Po
6 778.3
(5)
212Po
8 785.08
(12)
227Th
6 038.06 5 977.71 5 756.96
(15) (10) (IO)
223R,
5 5 5 5
(4) (29) (30) (9)
211Bi
6 622.9 6 278.8
(6) (6)
21gR"
6 819.1 6 553.0 6 424.7
(3) (3) (3)
215Po
7 386.2
(8)
226~3
4 784.38 4 601.7
(25) (2)
22%"
5 489.52
(30)
218Po
6 002.40
(9)
214Po
7 686.90
(6)
(5) (5)
Data taken from Rytz (1979)
*Uncertainty
in units of last digit(s)
747.2 716.16 607.34 539.8
Radioactivity measurements: principles and practice
4.11.3. Beta-Darticle and
eleCtrOn
829
SDeCtra
4.11.3.1. Suitable detectors and their main orooerties Electron energies can be measured by means of gas proportional counters (operated over a wide range of suitable pressures), scintillation detectors (inorganic, organic, plastic or liquid scintillators) or by semiconductor detectors (Li-drifted Si and Ge, HPGe, or surface-barrier detectors, and many others). In gas proportional counters about 30 eV (35 eV in CH,) is needed to produce one ion pair. The detector must be larger than the path length. Such counters of 30.cm diameter have been used successfully for measuring spectra of conversion electrons (see NCRP, 1985). 4a gas proportional counters operated at pressures of up to =7 MPa (70 atm) have also been used for the same purpose (see A.P. Baerg HN, 1973, p. 95; J. Legrand et al., HN. 1973, p. 101). Lithium-compensated silicon detectors are preferred for electron spectrometry and have They have a calculable been well investigated for energies between 0.015 and 5 MeV. response and a good resolution if the thickness is greater than the maximum penetration At 300 K, the distance. The low atomic number of silicon favours low backscattering. energy needed to produce one electron-hole pair is 3.6 eV. Si(Li) detectors are generally used at liquid-nitrogen temperature, but they do not seem to deteriorate when it is necessary to let them warm up to room temperature, from time to time. Ahmad and Wagner (1974) report I!WHM values of 0.88, 1.06, 1.50 keV for electron energies of 115, 194. 624 keV, respectively. The dead layer was 0.6-pm thick, corresponding to an energy loss of about 20 keV. 4.11.3.2. Shaoes of B-oarticle and electron soectra Beta-particle energy spectra are continuous, and extend from zero to the maximum A spectrum with superimposed lines from conversion electenergy E,,, (see also 12.4.3). rons and subsequent Auger electrons is represented in Fig. 2-7. Such spectra can in principle be used for activity comparisons, but it is important to account for the various disturbing effects, among which scattering and self-absorption are prevalent, especially at 1OW energy. As scattering and backscattering increase with atomic number, silicon detectors are superior to germanium detectors. A spectrum may be further disturbed by electromagnetic radiations and secondary effects. 4.11.3.3. Some imoortant calibration enereies There are not many suitable calibration standards for monoenergetic examples are given in Table 4-3.
electrons.
Table 4-3 - Calibration energies for electrons
Source 1251
55Fe
keV 3.7 4.9 to 5.2 5.7 to 5.9 6.3 to 6.5
Intensity, percent of source decays
Radiation
79.3
Ce-K
48.5 11.0 0.9
Auger-K
133Ba
17.2
10.6
ce-K
125I
21.8 to 23.0 25.8 to 27.4 29.8 to 31.7 30.5 to 31.2
13.1 6.0 0.8 10.7
Auger-K
ce-L
133Ba
45.0
45.2
ce-K
131I
45.6
3.5
ce-K
'99Al.l
125.1
5.5
Ca-K
'03Hg
193.6
13.5
Ce-K
lJlI
329.9
1.5
ce-K
207Bi
481.7
1.6
ce-K
13'CS
624.1
8.1
ce-K
Data taken from NCRP (1985) and Lagoutine et al. (1975)
Some
Radioactivity
830
4.11.4.
Snectra
4.11.4.1.
of electromagnetic
Suitable
detectors
measurements:
principles
and practice
radiation
and their urouerties
For photon spectrometry, detectors made from high-2 material are essential in order to obtain the greatest possible absorption of energy within the detector. This explains why the thallium-activated NaI crystal is by far the most frequently used detector for photon spectrometry above about 50 keV. But for high resolution semiconductor detectors must be used. (For higher resolutions, semiconductor detectors are used.) 4.11.4.2.
Thallium-activated
sodium-iodide
detector
The relatively high atomic number (2=53) of iodine ensures high photoelectric absorption, high photo-fraction (ratio of the photopeak area to that of the whole spectrum) and high detection efficiency. Response functions have been calculated for many different photon energies and crystal dimensions. These theoretical spectra reproduce many features of the experimental curves, except for low energies. The detailed study of a response curve gives a deep insight into the various phenomena of photon interactions with the detector material, and helps to determine the most favourable conditions as to the choice of detector dimensions and measuring geometry. The almost exclusive aim of photon spectrometry is the measurement of the photopeak area for each single line of a spectrum. The precision with which this can be accomplished depends on the energy resolution, defined as R = AE,/E,, where E, is the -/-ray energy and AE, is the full-width at half-maximum (FWHM) value of the number-of-events peak (see Fig. 4-14). For any specific detector, the resolution as a function of photon energy is given by
h (a+bE,) RZ-----
(4-5)
E, where E, is the photon energy, and a and b are constants that can be measured experimentally for every specific detector assembly. The intrinsic resolution of a scintillation crystal is of the order of 1 to 2%, for excellent light-reflection conditions. Because a scintillation crystal is always used multiplier phototube (see Fig.4-11), loss of resolution l l l l l
in combination with an depends on the following
electronfactors:
the statistics of photoelectron collection (in the phototube); the electronic noise (almost negligible); the sensitivity variation over the active detector volume; gain fluctuations in the phototube; drifts.
By convention, the resolution is often expressed with respect to the 662-keV 7 rays from the decay of 13'Cs, For NaI(T1) of 76.2-mm diameter and height (3" x 3"), resolutions of between 6 and 7% may be considered very satisfactory. For 7 rays from the decay of a'Co (E, = 122 keV) current values are 10 to 11%. The quality of commercial NaI(T1) crystals is such that very reproducible efficiencies are obtained for specified geometries. The most frequently used configurations are the right cylinder with height equal to diameter, and the right cylinder with a reentrant cylindrical well. The latter is especially useful for the measurement of weak sources because of the large solid angle and the low dependence on source position inside the well. Efficiencies, so-called total and absolute, as well as intrinsic and peak-to-total, have been measured with high precision and presented in spectra, graphs and tables by various authors (also see 7 5.2.1.5). Good definitions of the first three of these four qualifiers of "efficiency" can be found in Knoll (1979). Background may be important, mainly in low-level activity measurements. External causes are cosmic radiation (that is normally dominant without shielding) and ambient l-ray sources. The remainder is due to photons from contamination and interactions in structural and shielding material. Besides cosmic rays the mo.st important sources of background radiation are 4oK (mainly in the phototube envelope), '*'Rn (in the air) and various contaminants of the shielding material. However, 5 cm of lead lined with 1 mm of Cd sheet (to absorb the K-shell photoelectrons from lead) is an adequate shield for many applications. In the event that a new laboratory is being built to house the counting equipment, particular attention should be paid to checking the aggregate of the concrete that is to be used in the foundations, walls and floors of the structure. This is of utmost importance when the laboratory is to be used for low-level mea.surements and environmental monitoring for radioactivity. When NBS moved to a new site just over 20 years ago, aggregates tested were found to have an appreciable range of activity, After the move the backrounds of solid-state detectors in the basement laboratory at the new site were found to be about half of what they had been in the basement laboratory at the old site probably largely due to the choice of a very inactive aggregate for the concrete used.
Radioactivity
measurements:
principles
Nowadays scintillation crystals are almost with phototubes. Further needed components are: l l l l l l
always
a stable dc power supply of 1 to 3 kV; a preamplifier mounted closely to the phototube; a linear amplifier; a single-channel analyzer or better multichannel a scaler-timer. optional: pile-up rejector; spectrum stabilizer;
Available consulting 4.11.4.3
and practice
purchased
The detectors lithium-compensated
detectors
and shapes
integral
analyzer
(at least
recorder
and xy plotter.
forms and sizes of crystals, and their prices, may manufacturers' brochures, announcements and catalogues. Semiconductor
as
831
of eamma-rav
best
assemblies
1000 channels);
be
determined
by
suectra
most frequently used for photon spectrometry silicon (2=14), germanium (2=32) and high-purity
are fabricated from germanium crystals.
Si(Li) detectors have photoelectric cross sections lower than those of NaI by a factor of about 50, but that is still sufficient for the detection of low-energy or x rays (LEPS, Such thicknesses of a few millimeter* are sufficient. low-energy-photon spectrometry); detectors give less prominent x-ray-escape peaks and smaller leakage current thdn Ge detectors. Cooling can be interrupted by warming-up cycles to room temperature, with no Below 55 keV the photoelectric process is more deterioration of detector performance. is complete (see probable than the Compton effect; below about 30 keV, charge collection Peaks due to x-ray Fig. 5-6) and produces single full-energy peaks of Gaussian shape. escape occur 1.8 keV below the photopeak, whereas in germanium they would be much larger and occur 11 keV below the photopeak. Above 3 MeV, pair production is not so overwhelming Dead layers in silicon as in germanium and the detection efficiency is normally adequate. are of the order of 150 nm. They are Ge(Li) and HPGe detectors are mostly used at medium energies (2 100 keV). commercially available in many different forms and useful sizes up to 100 cm3, and more. At low energies the peak width is dominated by electronic noise, to an extent depending on as a result of bias voltage. Therefore, small detectors are somedetector capacitance, times preferable. At an energy of 5.9 keV (55Fe x rays) resolutions (FWHM) of 150 to 250 eV are possible; typical best values at 122 keV and at 662 keV are, respectively, 400 to 500 eV and over 1 keV. The entrance window is about 400-1~~ thick. the resolution of a semiconductor It is very important to note that, bv convention, detector is given as AE, (the FWHM) at a specified energy E,. If it is assumed that the photopeak approximates a normal ("Gaussian") distribution, in which case AE, would be approximately equal to 2.350, i.e. extending above and below the mean, E,, by approximately 1.17717 (see Fig. 2-3 and Mann et al., 1980). Also,
if Ep is
the average
energy
AE, = 2.35
(E,E,)'
If the Fano factor is also taken becomes (Mann et al., 1980; NCRP, AE, = 2.35
required
to produce
one electron-hole
.
into account, 1985)
X- and ?-ray
the resolution
of a semiconductor
(FETE,)'
calibration
then
(4-b) detector
(4-7)
Examples of the shapes of y-ray spectra are given in Fig. 2-11 for a %o Fig. 4-17 for an lg21r source, each with NaI(Tl)and Ge(Li) detectors. 4.11.4.4
pair,
source,
and
in
energies
Recommended energy values for the calibration of photon detectors have been published by Helmer and van Assche (1979); also see Appendix 10 of Lederer and Shirley (1978). A 182 of NCRP (1985). comprehensive table of such energy values may be found on page 4.11.5.
Ouantitative
4.11.5.1
Aims,
spectral
possible
analysis
Drocedures
and problems
involved
Pulse-height equipment can reveal a large amount of spectra taken with modern information not only about the incident radiation but also about the performance of the detector. The aims of quantitative analysis of nuclear spectra are: l l l l
identification of the radionuclides in the source; activity measurements and impurity assays (with uncertainties); efficiency determination and estimate of detection limits; establishment of detailed efficiency functions.
Information-extraction required. They vary also
procedures depend on spectral quality and on the accuracy according to the radiation source, the radiation nature and the
Radioactivity
832
measurements:
principles
and practice
Fig. 4-17 Main part of the 19*Ir spectrum taken with a 76 x 76 mm NaI(T1) detector (WHM -8% at 1.33 MeV) and with a 50 cm3 coaxial Ge(Li) detector (FWIM ~0.15% at 1.33 MeV); numerical data from Heath (1964) and Heath (1974). detector type. It is not possible to discuss here the various procedures in detail, and we shall confine ourselves to just one kind of radiation (photons) and one type of detector (germanium detectors: Ge(Li) or HPGe). Single-channel analyzers (see Fig. 6-20) for differential counting are now almost completely superseded by highly sophisticated multichannel analyzers. The high stability of these very versatile instruments allows one to store very reliable pulse-height spectra directly on to magnetic tape or computer discs. Peak-area integration, a most important task, can be performed manually, for simple problems, or by computer, but the fullest analytical advantages of -(-ray spectrometry can only be achieved by means of elaborate computer programs. Many different programs have been developed and published which provide a completely automatic and detailed analysis of the identified nuclides and their with graphical and numerical print-out of a list Such an extensive treatment includes, of course, smoothing of activities or abundances. of background, peak search and identification, peak-shape analysis the data, subtraction and fitting, and peak integration for intensity calculation (also see g5.2.2.5). In can be evaluated and disturbing effects, such as sum coincidence or addition, uncertainties pile-up, can be taken into account (also see 75.2.4.3). 4.11.5.2
SiniDle peak
integration
methods
(manual or Commuter-aided)
The measurement of a differential pulse-height spectrum (dN/dH vs. H) involves the determination of AN/AH as a function of the pulse height AH, whereANis the whole number of pulses observed in a small but finite pulse-height interval AH, usually a whole-number channel width (but converted to energy by an energy/pulse-height scale calibration factor). in a spectrum with peaks of mean pulse height &,, if one It is, in general, convenient full-width at half-maximum height of a peak could occupy about 3 to 4 channels, and seldom Defining the detector resolution by R = FWHM/%, then, for R = 0.4% (i.e. more than 5. AE,'E = 4/100), the total number of channels to be provided for recording the full range of Similarly, assuming a quite realistic FWHM of pulse amplitude up to E, is 4/R, or 1000. On the other hand, 1.5 keV at 3 MeV, the multichannel analyzer should have 8000 channels. the total number of channels to be used also depends on the total number of counts that can be collected in a reasonable time. A simple example of the use of gamma-ray spectrometry is the measurement of the unknown activity of a source, A_, of a given radionuclide relative to the activity, Ak, of a standardized source of the same radionuclide by comparing the numbers of detected events, This can be done by adding up N, and N,., under the full-energy peaks (photopeaks) of each. channel contained within the limits of the "known" and the contents of every analyzer The background to be subtracted from the sum of events in the photopeak "unknown" peaks. channels is often obtained by taking the average content of the channels on either side of the pulse-height distribution that is estimated to represent the upper and lower limits of The activity of the unknown source is then given by %= A,N,/N,. A the photopeak.
Radioactivity
measurements:
principles
and practice
833
satisfying application of this technique was by Christmas and Cross (1983) in calibrating a relative to the U.K. sealed within a platinum-iridium needle, new radium standard, Hanischmid radium standard, using the 15%.abundant '14Bi 1.7645-MeV gamma ray in the decay chain of z26Ra. As all the radionuclides between "'Ra and 'lLBi are relatively short50-year difference in the dates of sealing of the two 226Ra lived, the approximately sources is immaterial and the high energy of the gamma ray reduces the significance of differences in attenuation or self-absorption by the source containers. For an ideal NaI(T1) crystal, the distribution to normal and can be written as
function
of the frequency
density
is close
N
P(x) = 4 (2x0)
exp
(-(x-x,)z/20z),
(4-S)
where x is the pulse height (proportional to the channel number, or energy of the detected standard deviation, and photon), x, is the pulse height of the photopeak maximum, o is the For a normal distribution the N is the number of pulses recorded in the photopeak maximum. full-width at half-maximum (FWHM) would correspond to the interval between x,-2.3550 and x,+2.3550, and the interval from x,-30 to x,+30 (= 1.3 FWHM) would contain 99.7% of the number of counts recorded in the photopeak; so that less than 0.3% lie beyond f30 from the In the foregoing discussion it photopeak and it has fallen practically to the background. has been assumed that the distribution of the frequency distribution is close to normal, but in practice the number of recorded events is finite and use of the estimated standard deviation s, would be more appropriate than 0. to a peak But, as a general rule, the interval corresponding may be of k+l channels above and below the peak channel, where k is the channel The total number of channels occupied by a recorded spectrum 1.3 FWHM. depends, of course, energy interval corresponding to a single channel) pulse amplification (also see 75.2.2.5). The simple facilitated with Inclusion used. also increase the 4.11.5.3
Computer
defined as that corresponding to (and thereby the on the selected
procedure for peak analysis just described can be accelerated and the aid of a small computer, whereby non-integer channel numbers may be of automatic smoothing and peak searching may not only save much time but consistency of the results. procedures
sophisticated computer programs have been developed and described (e.g. in Many Canberra, 1981; and by Helmer and McCullagh, 1983) by which a fully automated and complete Within the scope of this report it is spectral analysis can be performed (see 75.2.2.5). possible only to cover general principles, and not to keep up with the spectacular and To keep abreast with these the reader rapid developments in nucleonic instrumentation. should consult the literature, especially the very informative technical brochures that are available from the manufacturers. In these days of integrated microcircuitry, it is almost always easier to purchase a desired function than to create it from separate components. If one predicates that gamma-ray photopeaks follow a normal (i.e. "Gaussian" probability distribution P(x), with (for linear pulse-energy output) an underlying linear background, then a peak may be represented by the function N(x) = P(x) + Cx + B, where C and B are constants. But, instead of this theoretical and continuous function of the channel number x, the observations always comprise only the discrete and integral experimental values of counts in adjacent channels of equal energy increments, AE. Moreover, these values are subject to statistical fluctuations. Therefore, the existence, position and content of a peak can be determined only within certain limits of uncertainty that must also be evaluated. The following very abbreviated description of a detailed program given as an example of how the complete analysis of a pulse-height achieved: A.
Location
of peaks
(Canberra, spectrum
1981) is might be
of interest:
(a) (b) (c) (d)
Read experimental spectrum; Smoothing of the data read; Establish weighted first-difference spectrum; Search for possible peaks: zero crossings of (c) with negative slope, define regions where data increase above background in a statistically significant way; (e) Establish unsmoothed third-difference spectrum; (f) Peak-by-peak search for multiple peaks: zero crossings of (e) with positive slope and limits defined in (d); B.
Calculation deviation;
C.
Fitting of theoretical parameter uncertainties,
of peak
areas,
background
subtraction,
standard
peak shapes by non-linear evaluation of multiplet peak
least areas;
squares,
estimates
of
Radioactivity measurements: principles and practice
834
D.
Lower limit of detection, test whether a peak has a high enough probability to be "real";
E.
Detector calibration, using standard sources; (a) energy calibration and establishment of a relation of energy vs. channel number; (b) efficiency calibration;
F.
Peak identification by comparison with library data;
G.
Plotting and listing of identified radionuclides, output: energies, activities and uncertainties.
with their photopeak
5.
METHODS OF RADIOACTIVITY MEASUREMENT
5.1. INTRODUCTION 5.1.1. General The full description of a radioactive decay process would comprise all parameters of the initial state of the parent atom, the final state of the daughter atom, and the types Thus the metrology of radioand energies of all radiations in the process of decay. nuclides implies, in its broadest sense, a knowledge of the mass, charge, energy, magnetic dipole moment, electric quadrupole moment, half Life, spin and parity of the parent and daughter nuclei, and mass, charge, energy, intensity, spin, parity, polarisation, angular distribution, direction, and momentum of the emitted radiations. Many compilations of A narrower nuclear-decay data supply the latest known values of these paramaters. description of radionuclide metrology is restricted to measurements of activity (events par unit time) or radiation-emission probabilities. Radioactivity is usually measured in terms of the radiations that are emitted during Thus activity can the nuclear transition itself; but it can also be measured indirectly. This be derived from the mass, or number, of parent atoms if the half life is known. latter method has recently been used successfully in the method of accelerator mass spectrometry (74.9.1). Also, the activity of a parent can be derived from the numbers of daughter atoms (e.g. numbers of recoils produced in unit time). In this chapter the most frequently used methods, which are all based on electrical-pulse counting of the emitted radiations, are discussed in some detail, while the less frequently used special methods Some other methods that are less directly applicable to measureare treated only briefly. ments of activity in regional laboratories have also been mentioned in earlier chapters, and references made to appropriate texts where further information may be obtained (e.g. calorimetric and chemical dosimetry in 82.6, exe-electron and thermoluminescent dosimetry in 84.6.2.2, and resonant-ionization spectrometry, accelerator mass spectrometry and microcalorimetry in (1q4.8, 4.9 and 4.10. Other methods of detection based on excitation are the counting of tracks in photographic emulsions and autoradiography (Rogers, 1980); solid1975) and stimulated electrical discharges state track detectors (SSTD's; Fleischer et al., in spark and streamer chambers (Allkofer, 1971). The various measuring methods can be grouped into classes according to (i) the kind of radiation to be measured, (ii) the type of detector used (based on the physical principles involved, and (iii), the mode of measurement employed, such as pulse counting or current-reading, peak-area computation, single-channel or concidence counting (direct or by direct ("absolute") or relative (indirect) measurements, extrapolation techniques), source-detector geometry (external or internal source, lO", medium, 2s or 4n effective solid angle), physical state of source and detector (gaseous, liquid, solid; thin source or thick source), energy sensitivity, or position sensitivity. The physical principles involved and the many ways that they have been applied to radionuclide metrology are of basic importance; the principles have been discussed in some detail in chapter 4, and specific applications will be in the following sections. Many historical references to the early development of radiation detectors have been given by Spernol (HN., 1973). 5.1.2. Tvnes of radioactivitv measurement 5.1.2.1. Dieital. analoaue. peak counting. extrauolation The mostly used mode of measurement is single-channel (electrical) pulse counting (see The primary effect caused by the emitted radiation can also be integrated and Ch. 6). If the detector is energy sensitive and its measured as analog signal, e.g. a current. output signal proportional to the input, the number of counts in an energy interval, e.g. Further, measurements can be repeated under different under a peak, can thus be measured. The best mode of a conditions and the results extrapolated, e.g. to 100% efficiency. measurement is defined by many parameters and depends on the details of the methods used, as is discussed in the following sections. 5.1.2.2. Number of channels: coincidence and anticoincidence methods In single-channel measurements, electrical pulses induced in a single detector are counted in a single chain ("channel") of electronic instruments. But for certain purposes, two- or more-channel methods can be used with special advantage. Here, in general, two or more radiations and their coincidences are counted. These methods are restricted to nuclides that decay with the emission of two or more radiations and they need detectors that are each sensitive to one radiation only. These methods belong to the most accurate ones for the measurement of decay rates. This is due to the cancellation (in a first
835
Radioactivity
836
approxunation)
of the detector
measurements:
efficiences,
principles
and practice
c1 and Lo, in the coincidence
equations:
N, = N,N,/N,
= (~1N,)(~,N,)/(~1~2N,)
(5-l)
The coincidence method can not only be used for very accurate decay-rate measurements, but is also especially suited and powerful for the measuring of decay-branch probabilities or "intensities". If two radiations from a branch "a" of "intensity" (i.e. probability of emission), P,, can be measured separately and in coincidence, and N, (the activity of the nuclide itself) is known,then the value of P, can be computed from the classical coincidence equations, i.e.
Pa = NI,.Nz,./N,,.N~ where
(5-2)
9
N, 8 = P,al,,N,, N, a = Pa~z .N, and N, ci= P,e, acZ,.N,
Coincidence measurements can be extended to still more selective multiple-coincidence and anticoincidence methods. The latter have the additional advantage of the absence of any dead-time problems, but yield in general the same information as coincidence methods (see 75.5). Also, a comparison of single, double and multiple coincidence results can be used for the calculation of decay rates or branching ratios. 5.1.2.3.
Direct
("absolute")
and relative
(indirect)
methods
The great majority of applied radioactivity measurements are performed by comparison with a well-known standard. Such relative methods should be used wherever possible, because they are, in general, made much more easily, and cheaply, than direct measurements. They might even, be under certain conditions, more accurate than direct measurements. For example, the measurement of an 55Fe sample relative to standards of 54Mn and 51Cr is normally much more accurate than a direct measurement of 55Fe (see also 83.4.1). But finally all radioactivity measurements are based on some very accurate "absolute" or direct measurements. 5.1.2.4.
Use of statistical
laws
Pulse-mode counting, i.e. the measurement of the number of decays, within a certain time interval, is, statistically speaking, the simplest grouped-data-counting method. But other methods, some based on statistical laws and principles can be used to measure radioactivity. Such methods include Campbelling (Oda et al., 1976), multiscaling and correlation counting (Williams, Lewis and Smith, HN, 1973; NCRP. 1985, 73.2.4) selective sampling (SESAM; Miiller, 1981), module-Z counting (Mylon et al., 1983), time-of-event counting, and zero-probability counting. 5.1.2.5.
Suecial
auulications
Radioactivity-measuring methods are applied in quite different ways in as far-different fields as medicine and safeguards or mining and cosmology, etc. They are highly adapted to the individual problems and often extremely specialized, from protoninduced x-ray emission (PIXE) to extended x-ray absorption fine structure (EXAFS), and from wiping tests to flow-through methods, etc. These many special applications cannot be treated here. Thus, only the general principles and procedures of radionuclide metrology will be discussed. 5.1.2.6.
Most
freauentlv
used methods
While there are hundreds of special applications of different radioactivity-measuring methods, only a few of them are used frequently. These are the relatively simple and relatively accurate defined-solid-angle methods using modern solid-state detectors (NaI(Tl), Ge and Si(Li)). They are not only used for counting but also for identification of the nuclides emitting the detected radiations, These methods can be subdivided into relative methods for strongly scattered and weakly absorbed radiations (gamma rays of energies higher than about a few tens of keV) and direct methods for strongly absorbed and weakly scatterd radiations (mainly low-energy alpha-particles and electromagnetic radiation, but also electrons and fission fragments). The accuracy of the defined solidangle counting method in many cases is, however, limited by the accuracy with which the geometrical efficiency can be measured. For direct measurements, 4a methods, in which all the radiations from the source are emitted into the whole solid angle of 47r sr and counted techniques (T5.5), such as 4np-1 counting with efficiency extrapol(ll5.4), or coincidence ation, have been developed to a point where, in general, they are the methods of choice to results with low estimated uncertainties. But these methods when appropriately applied have been developed to give great accuracy, today of the order of 0.1 to 0.5%, and are in frequent use in national and international standardizing laboratories. Given an accurate direct standard of a suitably energetic gamma-ray-emitting nuclide, relative standards of low uncertainty can best be produced by means of a well-calibrated high-pressure ionization chamber, that can in optimum conditions give measuring reproducibility of the order of 0.1% or less.
Radioactivity
5.1.2.7.
Choosine
an optimum
measurements:
principles
and practice
837
method
If a certain radioactivity measurement has to be performed, several methods are often available, and a choice of the "best" method has to be made. Many parameters define what is "best", the most important ones being the desired accuracy which depends on the type of the decay and of the emitted radiation, simplicity, and price. It should be emphasized that, in cases where a good national or laboratory standard is available, relative methods of measurement are to be preferred. Optimum methods of calibration for some of the most frequently used radionuclides are indicated in Table 2-5. "Accuracy" figures given in Table 2-5 should be regarded as only rough estimates for "average" measuring conditions for various direct calibrations in column 1 and mostly relative measurements in column 2. The actual experimental conditions may vary considerably, and so too the attainable accuracies. For the establishment of a highly reliable system of radioactivity standards, that is traceable to national or international reference standards (see 72.2.3), and of reliable nuclear-decay data, it is necessary to make extremely accurate measuremeits. It is also important that these should be made using any available different and independent methods in order to reduce the probability of the presence of hidden systematic biasses (De Roost et al., 1972; Christmas et al., 1983). 5.1.2.8.
Characterization
of individual
methods
As radioactivity-measuring methods can be very different, an attempt has been made in 7q5.2 and 5.5 to describe them according to a common scheme. First the principle used (i.e. the physical effect measured and its mode of measurement) is described, with, if possible, an analytical description of the measurement (including geometry) and the radiations and nuclides that can advantageously be measured by that method. All methods are essentially determined by the detectors used and the experimental procedures applied. Therefore the detectors, source preparations, counting procedures and instrumentation used are then briefly described. and in most cases, the evaluation Finally, of the results corrections that must be applied and the attainable accuracy. 5.2.
RELATIVE LOW- AND MEDIUM-GEOMETRY SPECTROMETRY
5.2.1.
DEFINED
SOLID-ANGLE
is
COUNTING.
discussed,
including
INCLUDING
Introduction
5.2.1.1.
Princioles
Many radioactivity measurements are performed by low- or medium-geometry solid-angle counting, the simplest radioactivity measuring method. This method is characterized by the solid angle subtended at the source by the detector or by a diaphragm in front of it (Fig, 3--7). Only the radiation emitted from the source into this "effective" solid angle, n,,,, can be counted, neglecting scattering. The ratio of the whole solid angle (4n sr) to the effective solid angle, which can be very close to 1 (Fig. 5-l), is usually named the geometry factor, G (Eq. 3-6). The measured count rate must be multiplied by G and by the number of particles emitted per decay, in order to obtain the source activity, provided that the radiations are isotropic The geometry factor can be calculated for every source-detector geometry, but this can sometimes be tedious. Therefore, in practice, attempts are frequently made to approximate to the simplest case, namely a point source radiating isotropically a part of which radiation is incident normally upon a flat-surfaced detector masked by a circular diaphragm of diameter 22, at a distance a from the source (Fig. 3-7). In this case the geometry factor G is derived from the following simple formula G = 4n/n,,,
= 4n/[2n(l = 2/{1
so
that
- cos B,,,)]
zJ(a2 - 9))
,
G = 4z2/aZ
This expression (Fig. 5-1) can often be used as a first approximation geometrical situations and for the comparison of two geometries.
(5-3) in more
complex
838
Radioactivity
10
0
Fig. 5-l
measurements:
Geometry
factors,
30
20
G
principles
=
40
4a/Reff
and practice
50
for circular
diaphragms
with diameters 5 and an axial point source. 5.2.1.2.
Terminolopy
The terminology for defined solid-angle counting methods is not used uniformly. Because the geometry is such a very important parameter of a detector it, the geometry, is very often coupled with the descriptive name of the detector. It also indicates the nature of the geometrical factor that must be used in the computation of the efficiency of the detector system. In usually
this context, detectors with a termed b-geometry detectors.
solid angle of only a few percent of 4x sr are The term medium geometry is reserved for solid
angles from a few percent of 4n sr up to a few percent less than 2a sr. A method using a detector that subtends a solid angle of a few percent above or below 2?r sr to the source And methods using detectors subtending solid angles to the source are known as 2~ methods. percent less than 4n sr are designated as 4~ methods; and methods using of only a few solid angles lying a few percent above or below 2n sr and a few percent below 4a sr are Methods using very precisely measured diaphragms usually called m-geometry methods. placed in front of the detector to define the solid angle of detection subtended to the defined-solid-anele methods. It source are usually known as low-, or medium-geometry should also be emphasized that the term defined solid-angle counting includes the use of such as solid-state, that are used in a fixed source-to-detector geometry, all detectors, as in y-ray spectrometry. 5.2.1.3.
Relative
(indirect)
and direct
("absolute")
measurements
Two different types of solid-angle counting method have proved to be especially advantageous and are frequently used with remarkable success. They depend crucially on the radiations to be measured and on the detectors applied. For strongly absorbable and weakly scattered radiations (alpha particles, ions, x rays with energies below about 50 keV, and, electrons) direct counting can be performed with very high accuracy, less satisfactorily, especially if detectors that are 100% efficient for the measured radiation are available. On the other hand, for relatively weakly absorbable and more strongly scattered radiations relative measurements (with reference to otherwise well(7 rays and, less so, neutrons) especially if energy-sensitive detectors of offer great advantages, calibrated sources) The energy ranges considered here are, as usual, those covered high resolution are used. by radiations from radionuclides (from eV, but, mostly, a few keV up to about 3 MeV). The two methods are very different in several respects. For direct counting the crucial problem is to obtain the most accurate possible estimate of the corrections, but the accuracy of relative measurements depends on the similarity of the unknown and the standard source. Direct measurements are mostly made on nuclides with one characteristic radiation and small while relative measurements are mostly performed on nuclides with measurable backgrounds, considerable background caused by them. Therefore, several radiations and, consequently, relative solid-angle counting and direct defined-solid-angle counting are treated in two different sections (775.2 and 5.3).
Radioactivity measurements: principles and practice
5.2.1.4. Descrintion of solid-anele counting In direct ("absolute") measurements, generally of one radiation, all pulses per unit time, M, above an adequately chosen discrimination level are counted during any suitable period of time and can be used to calculate the source activity in terms of the computed solid angle and the photopeak (i.e full-energy-peak) efficiency, s,(E), of the detector. In the case of relative measurements, in which sources of radionuclides, with one or more 7 rays, are to be assayed against a calibrated source of the same radionuclide, only the counts contained in full-energy peaks of individual radiations are used for the comparison. Then, if the laboratory standard (subscript st) and the unknown source are equivalent in every respect, including source preparation (but not necesarily in half life, which is neglected in the following), Eq. 3-6 can be reduced to N = N,,W
B)/(M,,R,,
- B)
= Cm - B)/c,W =
(5-4)
M/<;(E)
where N is the number of decays occurring in the source during the chosen counting time, T, N is the number of counts in time T, R is the relative correction for dead-time losses and pile-up, B is the background count in time T, and r,(E) is the photopeak efficiency for 7 rays of energy E; c;; is sometimes used to denote the photopeak efficiency including deadtime, pile-up and background corrections, but this is, in general, not recommended. Equation 5-4 shows clearly the advantage of the relative method. The efficiency, e,(E), can be measured with suitable well-characterized calibrated sources for different energies, and an efficiency-calibration curve can be established. From the calibration curve the efficiency at any energy can be read and the activity of the source emitting the radiation selected for the measurement can be computed by use of the simple equation 5-4. The establishment of an efficiency curve is therefore the central problem of every relative counting method (75.2.3). It is also necessary to obtain accurate values for M, R and B, and this question is discussed in the following section. However, when the standard and the unknown source are not quite equal, matters become much more complicated. In such circumstances, corrections for all or part of the factors of Eq. 3-6 must be applied to Eq. 5-4, and this can lead to large uncertainties. 5.2.1.5. Peak. total and intrinsic efficiencies The full-energy-peak, or photopeak, efficiency cp is always defined as the probability of observing one count in the photopeak per particle, or per photon, emitted by the source. In principle, it is not necessary to know the efficiency provided that the measuring conditions for both the standard and the unknown source are very closely the same. Thus, for example, only the numbers of pulses above the energy corresponding to the peak maximum might be taken into consideration. But in order to make some of the corrections, especially that for coincidence summing in the case of photons, the whole peak count rate due to the photoelectric effect must be known. Therefore, all practical definitions of the photopeak efficiency should include as many pulses in the photopeak as possible. Several other definitions of efficiency, besides that of the very important photopeak efficiency, are used in defined solid-angle counting. The total efficiency, et, generally includes all pulses with energies above background, often obtained by extrapolation of the differential pulse-height distribution to zero energy. The total efficiency is used chiefly in activity measurements made with cylindrical NaI(Tl)-scintillation detectors and, with less accuracy, for the coincidence-summing corrections to measurements made with germanium detectors. The definition can be somewhat different for different purposes, e.g. x-ray It is, therefore, always of great importance to say pulses could be included or not. exactly how a total efficiency is defined; also the term "intrinsic efficiency," which is used in different ways (see, e.g., Knoll, 1979). 5.2.2. Practical nrocedures and instrumental details 5.2.2.1. Countinp svstems Most systems used for low- or medium-geometry counting consist of an appropriately designed unit comprising a source holder and detector, and electronic pulse-processing components connected to the detector. In many cases, the source-detector unit consists of an enclosure that can be evacuated (or flushed with helium) in order to count strongly absorbed radiation, such as a particles, and it can, in general, be shielded to enable the counting of 7 rays (see also 83.4.3.). Many different source holders and source-detector geometries are in use. Most systems can accommodate sources on thin plastic or metal foils. The gamma-ray counting systems are also usually suitable for sealed sources in many forms, such as ampoules and bottles, either within reentrant cavities in the detectors, or at different distances from the detector, or in some cases with the source surrounding the detector that is located in a reentrant cavity within a container known as a Marinelli beaker (Debertin, 1980). The systems used for metrological FIR1
39/8-I
work of high precision are often quite elaborate,
839
Radioactivity
840
measurements:
principles
and practice
but those for normal routine work in the laboratory are usually much simpler, but are often provided with automatic sample changers and automatically operated pulse-processing and The systems used in the field are kept as simple as possible recording electronic systems. But it is important in every case, not and are, therefore, not usually of great accuracy. The photopeak efficiency can vary even, to change any system components after calibration. for example, with the level of the liquid nitrogen in the cryostat of a Ge detector (Jedlovszky et al., 1983). Examples of defined-solid-angle counting systems are shown in Figs. 5-2 and 5-3 for gamma-ray counting, and in Fig. 5-4 for alpha-particle counting.
Simple, versatile x- and Y-ray spectrometer Fig. 5-2 measurements with a 3" x 3" NaI(T1) detector.
Typical arrangement of a Ge(Li) Fig. 5-3 for relative Y-ray measurements.
5.2.2.2.
or cooled
for relative
Si(Li)
detector
Detectors
Many different types of detector can be used for relative defined-solid-angle counting, but NaI(T1) and Ge detectors are nearly exclusively employed for ~-ray spectrometry. Other detectors, for special applications or for other radiations, are Si(Li) and SiSB (silicon surface barrier) detectors, ZnS(Ag) and other inorganic scintillation detectors, To day, Ge detectors plastic and other organic scintillators (see 74.6 et seq.). are mostly used for r-ray spectrometry, and there are already so many types and sizes on the market that, for any given purpose, a judicious selection is necessary; and manufacturers catalogues can be usefully consulted. Coaxial Ge detectors (truly coaxial with a central hole along the entire length of the right-circular cylindrical crystal, and one-end drifted coaxial) are the preferred types for gamma-ray spectrometry at energies above about 100 keV; but for lower energies (below about 300 keV) planar and high-purity (HPGe) detectors, and especially windowless detectors are most advantageous. High-purity germanium detectors and they can also be used for lower do not deteriorate if raised to room temperature, energies. If the size of a NaI(T1) detector is not critical for the experiment, a 76-mm x This size is a 76-mm right-circular-cylindrical crystal should be given preference. widely accepted standard with which many measurements, and for which many calculations, have been made (Heath, 1964; NCRP, 1985).
Radioactivity
measurements:
principles
and practice
841
Typical low-geometry alpha-particle counter with exchangeFig. 5-4 able components. Detectors are chosen for those of their properties that are important for the measurement. The detector material, volume (or at least approximate volume), geometrical form, and the encapsulation material and geometry are trivial parameters, which must be known. The most important characteristic properties are, however, the resolution and efficiency which must be measured. The resolution (R) of a detector for a certain radiation and for a well-defined geometry is given by the full width at half the maximum of the photopeak of this radiation, either in terms of the energy (keV), or relatively, in percent of the energy corresponding to the peak maximum. The resolution is strongly energy-dependent, and, to a first approximation, is proportional to E-'/z. Typical resolutions for good "standard" ?&cm x J&cm n x 3”) Na(T1) crystals are 50 keV (or 7.5% of the peak energy) for the 662-keV peak in :t decay of 13'Cs; and 80 keV (or 6.0% of the peak energy) for the 1333.keV peak in the decay of "Co. The corresponding data for a 50.cm3 Ge detector are 1.4 keV (or 0.2%) at 662 keV, and 2 keV (or 0.15%) at 1333 keV (current best value about 1.7 keV). Directly connected with the resolution is the peak-to-Compton ratio (P/C ratio), the ratio between the peak maximum and the mean of the counts in the Compton region (1040 to 1100 keV for the 1333-keV peak). but, normally, values The best Ge detectors reach a P/C ratio of 200, between 30 and 60 are available; the corresponding NaI(T1) values are 10 and around 5. The efficiency of a detector depends on its nature and geometry and on the energy of The efficiency is defined in different ways (75.2.1.5.). the radiation to be measured. the most important definition is that of the For the characterization of a detector For NaI(T1) detectors the photopeak efficiency is almost always photopeak efficiency, cp. distance of 10 cm. indicated for the 662.keV peak using a 13'Cs source at a source-detector It can be compared with the photopeak efficiency (0.0125) of a good 3" x 3" NaI(T1) crystal. For Ge detectors the reference conditions are not so clearly defined, but are generally referred to the 1333.keV peak using a 6oCo source at a source-detector distance efficiencies of a Ge of 25 cm and a crystal volume of 50 or 100 cm3. The relative detector, c2, are stated in percent of that of a 76. x 76.cm (3. x 3-inch) NaI(T1) crystal For large Ge detectors cy can exceed at 1333.keV for a source-detector distance of 25 cm. 10%. Typical values of efficiencies are given in Figs. 5-5 and 5-6, and in Table 5-l. The stated values can only be an indication of orders of magnitude, but are very useful for the planning of experiments. Table
5-l.
Typical efficiencies for NaI(T1) and Ge at 1333 keV
Efficiency Et (0) cp (0) tp (10) ep (25) $/Et (10)
3" x 3" NaI(T1) 0.35 0.12 0.0065 0.0012 0.3
50-cm3 Ge 0.1 0.01 0.0005 0.0001 0.1
for the
Radioactivity measurements: principles and practice
842
should The characteristic properties of detectors (such as cp, et, cr, R, P/C, FWHM) not only be measured before use, but must also be continuously tested, because detectors The necessary measurements are discussed are often not stable over long periods of time. in 75.2.4.6.
Typical photo-peak efficiencies, ep for some frequent lY Fig. 5-s used detectors and source distances, d (numerical data taken from Crouthamel, 1960; Heath, 1964; Helmer, 1982; Moens and Hoste, 1983: Morel et al., 1983).
Intrinsic photo-peak efficiency of some common x-ray detectors Fig. 5-6 (numerical data taken from McMaster et al., 1969; Israel et al., 1971; Gallagher et al., 1974; Banham and Jones, 1983). 5.2.2.3. Electronics The counting
electronics (see chapter 6) connected to a detector of a defined-solid-angle system can vary from very simple and manually-controlled instruments to very The minimum completely automatic systems, controlled by high-capacity computers. COlllphX, electronic equipment necessary is a low-noise preamplifier (which is, in the case of a solid-state detector, usually cooled in the detector cryostat), a stable linear amplifier, To this an integral discriminator, a scaler, and the power and high-voltage supplies. minimum there might be added a multichannel pulse-height analyzer (MCA) with live timing, or a small on-line computer for data processing, spectral display and printer read-out of Very useful, and necessary additions for good accuracy, are a pulse rate vs. energy. precision pulser, that can be connected to the preamplifier, and a biased amplifier, which can expand any part of the pulse-height spectrum above a chosen level. The adjustment of the amplifier for optimum resolution, and to minimize corrections, is a crucial experimental problem, especially because it depends also on the spectrum and The main adjustment is that of the time constants of intensity of the measured radiation. all the amplifiers, but also pole-zero cancellation, base-line restoration, pile-up rejection, stabilization of amplification, and d.c. level must, if existing, be properly chosen (see 16.4). Usually time constants around 1 ps are chosen for the fast solid-state detectors, but much larger one.s can be used advantageously under certain conditions, especially if the highest resolution is not needed (Bouchard and Vatin, 1977; Gehrke,
Radioactivity measurements: principles and practice
843
1982). Pulsed optical-feedback preamplifiers (POFP's) should be used with caution (Funck, 1983), especially if the pulser method is used for dead-time correction (see (5.2.4.2). Very sophisticated electronics may even provide computer control of the time constants. As so many parameters have frequently to be adjusted, it would be most advantageous if a relatively simple second electronic channel could be used in parallel to the main channel, in order to check the crucial adjustments and to monitor the stability of the whole system. The most expensive part of the electronic instrumentation is the multichannel analyzer If it is not necessary to know the spectrum of the measured or a comparable computer. radiation, a detector with a simple integral discriminator (the threshold of which must be And a very simple well chosen and defined) is sufficient for relative measurements. spectrometer system using a 127 x 127-mm right-circular NaI(T1) detector (e.g. Fig. 5-2), with energy-calibrated integral discrimination, is an extremely useful instrument for relative defined-solid-angle counting that should be available in every laboratory. But as l-ray abundances are generally evaluated from -/-ray photopeak areas in -j-ray spectra,xA's The minimum number of MCA are standard instruments for such relative measurements. on the range of energies to be measured and the required channels needed, depends accuracy. For accuracies around 1 percent, at least 5 to 6 channels are needed to cover the full width at half maximum (FWHM) of the recorded photopeaks. This would require, for a usual FWHM of about 2 keV (at 1333 keV), an energy increment of approximately 0.35 keV/channei. Therefore, if an energy range of 2.5 MeV has to be covered, with an accuracy For an accuracy of about 5%, only about 1000 of l%, about 8000 channels would be needed. But even 100-channel analyzers could be very useful for many channels would be needed. Although such analyzers are not now tasks, especially if used with a biased amplifier. commercially available very inexpensively from they could probably be constructed integrated-circuit components that can be obtained commercially. Multichannel analyzers offer, in general, many advantages. Very advanced systems, especially those connected to larger computers, provide direct energy- and peak-area computations, and radionuclide identification. Even some of the simpler systems now offer "live timing" in addition to the usual clock timing. Live timing means, in general, that the time for which the MCA is not blocked to incoming pulses is recorded. Live timers thus yield, directly, the required count rate. Unfortunately, many live timers are not very accurate, especially at higher count rates and should, therefore, be carefully tested. If peak areas are being measured without a live-timing MCA then a correction is necessary for both dead-time losses and pile-up. Pile-up happens if a pulse overlaps randomly with another, or in coincidence with another from the same event, then amplitudes will add to give a summed- energy pulse (see 10-111-E in Knoll, 1979). Corrections for both dead-time loss and pile-up can best be made by using the pulser method described in or checked by using 75.2.4.2. Sometimes these two corrections can be better evaluated, the MCA live timers and calculating the pile-up. 5.2.2.4. Countine orocedures Relative defined-solid-angle measurements can be made with most instruments under different geometrical conditions, especially with different source-detector distances. Frequently, sources of different activities can also be used; such sources can be readily In this way optimum counting conditions can be chosen, such as a prepared from solutions. source distance of 10 cm, or more, to keep summing corrections low, and count rates below 1000 s-1, in order to reduce dead-time loss and pile-up correction, without having to count for too long a time. The unknown source to be measured, which is always made as similar as possible to the standard sources used for the calibration, must be very cautiously positioned in the measuring chamber. The neglect of this requirement is a frequent cause of error, especially The length of the counting period is chosen to give a total of at low source distances. counts commensurate with the required uncertainty, remembering that the relative estimated standard deviation equals N-l". It is advantageous to subdivide the total counting time, T into 4 to 10 equal periods in order to check the stability of the equipment of the equipment and the statistical behaviour of the results. The latter are mostly evaluated by measuring peak areas (774.11.5.2 and 5.2.2.5). Just the counting above a well-chosen integral-discriminator threshold with quite simple instrumentation can yield very valuable results (Vaninbroukx and Grosse,1966). By using the peak-area-counting method the unknown activity of a source can be obtained as follows: (i) the total counts under a chosen peak are measured and then corrected for all systematic biases (q5.2.4), and (ii) by the efficiency, c, derived from a calibration curve or a direct calibration with a standard of the same nuclide (a5.2.3.3), the activity of the unknown source is computed using the following equation: A
=
N/T
=
(MR
-
B)UC,/oT
= (M - B)IICj/('T) ; = (M - B)lIC,f/(cN,).
6 = Cst 3
(5-5) (5-6)
Radioactivity measurements: principles and practice
a44
The correction factors, Cj (IIC,= RIIC,),are those discussed explicitely with equation (Eq. 3-6), B is the number of background counts (all pulses below the peak), and the last term (Eq. 5-6) applies if the pulser method (75.2.4) is used for the correction of dead-time loss and pile-up (f = pulser frequency, N, = counts in the pulser peak). Also other procedures are common and important for accurate measurements, several test procedures. The latter are discussed in some detail in 75.2.4.5.
especially
5.2.2.5. Peak-area evaluation The evaluation of the total number of counts within the area of the photopeak, due to a given radiation, constitutes a serious practical problem in all relative definedsolid-angle gamma-ray measurements (see 74.11.5). This difficulty arises because photopeaks from semiconductor, and other detectors are asymmetric, with an additional component at the low-energy side of the assumed normal distribution. Furthermore, the backgrounds below the peaks show a step down, towards higher energies, below about the peak maximum (McNelles and Campbell, 1975). Therefore, the evaluation procedure is always rather complex. It can be performed manually by a simple addition method and can be partially or fully computerized using curve fitting by a least-squares method. For the manual evaluation (e.g. Debertin, 1980), the peak energy is first determined and the FWHM is calculated either from a Gauss function fitted to the higher-energy side of the peak or estimated from experience. Then the "peak region" is defined, and counts above background summed in that region. The best choice of the peak region seems to be given by E, + 5s (Jedlovszky et al., 1983), where Em is the energy corresponding to the peak maximum, and s is the estimated standard deviation (FWHM = 2.355s). But Em f 3s has also been recommended by Debertin (1980), and asymmetric definitions can also be applied. Then the background in the peak region must be determined. The simplest way to do this is to assume a linear background between the count rates in the channels (or the mean of a group of channels) just below and above the limits of the peak region (Debertin, 1980). For greater accuracy a step-like background (with a step height of about 1.5 percent of the peak maximum), possibly combined with a linear background (Jedlovszky et al., 1983) can be The sum of the numbers of pulses in the peak region minus the number of subtracted. background pulses yields the required number of counts. This simple procedure is Its accuracy is, in general, satisfactory for most cases and can be easily computerized. comparable with that of the best computer evaluations, but its applicability is limited, and it cannot be applied to measurements of double or multiple peaks or to very weak ones. Many different procedures and programs for a fully or partially computerized peak-area evaluation are reported in the literature (Kokta, 1973; Yoshizawa et al., 1980; Prussin. 1982; Houtermans et al., 1983; Helmer and McCullagh, 1983; Jedlovszky er al., 1983). 5.2.3.
Calibrations
5.2.3.1. Introduction Defined-solid-angle counting systems can be used for two purposes, (i) the identification of radionuclides by identifying the energies of their emitted radiations, and (ii) For the the measurement of the abundances of radiations or the activities of sources. first, in which a knowledge of the solid angle is not required, the system must be calibrated for energy-us-channel number (75.2.3.2.). For the second, the efficiency of the detection system (75.2.1.5) must be measured, for which the necessary procedure is described in (75.2.3.3 to 5.2.3.6. This must be done in both cases by the use of adequate reference sources because calculations are often not accurate enough, especially for Ge detectors because their dimensions (and edge effects) are not sufficiently well known. Nevertheless, calculations of total efficiencies of NaI(T1) detectors (e.g. Grosjean and Bossaert, 1965) and Ge detectors, and of photo-peak efficiencies of NaI(T1) detectors (Birattari and Salomone, 1980) and of Ge detectors (Moens and Haste, 1983; Nakamura and Suzuki, 1983) can be very useful. They allow one to check the experimental values, help to establish calibration curves, and can directly be used for interpolation and extrapolation, e.g. to higher energies, not available with long-lived radionuclides. The efficiency calibration of solid-angle counting systems can be performed by different techniques, namely by the use of one single calibrated source of the nuclide to be measured, or by means of a series of calibrated sources, preferably with each emitting 0lle radiation only, (75.2.3.3), of one standard prepared from a suitable mixture of or one calibrated multigamma-ray source of a single suitable radionuclides (75.2.3.4) of an All these measurements aim at the establishment radionuclide (75.2.3.5). efficiency-calibration curve with the highest possible accuracy (75.2.3.6). The most important, often violated, condition for precise relative counting is the near or complete equivalence of the unknown source and the calibrated sources and of the measuring conditions. The actual differences (such as dimensions and absorption) can be corrected for satisfactorily (75.2.4), but the differences between the shapes of r-ray and x-ray Despite these differences, calibrated x-ray peaks are more easily overlooked. sources can also be used for the measurement of r-ray efficiencies, or vice versa, if suitable corrections are applied. These can amount up to about 10% for radionuclides of
Radioactivity
measurements:
principles
a45
and practice
high-2 values and are always negligible for low-2 values (Schulte et al., 1980; Debertin the peak shapes of annihilation radiations and normal 7 Similarly, and Pessara, 1981). rays differ considerably from each other, which can easily be seen by comparing a spectrum Also the shapes of escape peaks and r-ray peaks of %r with that of an annihilation peak. from excited states, following nuclear reactions, are slightly different from the shapes of radioactive r-ray peaks. The relative efficiencies of solid-angle measuring systems are usually obtained using But for higher energies, above about 1.5 MeV, suitable photopeaks from calibrated sources. the calibration can be better made using doubleor, less and small Ge detectors, advantageously and less important, single-escape peaks (Fig. 5-7). Such a calibration is made in the same manner as that for the photopeak.
1 ?;‘A:
0.003
! ll!lllN 0.02 0.05
0.1
!
a2
‘?E
3.;13.;Na!lTC?j
~LLULLM 1517 2 25 3 3.5 4 4.5
Typical escape-peak-to-photopeak efficiency ratios for x-ray Fig. 5-7 and double ( cDE) annihilation-radiation escape ( C& and single (( escape for some Ge(Li) and @ aI(T1) detectors YS energy of incident radiation. Photon efficiency calibrations in the x-ray region (below about 100 keV) suffer from The first is the which are not present at higher energies. additional effects,
two excitation of fluorescence x rays in the material surrounding the detector, especially the The second effect is the partial penetration of radiations diaphragm in front of it. through the edges of the collimating diaphragm in front of the detector, resulting in an The use of diaphragms of different absorption-edge-like feature of the calibration curve. materials (such as Pb, Ti, Sn, and Fe) and of different thicknesses allows one to estimate the amount of these effects. There is also the K edge of Ge at 11.1 keV (Pessara, 1983). 5.2.3.2.
Energv
calibration
output-pulse with linear components give Energy-sensitive detectors electronic to the energy, E, absorbed in the detector so that V = heights, V, that are proportional If the output pulses are recorded in a multichannel analyser in aE, where a is a constant. which the relation between the pulse height and channel number, k, is also linear, then V = bk, for constant b, and E = bk/a.
(5-7)
In principle, two calibration points (preferably at the two ends of the energy range The evaluation of such measurements can, used) suffice to define the linear relationship. of 0.5 keV and under normal conditions, easily be done manually with a maximum uncertainty fractional channels being taken into account. Because the deviations from 0.5 channel, is linearity are also generally lower than 0.5 keV, such a two-point energy calibration of radionuclides or single sufficient for most purposes, especially for the identification peaks (Debertin, 1980). For energy calibrations of y-ray spectrometers, higher accuracies may be needed and In these cases a calibration checks of linearity over the whole energy range are useful. This can be done with several individual sources (e.g. for many energies is necessary. those listed in (5.2.3.3. or - much more easily - with a single source of mixed single-nuclide radionuclides (e.g. those discussed in 75.2.3.5) or with a multi-Ramma-ray
Radioactivity measurements: principles and practice
846
source, wo ) l=Eu, etc. (also see 75.2.3.4 and Fig. 5-8). e.g. For the highest accuracies, the position of the peak maximum (in channels) is, in general, calculated by fitting Gauss functions to the experimentally observed peaks. The deviation from linearity of the energy-vs-channel calibration curve is usually expressed as the difference, between a well-known peak energy, E, and its energy, Es, derived by linear regression. This difference E - ER, is, in general, a small fraction of 1 keV, and the uncertainty of this difference, and that of the whole calibration. can be less than about 15 keV, and, in special cases, much less.
Fig. 5-8
Typical
Y-ray spectrum of a mixed-radionuclide source
57Co 13gCe, 5lCr, 8%r, l37Cs, 8%. 65Zn) and of a multi-y-ray sour& (56~0) taken with a large Ge detector. The energies of the radiations most frequently used for these energy calibrations are Debertin, Yoshizawa et al., 1980; known with extreme accuracy (see Thus, for example, the energy of the standard 1980; and Table 10 of NCRP 58, 1985X). transition in the decay of ig8Au is 411.8044 keV f 0.0001 keV. Therefore the uncertainties in the energies of these standards can mostly be neglected. can be disturbed by peak shifts due to physical effects, Energy measurements This alone can especially by low-angle scattering and self-absorption (also see a5.3.4). source-detector measurements in different discrepancies between cause significant Corrections must be applied for these shifts, especially when higher accuracy geometries. is needed. 5.2.3.3.
Full-enerev-ueak
efficiency calibrations using sinele radionuclides
To measure the activity of a source of a single radionuclide, the simplest and, often, most accurate method is to make a comparitive y-ray, or x-ray measurement with a well characterized standard of the same radionuclide under the same geometrical conditions of source and detector. The activity of the unknown source is then obtained from the simple relation A = A,,N/N,t = &M/M,,
v
(5-8)
where A and Ast are the activities of the unknown source and the standard, and N and NSt and M and MSt are, respectively, the corrected and directly measured count rates recorded If the activities of two sources are by the detector system for each of the two sources. nearly equal, the approximation of Eq. 5-8 will often give the activity of the unknown with sufficient accuracy. But corrections, such as indicated in Eq. 3-6, for ever-present small differences between the two sources or the measuring conditions must almost always be made. The use of several radionuclides each emitting only one, or, but less desirably, two y rays is also the most accurate method of establishing a calibration curve for a The preference for one 1 ray is because scattered Compton photon-detector system. radiation from the more energetic of two cascade y rays increase the uncertainty in the
Radioactivity
measurements:
peak-area evaluation of the lower-energy coincidence summing between the two y rays
principles
7 ray, and is avoided.
a47
and practice
the
possible
need
to
correct
for
Today many multi-gamma-ray sources are available from national standardizing laboratThose with half lives longer than one month are ories and also from commercial suppliers. Some shorter-lived ones may be useful for special calibrations, such listed in Table 2-4. Some pure x-ray emitters, such as 37Ar, as, for example, s'Ga, "Br, l'O'"Hf,and "lT1. =Fe, 93mNb and 131Cs, may also be useful, but are difficult to standardize (see,however, 75.3). The double r-ray sources are also useful for indirect efficiency measurements. If the efficiency for one of the photopeak energies is already known, by a calibration using another radionuclide, then that for the other photopeak energy can be derived from photopeak measurments of both 7 rays. This method is of special interest in its application to measuring the intensity of neutron-capture 7 rays in the energy range between 2 and 10 MeV (see, for example, McCallum and Coote, 1975). 5.2.3.4.
Full-energy-oeak
efficiencv
calibration
using
multi-gamma-ray
emitters
Calibrations can be performed very rapidly if, instead of using many individual sources, just a single source (or, even two or three sources), that emits many Y rays of different energies is available. Such multi-gamma-ray sources can be prepared from a solution of a single radionuclide having a suitable decay scheme, namely one that emits many 7 rays that are evenly distributed over the required energy range. If such a radionuclide is not immediately available, then it may be possible to prepare a suitable source from a mixture of r-ray-emitting nuclides that cover the required range of energy. The simplest calibration is that with a single-nuclide multi-gamma-ray source, as all the 7 rays are decaying with the same half life. But it also suffers from considerable uncertainty because many 7 rays of different energy are in coincidence which, therefore, causes coincidence summing, the correction for which is difficult (75.2.4.3). This effect can, if neglected, lead to considerable errors in the efficiency, which might exceed 50% for unfavorable geometries. Therefore such single-nuclide multi-gamma-ray sources should only be used at sourceto-detector distances greater than 10 cm, in order to keep this correction small and calculable. But if high accuracy is not required, or if only routine monitoring of the stability of a detector system is to be performed, the use of such sources is very advantageous. Even for high-accuracy calibrations, multi-gamma-ray sources, also in over as many I-ray combination with other sources, can be used for efficiency calibrations peaks as possible, or as needed. Helmer (1982), for example, uses 19 sources of 18 7ray-emitting nuclides (including 5 multi-gamma-ray sources) with 58 evaluated 7 rays, for the calibration of an HPGe-detector system over the energy range of 30 to 2,800 keV. The selection of the most suitable multi-gamma-ray source for a specific efficiency calibration is not always easy. Its photon radiations should cover the energy range of For that, all component uncertinterest, and also provide the highest possible accuracy. ainties (especially those associated with the -/-ray-emission probabilities) must be taken into consideration Debertin. 1980; Helmer, 1982). Most calibrations pertain to the energy range between 100 and 1,500 keV, in which range "'Eu is, at present, the most suitable standard. It emits intense y rays with rather evenly-spaced energies between 122 and 1,400 keV, and also x rays of about 40 keV. The photon-emission probabilities are now rather well-known (Debertin, 1979; Meyer and Massey, 1983; NCRP, 1985). Some minor disadvan(such as a small disturbing peak at 409.2 keV, some double peaks, and probable tages contamination with ls4Eu) can be rather easily overcome (Debertin, 1980). 5.2.3.5.
Photoueak
calibrations
usine
mixtures
of radionuclides
The fast calibration by a simultaneous measurement at many peak energies can be performed without the intrusion of coincidence summing, if mixtures of y-ray-emitting nuclides, ideally with single r-ray emission, are used as the calibration source. The latter can be produced from a quantitative mixture of standard solutions of the individual deposition of drops of the individual standard solutions on to nuclides, or by quantitative a source mount, or its removable parts (e.g. a "sector source" such as described by Genka and Ishikawa, 1983). The radionuclides comprising the mixed source can be chosen to meet the purpose of the experiment, especially the energy range neededand the probable duration of use. The activities A, of the different nuclides should be so chosen that their corresponding peak heights will remain nearly equal for the duration of their use. Mixtures of single-gamma-ray and multi-gamma-ray nuclides can often be used advantageously, if appropriate corrections are applied. Typical mixed-radionuclide l-ray emission-rate standards are composed of 57Co, s°Co, s5Sr, "Y, 'OQCd, l'?Sn, l"Cs, or 13'Ce (Coursey et al., 1982), or, for longer use, lz5Sb, 154E~ or '55Eu (NBS SRM 4275b, solid, and 4276b,
a48
Radioactivity
solution),
or '&Mn, "Co,
measurements:
principles
652n, 60Co, lz3Ba, lz7Cs, or
lszEu
and practice
(Genka and Ishikawa,
1983)
A disadvantage of mixed-nuclide sources is the need to make a different decay correction for every measurement (different for each radionuclide component) which may introduce an additional uncertainty. Difficulties can also result from the evaluation of peaks of very similar energies, e.g. as with a 65Zn-15ZEu mixture, and annihilation radiation with the 514.009-keV transition in the decay of 85Sr. If the annihilationradiation peak is used for the calibration, or correction, at the energy of the 85Sr peak, the difference of spectral account (Debertin, 1980). 5.2.3.6.
Establishing
shapes
of annihilation
a calibration
and normal
7 radiation
must be taken
into
curve
The simplest way to construct an efficiency curve is the manual method using visual interpretation and some weighting according to the overall uncertainties of the individual results(e.g. Debertin, 1980, Helmer, 1982). An efficiency curve established in this manner suffices for most applications. The calibration curve can be better derived by computer analysis, for which an analytical function, relating efficiency and energy with adjustable constants, has to be assumed. Several functions, most frequently polynomials, have been proposed, as for example the following by McNelles and Campbell (1973) and by Meyer and Massey (1983)
In r(E) =
or the following
by McCallum
; ai(lnE)i l=O
and Coote
In r(E) =
,
(5-9)
(1975)
; b,(ln l/E)' i=O
(5-10)
In these expressions there are about five adjustable constants, a, or b, for the energy interval from about 100 keV to 10 MeV, or subdivisions of it. Other functions that are often suggested for the c~-vs.-E relation are semi-empirical equations with up to 10 adjustable constants for the energy range from 10 to 10,000 keV (e.g. Hajnal and Klusek, 1974). The constants of these relations are computed by least squares. The description of the efficiency-energy relation by an equation with five to ten constants is not very practical. It is, therefore,usually avoided by the subdivision of function can be the whole energy region into suitable sections, wherein the efficiency described by an equation with only a very few constants. The best subdivision depends on the actual measuring conditions and the purpose of the experiment. In general, energy ranges of about 1 to 60 keV, 30 to 120 keV, 100 to 400 keV, 200 to 2,500 keV, and 2 to 10 MeV are most appropriate (Debertin, 1980, Helmer, 1982) but others are also used successfully, e.g. 80 to 1000 keV, and 0.7 to 10 MeV (Meyer and Massey, 1983). In practically the peak efficmost important energy region, from about 200 to 2,000 keV, the experimental in a double-logarithmic presentation. iencies always vary nearly linearly with energy, Thus, one has for this energy region log cp =c+blogE,
or
Ep(E)
=
(5-11)
a Eb
(5-12)
The two adjustable constants a and b , which are usually calculated for the energy E, vary with the different conditions. This is especially so for a, but b always remains close to minus one. Frequently, second-order example, that due to McCallum
polynomials, with three and Coote (1975), namely
In C,(E) = a + b(log E-‘)
+
constants
are
used,
such
as,
for
(5-13)
c(log E-l)'.
The other energy regions can be treated in the same way. The energy region from about 5 to 60 keV is different from the others, in so far that detectors can be 100% efficient in that range. The detection efficiency then depends only on the geometry factor which is In this case the method calculable, under favourable conditions, with high accuracy. The additional problems met at these becomes a direct ("absolute") one (see also y5.3). It could be added that the Pb K-edge low energies have already been discussed in a5.2.3.1. jump in the calibration curve due to diaphragm penetration can amount to a few percent (Debertin, 1979). Also, the energy region above about 2.5 MeV and up to about 10 MeV can possibly be treated differently, because the efficiency-energy relation seems to be more closely linear on a semilog plot than on a log-log plot (Meyer and Massey, 1983). In order
to check
the accuracy
of the constructed
calibration
curve
and to facilitate
Radioactivity
measurements:
principles
and practice
relative efficiencies ep/tpO, can be interpolations and, less frequently, extrapolations, Here presented in a semilog plot, e.g. with a linear ordinate ranging from 0.95 to 1.05. cp,,is the photopeak efficiency calculated from an equation, the coefficients of which were with a = 0.5, b = 1, and E in keV). The adjusted by least squares (e.g. cpO = aKh, in general, reduced representation of the efficiency curve shows, only a few percent may be read from the curve can be done with deviations from unity, so that efficiencies (see also 75.2.4.5). sufficiently good accuracy 5.2.4. Corrections. 5.2.4.1.
accuracy
and system
monitoring
General
The overall uncertainty of any relative solid-angle measurement depends, according to associated with the measured number of counts, with Eq. 5-5, on the separate uncertainties the efficiency for the energy considered, and with the corrections that have to be applied. The uncertainty in the number of counts stems from their statistical nature and from uncertainty in the value obtained for the peak area. Both can be kept to below about 0.1% Thus, by careful attention to the quality of experimentation (Jedlovszky, et al., 1983). the overall uncertainty of the measurement of an unknown activity will usually be determined by the often considerably higher uncertainties associated with the detection efficiency, and with the corrections that must be made. The uncertainty in the detection efficiency is, in general, predicated on those of the various corrections and on the basic uncertainty of the calibration standard itself. If the unknown source being measured is directly compared with a very similar standard, in shape and substance and in the same geometry, the measurement approaches one that is strictly ralative, and some if not all corrections may cancel, and the final result may not even require that the detection efficiency be known. But this situation in which the uncertainty is minimal can not always be expected to occur, and, for general use, a detection-efficiency curve for the system must be established. In general use, pile-up corrections from corrections due too can be kept below unfavorable practical 5.2.4.2.
Dead-time
the most important uncertainties arise from dead-time losses and (75.2.4.2), from the coincidence-summing correction (75.2.4.3.) and to absorption and scattering effects (75.2.4.4). These uncertainties about 0.5%, if favourable measuring conditions can be chosen. But in cases, they can reach many percent.
losses
and pile-w
corrections
If only simple electronic counting channels are used, consisting of, say, an amplifier, integral discriminator, and scaler, corrections for dead-time losses can be made satisfactorily Because, according to the classical principles. are generally used even rather high in this simple case, dead times of a few microseconds While "normal" pile-up does not occur in such systems, the count rates can be handled. only possible disturbing pile-up arises from random summation of pulses smaller than the discrimination threshold (inclusive of noise) to form sum pulses exceeding this threshold. be avoided by proper choice of the measuring conditions. A very useful But this can discussion of dead-time and pile-up effects, by J.G.V. Taylor, is to be found in 72.7 of And comprehensive bibliographies on both subjects, edited by J.W. Mtiller and NCRP (1985). J.J. Gostely, respectively, have been published in BIPM (1981a and 1981b). For systems using multichannel analyzers (MCA's) and peak-area evaluation (or window discrimination) the dead times introduced by the analog-to-digital converters (ADC's) are, Pile-up (random and dead-time correction becomes necessary. in general, much higher, summing) also occurs and causes a transfer of pulses from the peak area under consideration especially severe for highThe pile-up is, of course, to a region above the peak. resolution detectors. For example, Helmer (1982) finds, for a typical Ge system, a pile-up At 6000 s-l, the correction amounts to correction proportional to the total count rate. photons. about 3% for 22.keV photons, and about 2% for 356.keV and higher-energy The simplest and yet fairly accurate method for measuring dead-time and pile-up Pulses from a precision pulser with losses is the pulser method (see NCRP, 1985, 72.7). precisely known low frequency, f, usually of 50 Hz, are fed, in this method, into the preamplifier together with the detector pulses. The position of the pulser peak in the accumulated spectrum is so chosen that the pulser peak neither interferes with the other If the shapes of the pulser and detector peaks nor does the background interfere with it. pulses are quite similar, the ratio of the number of pulses fed in by the pulser in time T, fT, to the number of pulses recorded in the pulser peak, N,, is taken as an approximate correction for dead-time and pile-up losses to every peak in the same spectrum. This for several reasons (Debertin and Schatzig, 1977), namely: correction is only approximate, (i) the shapes of the pulser and detector pulses are not exactly the same and are often influenced differently by the amplifiers and other electronic components; (ii) because of this difference in the shapes of the a pulser peak and a y-ray peak, they are differently in the peak-area evaluations: and (iii) distorted by pile-up, and this causes discrepancies the pulser pulses are periodic, not random, and the effects caused by this difference is Nevertheless, because the overall correction is generally not taken into consideration. not greater than a few percent, the approximate correction by the pulser method suffices in further most cases (Houtermans et al., 1983). But it cannot be used, without additional
a49
Radioactivity measurements: principles and practice
850
corrections,
feedback
if the source (Funck, 1983).
is rapidly
decaying,
or
if the preamplifiers
have
optical
Many other methods have been proposed for the correction of dead-time and pile-up losses (Houtermans et al., 1983). A very simple method is to measure the correction experimentally, using calibrated sources of different activities over a suitable range of activity (Macvani, 1984). Another simple method of wide applicability is to eliminate dead-time loss with a live-timer and to calculate the pile-up loss. With more complex electronic components, the live-time method can be extended to include correction (Andai av,dJedlovszky, 1983; GP1 and Bibok, 1983: Kennedy, 1984).
the
pile-up
In conclusion, automatic computer-based methods have been proposed, that can even be applied to mixtures of radionuclides with different, and also short, half lives (Westphal, 1979; Kennedy, 1984). 5.2.4.3. Coincidence-summine
correction
If a radionuclide emits two or more photons simultaneously, the probability of coincident pulses being detected and summed in the detector system is much greater than that for the pile-up of pulses from randomly emitted photons. The correction that must be made for summing losses from the peak-area evaluation is not count-rate dependent, but is a function of the photon-detection efficiency, which includes the solid angle subtended by the detector to the source. The summing losses depend essentially, therefore, on the distance between the source and the detector, and they can be very high (100% or more) for short source-detector distances and for detectors of large area. The uncertainty associated with the correction is also high. It is therefore very clear that conditions leading to such large values for the summing correction must be avoided. Therefore sourcedetector distances in excess of 10 to 15 cm are commonly used for calibrations when good precision is required. The calculation of coincidence-summing corrections is, in principle, very simple. If, for example, a radionuclide emits two photons in coincidence, each with 100% probability of emission as in the decay of 6oCo, then the summing-coincidence correction for the first photon, S(7'), is given by S(7)) = Ep(7')/[$(7')
- $(7’)+7n)l
9
(5-14)
where 7'l is the second coincident photon, and cP and Ed are the photopeak efficiency and the total efficiency, repectively. This correction is positive for single radiations, but negative for the overcross radiations in cascade decays. The principle of the calculation used above can be readily extended to more than two coincident radiations, but the resulting equations become more and more complex (Debertin and Schtitzig, 1979; Morel et al., 1983; Schima and Hoppes, 1983). Nearly all of the calculations reported pertain to point sources and do not take angular correlations into account. The theoretical estimates of the coincidence-summing corrections can easily be tested by experiment, especially by measuring a mixed source of a single 7 emitter and a double 7 emitter at different sourceto-detector distances. 5.2.4.4. Attenuation and scatterinp. corrections If the source to be measured and the standards used are not nearly equal, corrections must mostly be applied for the self-absorption in the source and the attenuation in any source cover or supporting material and in any absorber between the source and the detector. The self-absorption and attenuation corrections can, in general, be calculated with good approximation, especially if the source-detector distance is so large, compared with the source dimensions, that all radiations from the source to the detector can be regarded as perpendicular to the detector surface. An example that is often quoted is the correction for the 7-ray self-absorption in a flat surface of thickness f. In this case, one has that the number dn of 7 rays leaving the source in unit time from a layer of thickness dx at a depth x, is dn = %Aapdx
e-Px
,
here A, LIand p are, respectively, the area, specific activity and density of the source, and p is the linear attenuation coefficient for the radiation emitted. Integration yields
R
=
=
I dn = (Aap/2~)(1 - e-fit), I x=0 n t=m(l - em@).
(5-15)
Many other examples can be found in books on shielding. The attenuation correction is strongly energy dependent and can reach very high values at low energies. For example, a O.l-mm thick alumminium absorber between the source and the detector reduces the intensity of a 10.keV 7 radiation by about 30% (0.4% at 100 keV
Radioactivity measurements:
principles
and
practice
851
Even normal air-pressure variations can influence Low-energy and 0.2% at 500 keV). measurements which are, therefore, performed using vacuum chambers (Bambynek et al., 1966). Scattering is, in a wide energy range, the dominant interaction process of 7 rays. It not only Leads to an attenuation of the radiations, but contributes also to the spectra measured. At low energies, for example, backscattering at the detector can contribute considerably to loss of pulses from the peak. Scattering can be reduced by proper construction of the measuring chamber with as little material as possible near the source and the detector, or between them. As the amount of scattering is rather difficult to calculate, its effect is usually included in the efficiency (Eq. 3-6). This means that the conditions for scattering must be kept constant during the calibration and measurement of an unknown source. With regard to backscattering from the surrounding structure, a useful "rule of thumb" is that the source-detector configuration should be about 2 m from the room floor and ceiling and from the walls. 5.2.4.5. Overall accuracy The overall uncertainty of a defined-solid-angle activity measurement is calculated from the component uncertainties using the error propagation law, always at a level of one estimated standard deviation, unless otherwise stated ((3.4.1.2). In the case of a direct comparison of nearly equal sources, the contributing uncertainties are those associated of the activity of the standard and with the two peak-area with the measurement computations. In favourable cases, the former can be known to 0.1 or O.Z%, and the area This means that direct comparisons measurement can be made with about the same accuracy. of nearly equal sources can be performed with overall uncertainties of several tenths of a percent, down to about +0.3% for very favourable conditions. If an activity measurement is based on a previously established efficiency curve, the overall uncertainty is a combination of the curve uncertainty with that of the source measurement. As the efficiency curve too relies on a number of source measurements (standard sources, in this case), the component uncertainties are due to the corrections Helmer needed and are, therefore, similar for both, the known and the unknown sources. (1982) lists these component uncertainties for the measurement, with a typical Ge system, He also calculates overall total uncertainties for each of 58 different -/-ray peaks. peaks, ranging from 0.25 to 3.9%. With some smoothing of the curve, Helmer estimates the uncertainty of his efficiency curve to about 2% in the energy range from 30 to 85 keV, 1% Debertin for 85 to 120 keV, 0.75% for 120 to 420 keV, and 0.5% for 420 to 1,420 keV. (1979, 1980) states similar overall uncertainties of 0.7 to 2.0% for the energy region from 13 to 250 keV, 0.5 to 0.8% for 250 to 1,900 keV, and 1.5% for 1,900 to 2,800 keV. These Using figures can be regarded as conservative and typical data for modern Ge systems. these figures and the uncertainty of peak measurements (0.3 to 4%, according to Helmer) the overall uncertainty of a measurement of an unknown activity can thus be estimated to be about 0.6%, under most favourable conditions, and up to about 4%, in unfavourable cases. 5.2.4.6. System monitoring It is the most important feature of a relative measuring procedure, that the calibration is only valid for a well-defined particular state of the measuring system Every change of any component or condition can cause serious (including the sources). errors and uncertainties. Therefore, a continuous and careful check of the stability of the measuring equipment, especially of the detector, is indispensable for high accuracy work. Such monitoring following:
should be
frequently
undertaken
(e.g. weekly)
with
respect
to the
.
Energy calibration
. l
to the peak shape (FWHM, FWTM and, possibly, peak-to-Compton ratio), with a test pulse (of Gaussian shape), and of a source pulse;
l
for the photopeak efficiency at two or three different energies (one below 100 keV);
.
to the main corrections (dead-time and pile-up loss, and coincidence summing);
.
and to the overall repeatability (including source positioning).
(peak position);
Two kinds of sources are especially useful for these tests: well-known "Co standards (e.g. thin, reactor-irradiated cobalt foils in thin capsules) and "'ELI standards. It must be expected that present Ge detectors will change their efficiency up to several percent within a few years. 5.3. DIRECT LOW- AND MEDIUM-GEOMETRY
DEFINED SOLID-ANGLE COUNTING
5.3.1. Introduction Direct ("absolute") low- and medium-geometry defined-solid-angle counting involves the accurate measurement of the solid angle subtended at the source, of unknown activity, by a
a52
Radioactivity measurements: principles and practice
well-defined diaphragm, the aperture of which is completely covered by a radiation detector located behind it. (Spernol and Lerch, 1965; Bambynek, 1967; Blanchis, 1982) Only radiations passing through this diaphragm and interacting with the detector are Multiplication of the measured count rate by a geometry factor counted (Fig. 3-7). (75.2.1.1), yields (under ideal conditions) the source activity. The accuracy of an activity measurement is limited by the accuracies of the individual terms and factors in the analytical expression of the result (Eq.3-6). Some of the necessary conditions for the attainment of high accuracy are more or less "trivial", others influence the accuracy critically. The highest accuracy, in low and medium geometries, can only be achieved for strongly absorbed and weakly scattered radiations; namely those that neither penetrate the diaphragm nor are scattered out of, or into, the effective solid angle. Such properties are especially typical of a particles with energies below about 10 MeV, and less with x and 7 rays with energies below about 80 keV and, least of all, of electrons having energies below a few MeV. Some of the necessary conditions referred to above are: The electronic counting channel should be able to measure relatively high count rates of at least 104 s-1, in order to keep the statistical uncertainty and the measuring times The electronic components should be stable and also provide for within suitable limits. the possibility of applying accurate corrections for effects of limited resolution, dead times, and so forth. The background should be sufficiently well known and the effects of interfering radiations (from impurities, contamination, daughter products, nuclear reactions and higher-order processes)should be kept as low as possible and subtracted. Corrections derived from the decay scheme (branching ratios, etc.) and allowance for decay can nearly always be applied with sufficient accuracy. In addition to self-absorption and backscattering which are discussed inTy5.3.4 and 5.3.5, the sources themselves pose several basic problems, which can be understood easily but overcome only partially and with considerable technical difficulty. Extended sources should be sufficiently homogeneous; this can be checked by scanning with small apertures. Finally, supports and sources should be sufficiently conducting in order to avoid build-up A good example of the preparation and definition of of electrostatic surface charges. high-quality sources is the evaporation of homogeneous uranium layers on to platinum-plated quartz discs that have been mirror-polished (Moret et al., 1970; Miischenborn, 1971). Certain effects critically limit the overall accuracy and can cause errors of several These effects deal with the percent, if they are not properly taken into consideration. detector-response function or efficiency (75.3.2.4), with the effective solid angle (ll5.3.3), and with scattering and absorption occuring between the origin of the measured radiation in the source and its interaction with the detector (175.3.4 and 5.3.5). The direct ("absolute") low-geometry solid-angle method for the calibration of aparticle emitting sources allows one today to reach, under favourable conditions, accuracies of about 0.02% (Blanchis, 1982). 5.3.2. Instruments, detectors and practical urocedures 5.3.2.1. Countins! systems and electronics are very similar to The counting systems used for direct ("absolute") measurements those used for indirect (relative) measurements (see 75.2.2.1 and Fig.5.4as examples). The electronic systems should include a multichannel analyzer (MCA), at least for the inspection of the spectra. But, for accurate counting higher count rates, MCA's are often not Therefore, in general, a fast counting channel with a stable and wellenough. fast defined dead time should be used in parallel with the MCA (also see 75.2.2.3). 5.3.2.2. Source-detector chamber The source-detector chamber must be constructed with the greatest care, so as to minimize the difficulties in correcting for scattering and absorption effects. The effects of small-angle scattering (see 75.3.4.3), should be avoided by, for example, not using 2x The source holder should be of a rather rigid construction, which is also geometry. essential for an accurate measurement of its dimensions, and for the accurate positioning of the sources. Large-angle scattering (75.3.4.4), on the other hand, is lowest for low-Z values of the scattering material. Therefore, low-Z material, such as aluminium, should be The advantage lies not only in the lower-scattering used for the chamber walls. probability, but also in the fact that the residual energies of the scattered particles are also rather low (Fig. 3-8). Thus, backscattering of particles on to the detector surface leads to pulses corresponding closely to their initial energy without introducing any In addition, the energies of particles scattered from the walls are sufficiently errors. Large-angle lower than their initial energy that they can be discriminated against. scattering on the chamber walls might be important but will, of course, be lower with a
Radioactivity
Larger chamber
measurements:
principles
and practice
853
diameter.
Another critical problem is the choice of the shape and material of the diaphragms. Several shapes can be used (see Blanchis, 1982), but the body of the diaphragm must always and to avoid be at least several-millimeters thick, in order to ensure high stability The innermost edge, which deformation when the parts of the chamber are screwed together. but defines the effective solid angle, must be as thin as possible to avoid scattering, thick enough to exclude penetration and facilitate accurate machining. A few tenths of a millimeter are usually adequate, because the aperture diameter at such a thickness can be measured with the necessary precision of 0.05 mm, or better. Another important point is that the chamber should be constructed in such a way that its dimensions, which define the effective solid angle, can easily be measured with the An essential condition for that is the attainment of evenness and accuracy needed. plane-parallelism of all parts of the chamber. 5.3.2.3.
Detectors
solid-state detectors are most suitable. If large If high resolution is required, areas are needed, thin plastic detectors are best suited. If electrons should be excluded detectors of ZnS(Ag) coated on to thin plastic discs are most completely from counting, For the detection of although they are, in general, not 100% effective. convenient, below about 10 keV, and x rays, below about 3 keV, windowless low-energy electrons, For high-accuracy work fast organic scintillation counters are, in counters must be used. general, indispensable. 5.3.2.4.
Detector-resoonse
function
and efficiency
The response of the detector to the incident radiation is most completely described by that, under the probability any given the detector-response function R(E,E'), i.e. experimental condition, a radiation incident upon the detector with an energy E’ appears in This function is such that the relation the detector-output or spectrum at an energy E. between the incident radiation spectrum N'(E') and the recorded output spectrum N(E) is given by
N(E) = ti(E,E<)
N’(E’)dE’.
(5-16)
0
The complete knowledge of the response function would imply a complete knowledge of the continuous functions N'(E)and R(E,E’) for every value of E' < Emax, and for all relevant but a set of curves for a measuring conditions. That is, of course, not practicable, series of well-chosen parameters E' could be very useful. detector (e.g. thin The usual spectral reponse function of an energy-sentitive plastic) to incident radiation of energy E,, consists of a peak that is very nearly "Gaussian" around, very approximately, E,, plus a lower-energy tail that decreases with decreasing energy. However, towards very low energies a large increase occurs, due to background and secondary radiations, consisting mainly of conversion electrons and x rays. The low-energy tail is due to inhomogeneity of the detector, backscattering at the detector and its surface, window absorption, reduced charge collection (e.g. x-ray escape and field irregularities at the borders), recombination due to impurities, dust on the source or the detector, source effects, and energy loss by scattering. All these effects, except the last one, pertain to radiations emitted at their origin into the effective solid angle. These "right" radiations must be taken into account for the determination of the count rate. The radiations scattered back by the surroundings are "wrong" (i.e. not having been originally emitted into the effective solid angle), and must therefore be discriminated The choice of the discrimination level is therefore rather important. against. It can spectrum, that is reasonably be chosen at the minimum, or "valley" of the experimental located, in general, at about 2 to 3 MeV; and it is therefore, of course, an advantage if the peak-to-valley ratio is large (optimally much greater than 1O3). A comparison of the response function with the actual spectra, taken under varied experimental conditions, may then be used to estimate the influence of other disturbing effects (also see 775.3.4 and 5.3.5). The detector-response function can be obtained, to a good approximation, by using source of monoenergetic Q particles. Sources of 239Pu, 24lAm, and 244Cm electrodeposited
a
onto thin foils are, amongst others, suited for such measurements. If the source-detector chambers are properly constructed and the geometrical conditions well chosen, the measured spectra follow very nearly the response functions. The spectra obtaLned suggest that the detector efficiency is above 99.98%. 5.3.2.5.
Measurine
and testina
Drocedures
The practical procedures are, in the case those applied in indirect measurements (qf5.2.2.4 accuracy.
of direct measurements, very similar to and 5.2.4), but with more emphasis on the
a54
Radioactivity
measurements:
principles
and practice
Also the te.st procedures are similar in relative and "absolute" defined solid-angle In the latter case the tests of the reproducibility of measurements (including counting. source positioning and source preparation), of the response function (especially of the peak-to-valley ratio) and of the background (including interfering radiations) become the most important ones. Suitable test sources are prepared with long-lived a particle emitters having a small amount of secondary low-energy radiations, e.g. 239Pu or 244Cu. In a particularly interesting test source, as its this respect a z41Am source provides accurately measured coincidence activity can also be counting and by by liquid-scintillation counting. 5.3.3. Geometry-factor
measurement
The geometry factor, G = 4r/neff, is the most important term in direct low- or medium-geometry defined-solid-angle counting, because it normally takes on high values (from 10 to more than 104). It is evaluated using an analytical equation or a mathematical using the measured geometrical dimensions. In both cases the geometric data procedure, define the accuracy of the geometry factor. By far the most frequently used geometry is the on-axis point-source configuration, or close approximations to it. This geometry is the only one, that can be described by a closed analytical function (see Eq.5-3). The other important geometrical configuration is the off-axis point-source geometry, by using which solid angles subtended at extended sources can be calculated. As the exact expression for the off-axis point-source geometry cannot be integral represented many approximate solutions have been proposed in the literature and several analytically, computer programs were developed for that purpose. Let z be the source-to-diaphragm Then for off-axis distance, 2a the aperture diameter, and p the distance from the axis. smaller than the radius of the aperture (p < a), Eq.5.17gives distances of point SOUlYCS?S by far the best convergence for most practical applications (see Jaffey, 1954):
l/G =r 0.5(1
- :) D
3a2pG ___
8D5
15azp4z + ~ 32D'
[zZ
(3/4) aZ)
35aZp% _-
[24
(5/2)a2z2 + (5/8)a4] +
(5-17)
64D=
where D = (a' + z')~". Only for p = a and z/a < 0.5 is a two-term approximation less approximations for extended on-axis sources and accurate than 0.01%. Jaffey also indicates calculates their uncertainties due to those in the z, a or p values. An approximation for the general case (off-axis extended source) is given by Curtis et and Rogers (1962) tabulate, for example, 230,000 6-digit al. (1955). Masket inverse-geometry factors (l/G) with an accuracy of 10-e to 2x10m6, for z/a values from 100 to 0.3 and p/a values of between 1 and zero. Their table allows easy interpolations for most practical cases. The distance between the surface of the source and the plane of the diaphragm can be The simplest method is that of measuringthe thicknesses of the measured in different ways. length-measuring device, such as a individual parts of the chamber using a suitable Even if the sections of the chamber are very properly designed and machined, cathetometer. there will be a residual uncertainty in the source-diaphragm distance of a few hundredths together. A of a millimeter because of deformations that occur when the parts are screwed and source problems consists in using simple way to avoid intricate length measurements twin chambers and two identical detectors on the same axis and "looking" at a source placed Then only the distance between the two diaphragm edges halfway between them (Fig. 3-7b). of the source-diaphragm distance must be known with high accuracy, while the uncertainty may be larger by about two orders of magnitude. The diameter of the aperture should be measured in different directions (e.g. using measuring microscope) and a mean calculated (also see Morgan and Tolmon, 1966). The
combined
uncertainty
of
the
geometry
factor
is
derived
from
the
a
component
For more detailed investigations, more refined expressions uncertainties and Eq. 5-3. should be used, e.g. those derived by Jaffey (1954). As the relative uncertainties for all measured dimensions are about the same, the choice of larger dimensions is preferable. Source-detector distances of 10 to 50 cm and diaphragm diameters of 3 to 10 cm seem to be most suitable, if large detectors can be used. 5.3.4.
Scatterine
5.3.4.1.
General
effects
Radioactivity
measurements:
principles
and practice
855
The interaction of the radiations from the source with matter in the source, between and then by absorption in the detector can lead to counting the source and detector, minus errors. The radiation emitted originally into the ineffective solid angle (4s sr n,,,) can be scattered into the detector, while the radiation emitted into the effective detection (Fig. 3-7~). solid angle can be scattered out of it and escape The interaction of radiation with matter, although a collective effect, may be subdivided and treated as individual interactions between the particles involved, depending on their nature and energies. Considering only Q particles with energies below 10 MeV, the production of bremsstrahlung can be neglected, because of the high mass of the a particles and the low energy transfer to electrons. So that the dominating effect, at these energies, is due to electrostatic Coulomb interactions between the o particles and the electrons and nuclei of the matter traversed. These interactions can be divided into elastic and inelastic scattering. In elastic scattering only kinetic energy is transferred to the scattering centres, and the direction of motion of the incident particle is changed. In inelastic scattering, however, most of the transferred energy is spent in excitation and ionization processes. As, in the scattering of an incident a particle by an atomic electron, the transferred energy is more than three orders of magnitude greater than that transferred in scattering by the nucleus, only predominately inelastic scattering needs to be considered in accounting for the energy On the other hand, only the elastic scattering of e particles by losses of cx particles. nuclei needs to be considered for most angular effects. 5.3.4.2.
Rutherford
scatterins
and enerev
transfer
The Coulomb scattering of a particles by nuclei is governed by Rutherford's equation This equation, derived by Rutherford for the differential cross section (Siegbahn, 1965). Its in 1911, remains fundamentally the same even from newer and more refined derivations. This most characteristic property is a sin?(0/2) dependence on the scattering angle 0. relationship expresses such a strong dependence of the scattering probability on' the scattering angle, that multiple small-angle scattering and single large-angle scattering can be treated as two different effects ((g5.3.4.3 and 5.3.4.4). Another basic relation is still needed for the understanding of scattering effects in a-particle counting, namely that for the energy transfer to scattering centres by the The incident radiation as derived from the conservation laws of energy and momentum. results for the residual energy, Ei, after scattering into the differential solid angle, by a particle of mass M, at 2ssinBdB, of a particle of mass M, and initial energy E,, rest, are shown in Fig. 3-8. The most interesting result is the strong dependence of the residual a-particle energy, at a certain scattering angle, on the mass of the scattering centres. A study of this effect may lead to a reduction of this disturbance encountered in a-particle counting. (see 75.3.2.2) 5.3.4.3.
Small-arwle
scattering
Small-angle scattering can, in principle, only have an effect in defined-solid-angle counting of a particles, if it takes place very near to the border of the effective solid angle. Furthermore,it can only cause errors, if the density and, or, the nuclear charge of the particles on the two sides of this border differ considerably. Otherwise, the scattering into, or out of, this thin border layer compensate each other to a high degree, A difference of materials on the two sides of the border of the effective solid angle is nearly completely absent in low or medium-geometry solid-angle counting, but appears at the whole surface of the source in 2s counting. This may imply corrections and, or, errors of several percent (see end of this section). Measurements at very different solid angles and under very different geometrical conditions, with diaphragms having deep inner edges, with baffles changing the ratio of inward and outward scattering, show that, except for very small solid angles (G >lO,OOO), small-angle scattering changes the count rate by less than 0.01% (Blanchis, 1984). This value can also be estimated from 2s measurements. Hutchinson er al. (1976) and Lucas and Hutchinson (1976) derive the following equation for the ratio of 2s measurements, N,,, to the actual activity, N,, of thick sources: N&N, where
Z
is
the
atomic
= 0.5(1 + 0.5~1O-~Z)(l
number
of
the
source-backing
- O.Bt/R)
(5-18)
,
material,
t is the
thickness
of
the
of the a particles in the source material. Equation 5-18 is an source and R is the range At greater thicknesses the scattering effects approximation valid only for t/R < 0.15. (first parentheses) and absorption (second parentheses) can no longer be separated. 5.3.4.4.
Large-anale
scattering
Large-angle scattering can take place within the source, on the source support and holder, in the chamber gas and on the chamber walls, on the diaphragm and the baffles, on the detector window and in the detector itself and its surroundings. Its extent can be
Radioactivity
856
measurements:
principles
and practice
estimated using the Rutherford equation, and can also be measured with good accuracy. Because the scattering is proportional to the number of scattering centres the greatest effect may take place on the walls of the chamber. The calculations of the wall scattering (i.e. with a wide, not-too-long aluminium or steel show that, under normal conditions chamber), the correction due to this effect is considerably below 0.01% (Blanchis, 1984). pulses from large-angle But, if the chamber material has a low-Z value, any non-avoidable wall scattering can be discriminated against by proper choice of the energy threshold. Only if large source-to-diaphragm distances and narrow chambers are used, can scattering from the wall amount to as much as a few tenths of a percent to the count rate. If such the use of baffles (Fig. 3-7d) may improve the geometric configurations are unavoidable, measurements considerably. These baffles should be very thin and conducting, e.g. O.l-mm-thick steel or aluminium diaphragms. The scattering at the inner edge of the diaphragm is a special kind of wall scattering. It can be calculated in the same way as any other wall scattering and can easily be measured using diaphragms with different heights of the inner edge. For a steel diaphragm with a "normal" edge of 0.1 to 0.3 mm in height, and for reasonable geometries, the scattering effect on the count rate is much smaller than 0.01% 5.3.4.5.
Attainable
It has been due to scattering
accuracies
shown that, for a particles with energies can be kept below 0.01% by a proper choice
below 10 MeV, all corrections of the measuring conditions.
For other radiations such a high accuracy is out of reach. Beta particles that have energies below 2 to 3 MeV suffer much stronger multiple scattering and absorption than do o Even in low geometry their measurement is considerably disturbed by scattering, particles. Further, the continuous energy distribution of p particles especially backscattering. greatly complicates the situation, especially at low energies. So uncertainties of a few p radiation, must be expected in percent, and even considerably more for low-energy defined-solid-angle measurements of these radiations (Allen, 1965). Low-energy x rays are scattered according to the laws of the Compton effect which is analytically described by Similar calculations as for a particles can be performed using the Klein-Nishina formula. low1966). However, the final accuracy of x-ray and this formula (Bambynek, medium-geometry defined-solid-angle counting can not be reduced to less than a few tenths of a percent (Bambynek et al., 1966). 5.3.5. Absorption 5.3.5.1.
Enernv
effects loss and particle
absorotion
alpha-particle measurements can be completely The results of defined-solid-angle self-absorption in the source. It is absorption effects, especially falsified by reasonable to distinguish between two kinds of attenuation, namely energy loss and particle The first is the partial loss of the energy of a absorption (or attenuation, for 7 rays). the existence of which as an independent entity continues, the second is the particle, complete disappearance of a particle. If the remaining energy of a particle having suffered is still higher than the discrimination threshold, it will be counted and an energy loss Particle absorption, on the other hand, always causes a counting no error is introduced. For the calculation of the latter, the energy loss, for which a correction must be made. Penetration of after all absorption losses, must be known. spectrum of the particles, particles, through the edge of the diaphragm that defines the geometry, is a further effect is of the same order of For (I particles, the correction for penetration to be considered. of the measurement of its diameter. Therefore a crude magnitude as the uncertainty estimate of this correction is sufficient. 5.3.5.2.
Energy
loss. Bethe
theory.
range and ran=e-energy
relations
The dominant interaction which causes energy loss and finally particle absorption is inelastic scattering of the incident a particles by the electrons of the absorber atoms This process is rather complex as, for instance, LI particles undergo frequent (75.3.4.1). so that their mean residual charge decreases charge exchange with the atoms encountered, in an inelastic collision with The mean energy transferred, considerably with energy. is only a few electron volts, so that about lo5 collisions are needed, before electrons, theory does not Therefore, the energy-loss Bethe-Bloch the CI particle becomes absorbed. energy loss per unit describe the individual scattering process, but only the differential path length, dJ?/dx. Due
to the small
energy
transfer
percollision,
the real path
length
of a particles
is
nearly equal to their "range", i.e. the distance between the starting and end points of their paths, and the range variation, known as straggling. For the calculation of absorption effects, the relation between the mean range, R, and the energy, E, of the particles must be known. It can be calculated from the integral of the energy loss per unit path length,
R =
/E#‘,(dE,dx) 0
(5-19)
Radioactivity measurements: principles and practice
857
Bethe's theory indicates that the range is proportional to E: and (Z~,IY,Z,N,)-~, where E, is the energy, 2, the atomic number and M, the mass of the incident particle; and 2, the atomic number and N, the number of the absorbing particles per unit volume. More refined theories suggest an /?I* law for the range, a relation that had already been derived experimentally in 1910 by H. Geiger. More detailed theories lead to very complex expressions. For practical purposes several semi-empirical tables of energy losses, range and related data, with adjustments based on experimental data, are available, e.g. those by Northcliffe and Schilling (1970). The large differences between the values found in the various tables reflect the modest accuracy of these data. 5.3.5.3. Aloha-oarticle
loss due to source self-absorotion
Source self-absorption is the most important problem in a-particle counting, because it may be very large and can seldom be avoided. The model of van Schweidler (1913) (Fig. 5-9a) is very suitable for the calculation of particle absorption. It assumes a laterally infinite source, but with the same effective solid angle subtended at every point of the source (i.e. an "infinite point-source model"). As can be seen from this model, for 0,,, less than Bcmin (i.e. for an effective solid angle smaller than the critical minimum, that is equal to arccos (t-x/R,)), all particles emitted into this effective solid angle leave the source. Consequently, no net self-absorption loss can happen at all. Furthermore, for 0eff < @,*i, the spectrum of the emitted particles is relevant only at energies greater than E, = E, - E(t/cos R,,,). This can be more easily understood when looking at Fig. 5The term E(r) is the residual energy of a particle of original energy E, which has 9b. already travelled a distance r). So a discrimination threshold below E, can be chosen, which excludes all loss of particles by self-absorption. This is a fundamental asset of the low- and medium-geometry solid-angle method, except for 2s geometry, and for saturation-thick sources.
Fig. 5-9 "Extended point-source" model for the calculation of spectrum distortions due to selfabsorption in the source. a) Von Schweidler's cylindrical-coordinates model, b) spherical-coordinates model. If o,,, ' @C,,,, the absorption loss can be calculated using the model proposed by van Schweidler, who employed it only for 2n geometry, but it can easily be extended to solid angles smaller than 2asr. In such cases, using x1 = t - R,cos 8,,, (as cos 0, = (t - x1)/R, = cos 8,,,) and the activity per unit source thickness n0 = N,/t, one obtains
= (n,/2)
Xl dx[(r
_I-
- x)/R,
- ~0s
e,,,]
0
=
(N,R,/4t)(t/R, - cos @,ff)'
(5-20)
With the number of particles, N,, emitted originally into the effective solid angle,
Radioactivity
850
N,
one has,
for the relative
measurements:
n&(1 -
=
cos
absorption
8,,,)/2
yields
and
sources AN,/N,
for saturation-thick
,
(5-21)
8,,,)'/2t(l
- C0.s o,,,)
(5-22)
AN,/N, = t/2R, for 2s geometry AN,/N, = (l-co?. O&/2
for saturation-thick
and practice
loss,
AN,/N, = R,(t/R, - COS
This equation
principles
sources
(5-23)
= 0,,,/4r = l/G
,
(5-24)
(t 2 RO), and =
l/2
,
(5-25)
in 2s geometry.
The last result, Eq. 5-25, was probably first derived by von Schweidler. The simple result of Eq. 5-24, that has probably never been published, may be of some importance for the measurement of thick alpha-particle sources, such as fuel elements. 5.3.5.4.
Spectra
distorted
bv self-absorption
Figure 5-10 shows some spectra calculated for different geometrical conditions, using the model of Fig. 5-9b and following, to a certain extent, the derivation of Abrosimov and Kocharov (1962). It can be seen from Fig. 5-10 that E, is then very close to E, and the spectra are thus nearly undistorted by source self-absorption. On the other hand, effective solid angles with O,,, > Bcmin, saturation-thick sources, near-saturation-thick ones in every geometry, and all sources of any thickness in 2s geometry, give rise to strongly deformed spectra down to zero energy.
r
0
1
2
3
Source-selfabsorption-distorted Fig. 5-10 different geometries.
4
5
alpha-particle
spectrum
for
It is noteworthy that all quantitative and qualitative results derived here confirm completely those derived from von Schweidler's model (75.3.5.3) Also Haeberli et al. (1953) get compatible results, although they use a very simplified van Schweidler model with R = E (or a = b = 1 in R = & and E in MeV). If the experimental conditions are well-chosen, only the source self-absorption and the detector-response function affect the particle-energy spectrum at the detector output significantly. By folding of the self-absorption-distorted spectrum with the essentially "Gaussian" response function one obtains a spectrum that can be used for the evaluation of the finite discrimination correction (Abrosimov and Kocharov, 1962). In practice, however, conditions are chosen so that the low-energy tail of the final spectrum is so low that the particle loss by discrimination can be neglected.
Radioactivity measurements: principles and practice
859
5.3.5.5. Penetration of foils, and transmission throueh diaphraFm edees The penetration of foils by a particles can be understood and calculated in the same For a point source of activity no located just way as the self-absorption (75.3.5.3). below the centre of the absorber foil of thickness t, and again for 8,,, < B,,i,, there is no counting loss, and for 8,,, > Bcmin,one obtains the following counting loss
AN = N,(2*/4*)
=
Beit sinfl d0 = (N,/~)(cos~, - case,,,) I9 CUli" (5-26)
(N,/2)(t/R, - cos 19&
For N, particles emitted into the effective solid angle, the relative counting loss is, according to Eq. 5-21, AN/N, = (t/R, - cosO,,,)/(l -
cost',,,)
(5-27)
This yields, for 8,,, = 2a, the often used expression N=
N,
- AN = (N,/2)(1 - t/R,) .
(5-28)
The residual energy spectra after penetration can also be calculated using the model of Fig. 5-9b and an assumption for the range-energy relation. The main result is interesting in that even for a rather strong reduction of the initial energy by a relatively-thick absorber, the broadening of the original a-particle-energy distribution is relatively low, for small effective solid angles. This allows one to use, for these conditions, relatively thick cover foils that separate the source and detector parts of the central chamber This is important for without introduction of additional corrections and uncertainties. measurements of nuclides with gaseous daughter products. The assignment of a value to the effective solid angle (q5.3.3) rests on the This is never quite assumption that all particles hitting the diaphragm are absorbed. Some particles are scattered (!J5.3.4), others penetrate the edge of the diaphragm true. ThLs latter transmission effect is defining the effective geometry, losing some energy. Such a small effect can be very small for D particles, because their range is short. calculated, with sufficient accuracy, in the same way as the penetration of 9011s The situation is similar for low-energy x and Y radiations, but the (Blanchis, 1982). discontinuous behavior of the cross section of the absorber material must be taken into For x and 1 radiations with energies above about 15 keV, and for neutrons, consideration. the transmission correction may dominate and may limit the attainable accuracy (Bambynek, 1967; Lee, 1982). 5.3.6. Overall accuracy. other radiations and examples of auolication 5.3.6.1. Overall accuracy The low- and medium-geometry defined-solid-angle method is discussed here in detail Firstly, it is an example of a very thoroughly investigated for four related reasons. Secondly, the discussion shows that a good understanding of the basic physical method. processes is of decisive importance in placing this method amongst those by means of which the highest accuracy can presently be reached, under favourable conditions, namely 0.01 to This is only possible because some basic technical conditions can be met, such as 0.02%. the availability of high-resolution detectors, fast and stable electronics, and because critical corrections for scattering and absorption can be kept small and well determined. thoughtful measures Thirdly, the method is a good example of the benefit to be gained by aimed at improving the accuracy of metrological methods (75.3.6.3). And, lastly, it is a rather simple method that can be applied using relatively simple instrumentation. 5.3.6.2. Other radiations In this context only fission products are of some importance in radionuclide metrology, but of not more than limited interest to those who are engaged in the establishment of regional radioactivity-standardization laboratories. (Also see 75.3.4.5.) 5.3.6.3. Examples of apolication With the improvement of the accuracy of this method from 1% to 0.02% for 01 particles and from 10% to 1% for low-energy x and 1 rays, during the last two decades, many useful practical applications have been promoted or made possible. High-accuracy a-particle counting made it possible to measure the half lives of uranium and transuranium nuclides with an accuracy of about 0.1% (e.g. Vaninbroukx et al., 1976). These, in conjunction with a-particle activity measurements, permit the evaluation, with comparable accuracies, of the amounts of such nuclides present in different materials. This is a basic condition for reasonable safeguards work and is important for the definition of materials in the nuclear-power industry. It also improves the measurement of
Radioactivity
860
neutron fluxes using branching ratios.
fission
measurements:
foils
and
is ideal
principles
and practice
for measurements
of a-particle-to-fission
The application of the defined solid-angle method to high-accuracy x-ray counting also led to the improvement of the accuracy of fluorescence yields by an order of magnitude (e.g. Bambynek et al., 1972) with corresponding improvements in the many x-ray measuring techniques applied to-day (Knoll and Rogers, 1982), Finally, it may be mentioned once again that an improvement in any individual method contributes to the improvement of the whole system of radionuclide metrology, because of the strong interconnections between the different methods. 5.4. 4Il METHODS 5.4.1.
Iiitroduction
5.4.1.1.
Principles
As geometry factors of defined solid-angle counting are usually much larger than one, their uncertainty often determines the overall uncertainty of an activity measurement made it can be advantageous to use methods which allow one to Therefore, by that method. measure all radiations emitted into the whole solid angle, 47r sr. This is not only the largest possible solid angle, but also the one that is known with the highest accuracy. There are therefore many practical configurations for 4a, or near 4n, counting. The 4a geometry can be a great asset in 4~~7, or 4ap-7 coincidence counting, although In this respect, the counting of "wrong" radiations (such as 7 rays in in a different way. or b bremsstrahlung in the 7 counter) can cause serious errors if the the ,8 counter, This correction for coincident "right" radiations are not detected with high efficiency. solid angle are radiations vanishes only if the efficiency and effective "wrong" This respectively 100% and 4n sr, and if, in addition, there is no source self-absorption. has been achieved to high degree of accuracy, and low uncertainty, by the method of 4np-7 counting using efficiency extrapolation to 100% p-channel efficiency. 5.4.1.2.
Possible
source-detector
arraneements
and aDDliCable
radiations
4?r configurations are currently used: A relatively small (usually Many different in the centre of a detector (especially 4a gas-ionization solid) source can be placed the activity to be measured can be homogeneously mixed counters, as treated in 75.4.2); (liquid-scintillating, 75.4.3, or Ferenkov counting); with, or dispersed in, a solution "internal" gas counting (75.4.4); "internal" solid counting (e.g. a NaI(T1) crystal "doped" with ZZNa); a source (or radiation beam)can be introduced into the centre of a detectorvia a reentrant tube (well or "pin-well" detectors, 775.4.5 and 5.4.6); and a thin source can be sandwiched between two or more thin solid-state detectors ("phoswich" counting). But for high accuracy it is necessary that the 4n Many types of detector can be used. This eliminates or reduces detector should strongly absorb the radiation to be measured. and sourcemost errors (especially those due to scattering), except source self-absorption mostly nuclides emitting which must be kept small. Consequently, mount absorption, such as pure p emitters, are suited to 4?r Imeasuring absorbable radiations, strongly 4?r measuring methods lead mostly to large For weakly absorbable radiations, methods. detectors (e.g. hadron calorimeters). 5.4.1.3.
Corrections
In 4?r counting methods residual corrections determine the final accuracy, and, as in But here, especially in other methods, they can be identified with the help of Eq. 3-6. the case of the classical 4n method with foil-mounted sources in a gas-ionization counter, must be made can be measured separately the dominating effects for which corrections (Smith, 1954; Mann and Seliger, 1958; Pate,1960). These dominating effects are foil absorption and backscattering and backscatter from one They can be evaluated by half of the counter into the other, from the gas and tlhe walls. counting the pulses originating from the top and bottom halves of a 4a counter (so oriented), separately and in parallel, and also the coincidences under different conditions In this case one can write that the measured count rate, of source backing or sandwiching. is given by mt, in the top half of the counter is, to a certain approximation, m, = (n,/2)F,[l + Br + B,(l - &)'(I
-
rf)‘l
I
(5-29)
of all corrections other than for where n0 is the source activity, F, is a combination backscatter by the foil, 8, is the backscatter or absorption, pt is the fractional backscatter from the bottom half counter into the upper one, and p'f is the fractional foil Similar relations can be derived for the bottom half of the counter and for absorption. It is clear from Eq. 5-29 that the evaluation of the coincidences between the two halves. its terms is only possible by making additional experiments with changed parameters and the And it should be remembered that deviations from the assumed model use of extrapolations. But will alter the energy spectra and will complicate the evaluation of the measurements.
Radioactivity
investigations measurements. 5.4.1.4.
of
Attainable
this
kind
help
accuracies
with
measurements:
to
improve
principles
the
and practice
understanding
and
861
accuracy
ot
such
examules
The accuracies of 4a gas-ionization methods depend strongly on the measuring conditions and the nature of the emitted radiations, whereas liquid-scintillation counting of a particles of about 5 MeV in energy can be carried out with uncertainties as low as a few hundredths of a percent. Biological 14C samples can be assayed using 4?r counters filled with gas and operating in the proportional region, but with accuracies usually not much better than within several percent. Nevertheless, such modest accuracy in assays of low-energy p-ray emitters is often sufficient. Therefore, 4n counters using gas-ionization detection in the proportional region are still frequently the instruments of choice, because they are simple and inexpensive. 5.4.2.
4n urouortional
and Geieer-Miiller nas counting
Defined-solid-angle counting at low solid angles has been used for six decades since the days of E. Rutherford, H. Geiger and E. Marsden. The second half of the 1940's saw the introduction, by many authors, of the 4rfl counter for the assay of @-particle, and later u-particle, sources. Pate (1960), in an extensive review, has referred to the different experimenters and authors of that period. Also at about the same time, Mann and Parkinson (1949) and Engelkemeir and Libby (1950) used the internal ("4n") Geiger-Miiller gas counter for measuring 14C activities in samples of CO,. An elementary 4aa or 47r,6counter consists of a source mounted on very thin plastic film (coated with a thin conducting film), completely surrounded in 4?r steradians by two proportional or Geiger-Miiller gas counters in various configurations (see Figs. 5-11, 5-12 and 5-13). More recently the 4a geometry has been applied to LI-, p- and r-ray low-level-activity metrology using liquid scintillation and solid-state detectors, as, for example, NaI(Tl)-shielded CaFz(Eu) sandwich detectors for a particles (Mayhugh et al., 1978); liquid-scintillation techniques for a- and p-particle, and electron-capture sources; and reentrant pin-well NaI(T1) crystals, and two large 4rr (203 mm (8 inch) in diameter) NaI(T1) shallow-well crystals arranged in 4rr geometry for the assay of photon emitters (J.M.R. Hutchinson et al., HN, 1973, p. 187).
Fig. 5-11 Cut-away representation proportional counter.
Fig. 5-12 Cross counter.
section
of a cylindrical
of a spherical
4a
gas-flow
4~
gas-flow
proportional
Radioactivity
862
measurements:
principles
and practice
Cut-away view of a pillbox-type 4a gas-flow proportional Fig. 5-13 counter. The success of the 4aa and 4r@ proportional or Geiger-Miiller counters depends primarily on avoiding losses of a or @ particles in the source and source mount and this involves the preparation of exceedingly thin conducting films on which the sources can be deposited in the form of drops and then spread out to form extended thin layers by means of wetting or seeding agents, the latter providing nucleation sites where large numbers of small source crystals are produced on drying (also see 73.3.3). Carrier should be kept to a minimum and should preferably consist of hydrogen ions provided by the addition of small amounts of acid. Carriers alone of the same salt may produce "clumping" with "islands" of source material separated by areas devoid of deposit, as shown by Seliger and Schwebel (1954) for KI by electron-shadow micrography. The basic source mount can be a very thin plastic film normally of VYNS (a polyvinylchloride-polyvinyl-acetate polymer) prepared by floating an organic solution of the plastic on water from which it can be lifted after evaporation of the solvent. The film then has a thin film of gold (or gold-palladium) evaporated upon it to render it conducting (to complete the cathode surface) and its surface density can be of the order of 1 pg cmez but should not be greater than about 10 fig cm? for routine use. The efficiencies for 4ao and 4x8 counting can be measured using radionuclides decaying In an international by o- and p-particle emission followed by prompt -/-ray emission. comparison of measurements of 241Am sources (Rytz, 1964) 4aa sources were found to have an Using efficiency of about 99.6 percent implying a source self-absorption of 0.4 percent. the same coincidence-counting technique, Gunnink et al., (1959) and Merritt et al., (1959) For measured the source self-absorption of beta particles for several radionuclides. sources having a mean superficial density of 2 pg cmmz, the source self-absorption varied from one percent for 24Na p particles (Em,, = 1.39 MeV) to between 20 and 40 percent for the 88.5.keV p-particle transition in the decay of 13"Cs. Other techniques include electrospraying of deposition on specially prepared ion-exchange-resin p. 353; and 73.3.3).
sources (Merritt er al., pads (Lowenthal and Wyllie,
1959) and HN, 1973,
Gas-proportional counters of 4~ geometry that can be operated at elevated pressures in order to increase the detection efficiency by decreasing the P-particle range in the counter, for the purpose of carrying out coincidence counting using the method of efficiency extrapolation developed by A.P. Baerg and his colleagues (see Baerg, HN, 1973, These counters can be operated at p. 143; Legrand et al., HN, 1973, p. 101; NCRP, 1985). 70 and 75 atm. (7.6 MPa), respectively, and can be used to obtain x-ray spectra following electron capture of nuclides with rather high atomic number. A 30.cm-diameter cylindrical 4a gas-flow proportional counter operated at atmospheric pressure has been used by Troughton (1977) to obtain the K and L+M x-ray spectrum following internal conversion in losmAgin the decay of l%d. A very extensive literature exists on both 471 gas counting and on the preparation suitable sources for 4n counting. Many useful references to this literature are given the Herceg Novi Summer School Proceedings (Herceg Novi, 1973) and in NCRP (1985). 5.4.3.
Liauid-scintillation
5.4.3.1. The
of in
counting
General preparation
of
sources
for
use
in
liquid-scintillation
counting
(LSC)
has
been
Radioactivity
measurements:
principles
and practice
863
process has been discussed described in q3.3.4.3 of this report, and the scintillation This section will outline the experimental procedures developed in the briefly in 74.6.2. It is, apart from often negligible applications of the method to radionuclide metrology. wall losses and escape from the upper surface of the scintillator solution, a method in which the effective solid angle is equal to 4~ steradians. The liquid scintillator comprises an organic scintillator such as anthracene dissolved The radionuclide to be assayed is introduced into the in a suitable aromatic solvent. [3H]-toluene or such as a labelled organic compound, scintillator either (i) as (ii) as an aqueous solution such as [%-water, using a second solvent [%-n-hexadecane, emulsion, (iv) as a finely divided solid (iii) as a liquid-liquid such as ethanol, or (v) as a precipitate or a filtrate on a solid support suspended in a gel scintillator, The counting sample is usually contained in a such as filter or anion-exchange papers. screw-cap counting vial 27 mm in diameter and some 60 mm in height, viewed by cylindrical, phototubes (in various modes of non-coincidence, or one, two or three electron-multiplier and the whole assembly is mounted in a refrigerated in double or triple coincidence), A double-coincidence system is especially useful for the reduction of phototube enclosure. The sample backgound "noise" as such "noise" pulses occur only randomly in coincidence. Further details should be rigorously purged of oxygen which is a strong quenching agent. "The Application of Liquid-Scintillation are given in Monograph BIPM-3 (1980), entitled In addition to six review articles this monograph Counting to Radionuclide Metrology". of which attention could well be given to the book by contains just over 300 references, and Spernol (1965), Birks (1964), and articles by Horrocks and Studier (1964), Vaninbroukx sample preparation Gibson and Gale (1968), Houtermans (1973), Peng (1977, that describes Another NCRP (1985) and Coursey et al. (1986). and contains some 250 references), and short treatise by Dyer (1980) has much practical advice and over 100 excellent references. Precautions must be taken against chemiluminescence and delayed phosphorescence, the latter resulting from sample or even vial-cap (Dyer 1980) exposure to ultra-violet light. Garfinkel et al. (1965) have even observed that vials closed with white plastic screw caps gave up to 44% higher count rates than the same vials closed with black plastic screw caps. 5.4.3.2.
Basic
urincioles
Liquid-scintillation counting can be applied to the assay of o-particle and Gibson has pointed out (BIPM, 1980) p-particle emitters, and of some electron capturers. that the energy deposited in a scintillator by a 5-keV electron if converted to light with But 95 to 99 percent of the energy is a wavelength of 425 nm would produce 1,700 quanta. so that in a typical scintillator it could give dissipated as heat in the scintillator, Of these, according to Birks (1964), some 40 percent will be rise to as few as 17 photons. lost by ionization quenching, so that a 5-keV electron may ultimately giverise to only as But these few as three photoelectrons incident upon the first dynode of the phototube. three photoelectrons are the mean of an assumed Poisson distribution of photoelectrons There is thus a finite generated at the photocathode and striking the first dynode. probability that no electron will be incident on the first dynode; a probability that is This is called the given, for a mean of three electrons, by em3 which is equal to 0.05. The assumption of the Poisson distribution has been tested and zero-detection probability. strongly confirmed by Houtermans (1973) who calcualted the frequency spectrum at the output of the phototube for the arrival of single electrons (so-called monos), and two, three or One more electrons for the 5.9-keV x rays and Auger electrons frm the decay of 55Fe. electron incident upon the first dynode of the phototube may give rise to an output pulse at the anode of between lo6 and 10' electrons. Likewise if other photons striking the cathode of the phototube give rise to 0, 1, 2, 3, or more photoelectrons at the first dynode, then there will also be a probability of in general, this effect is zero detection at the second dynode, and so on. But, negligible. The x rays and Auger electrons of 55Fe are just about at the threshold of detection for most LSC systems. Moreover, the resolution of the system is so poor that the threshold On the other hand, this poor resolution enables linear extrapolation is not well defined. of discriminator data to be carried out for B-particle emitters with high maximum energies, above about 150 keV (Vaninbroukx and Spernol, 1965). The effect of zero-detection probability is only serious with low-energy ,+particle emitters such as 'H and I‘C, for which the extrapolation to zero energy is no longer monotonous. This problem was largely solved by Horrocks and Studier (1964), Bryant ef al. (1967) These authors fitted curves based on the Fermi probability and Gibson and Gale (1968). distribution of p decay to the experimental data above the region of zero-detection probability, which arises simply as an artefact of the phototube. This method was further developed by Grau Malonda and Garcia-Toraiio (1982), and used by Ishikawa (1984) and Coursey in terms, usually, et al. (1986). The method is, however, a relative method of calibration in effect the tritium calibration covers the low-energy part of tritiated-water standards; It is thus, strictly, a of the spectrum where the detection probability can be zero. method of efficiency calibration, rather than of efficiency tracing, the latter term having been already preempted by Campion et al. (1960) for a method whereby a +‘?.y-emitting nuclide was used to standardize a pure @-ray emitter by coincidence counting (75.2.2.4). Grau
Radioactivity
864
measurements:
principles
and practice
Malonda and Garcia-ToraAo (1982) have presented the theory double-phototube system, and it has been described and the theory (1985) and Coursey et al. (1986).
of their method slightly extended
for a in NCRP
This method of relative calibration also involves the figure of merit of the The scintillator-phototube system and the empirical quenching parameter of Birks (1964). figure of merit has been defined by Gibson and Gale (1968) as the number of electrons at the first stage of the phototube divided by the energy deposited in the scintillator; by Birks (1975) as the pulse amplitude at the phototube anode divided by the energy deposited in the scintillator; and by Grau Malonda and Garcia-Toraiio as the energy deposited by a particle inthe scintillator (corrected for ionization quenching and wall effects) divided by the average number of photoelectrons incident upon the first dynode of the phototube. The ionization quenching is usually computed using an empirical equation due to Birks (1964), but it can also be measured by several methods, of which those using an extended y-ray source to produce Compton electrons in the liquid scintillator or the wall are now most frequently used (NCRP, 1985). 5.4.3.3.
Relative
calibrations
bv liquid-scintillation
counting
As mentioned in the preceding section a very useful relative method of LSC calibration can be achieved in terms of the Fermi probability distribution of p decay, the quenching the escape of primary particles from the upper parameter Q(E), a term W(E) representing surface of the liquid scintillator or to the walls with insufficient unquenched ionization to be recorded, and the figure of merit of the LSC system, as 0 keV_', the average number of photoelectrons striking the first dynode of any one given phototube divided by the energy, E, of a detected particle. Generally the method employs an LSC system in which the scintillations from the vial are presented to the two phototubes operated in coincidence to Only a brief description of the method reduce phototube noise and spurious pulses. follows, and the interested reader should consult NCRP (1985) and Coursey et al. (1986) more detailed information and further references. If a particle of energy E deposits all its energy in the scintillator then the number of electrons incident on the first dynode would on an average be #Q(E)W(E) if there were no zero probability of detection. But for an average number of qEQ(E)W(E) electrons the Poisson the first dynode of the phototube distribution gives a incident upon probability) equal to exp(-oEQ(E)W(E)), and probability of none (i.e. the zero-detection But for two the efficiency of a system with one phototube would be 1-exp(-qEQ(E)W(E)). background-reducing coincidence mode the efficiency is equal to phototubes in the and using the Fermi probability In the case of @-ray spectra, [l-exp(qEQ(E)W(E),12. P(Z,E)dE, the efficiency for the system in this coincidence mode, ec, for pdistribution particle energies between 0 and Em,,,, is
JE$?,E)[l
exp(l
- ~EQ(E)W(E)]]'
dE
-0
e,
(5-30)
=
EBmax
s P(Z,E)m 0
In the Grau Malonda and Garcia-ToraAo approach two radionuclides, one of known the activity, are introduced into identical liquid scintillators with equal quenching, figure of merit 7 of the system may be evaluated from the radionuclide of known activity Fermi probability and used to calibrate that of unknown activity, using the appropriate function for each radionuclide. In practice a small correction for quenching measured by Using an NBS [sHj-water standard, the Horrocks (1976) H-number method can also be made. r4C samples with an overall uncertainty (random plus Coursey et al. (1986) calibrated non-random) equivalent to one estimated standard deviation of 0.2 percent. Gibson and Gale use calculated values for the exponent in Eq. 5-30 (See Ch. IV by It therefore more strictly belongs J.A.B. Gibson in BIPM, 1980, or Gibson and Gale, 1968). to the next paragraph, but is a theoretical analogue of the more recently developed Grau But it is interesting to note, as pointed out Malonda and Garcia-Toraiio relative method. system and using typical values for 0, Q(E) and in NCRP (1985), that for a single-phototube qEQ(E)W(E))] is essentially equal to W(E) given by Gibson and Gale (1968), [l exp(1 The reason for this is that, while the unity between E = 20 keV and E = 3.5 MeV. efficiencies Q(E) and W(E) increase m and decrease from unity, respectively, with increasing energy E, the decrease in W(E) is more than compensated by the increase in E up to about 3.5 MeV (see Fig. IV-6 in Ch. IV by J.A.B. Gibson in BIPM, 1980). 5.4.3.4.
Direct
5.4.3.4.1.
calibration
bv liauid-scintillation
counting
Extrapolation
the For P-particle emitters with maximum energies greater than about 150 keV, losses due perturbation due to the "mono" spectrum (H. Houtermans, HN, 1973, p. 121) and to zero-detection probabilities at low energies become completely insignificant compared with the total number of b particles summed over the energy spectrum.
Radioactivity
measurements:
principles
and practice
865
Because the linear energy transfer (LET) of a particles is so much greater than that a liquid the ionization density in the "wake" of an a particle traversing of electrons, Thus the possibilty for scintillator is about 10 or 20 times greater than for electrons. recombination is much greater in the a-particle track than in the track of an electron, and In fact a therefore ionization quenching (a term coined by Birks, 1964) is also greater. 5-MeV a particle will deposit a net amount of unauenched energy in the scintillator that is equal to that deposited by a fl particle of about only 500 keV. Thus both a-particle emitters and energetic o-particle emitters can be very well Vaninbroukx calibrated by extrapolation of a discrimination curve to zero pulse height. and Spernol (1965) obtained calibration values for the activities of samples of 241Am and several high maximum-energy flemitters that agreed with values obtained by independent methods to better than kO.5 percent. 5.4.3.4.2.
Double-
and triple-coincidence
counting
methods
(1970) have developed a system of non-linear equations for a Kolarov et al. two-phototube LSC system giving the figure of merit and efficiency of detection for each for both in the summing mode and for the two in coincidence. When phototube separately, [%-water standard they applied to the measurement of a National Bureau of Standards obtained a result that was about 4-percent different from the certified value (R. Vatin, Ch. V in*IPM, 1980).
Pochwalski et al. (1981) introduced another phototube to give a symmetrical threephototube LSC system and measured the activity of the p-particle emitter in the liquid ratio known as the TDCR scintillator by measuring the triple-to-double coincidence cg are the respective counting efficiencies of all three phototubes in method. If ZT and coincidence and all three phototubes arranged in double coincidence, then eT = N,/N, and coincidence ratio K is given by Eo = N,/N,z whence the triple-to-double N,
ET
NO
'D
K=-=-_.
(5-31)
eT and They then changed the optical efficiency using a coiled spring and so varied As K increases with increasing efficiencies, cT, eD and K all approach EDI and also K. These authors fitted fourth-power unity and N, and N, approach to the disintegration rate. polynomials to the values of cT and cD to enable them to extrapolate to K = 1.
Broda
Extensions of both the theory and applications et al. (1988) and Pochwalski (1988).
of
the
TDCR
method
are
discussed
by
Wu et al. (1987), have described an interesting method for the direct standardization of 14C, in the form of ['%-n-hexadecane in solution in toluene together with the Their phototubes. scintillator PBD, in a vial viewed by two matched electron-multiplier circuitry was such that count rates N' and N" from each phototube could be recorded and (The phototubes here were used in the also the coincident count rates, N,, between them. mode to which Eq. 5-30 true coincidence-counting mode and not in the noise-reduction channel allowed integral pulseSingle-channel analyzers in each phototube applies.) with an appropriately fitted polynomial, to amplitude discrimination and extrapolation, and missed ionizing events in the "through" electronic noise zero pulse amplitude, Coincidence counting enabled the actual average rate of numbers of photons scintillant. emitted from the vial to be measured; a method first applied to measure the alertness (efficiency) of two observers by H. Geiger and A. Werner in 1924 (as illustrated in Fig. & The rate of numbers of photons exiting from the vial was also 6 in Mann et al., 1980). obtained using two optical-diaphragm discriminators with extrapolation to zero reciprocal This phototube anode current, I, that was equivalent to an infinitely wide-open aperture. use of a diaphragm as an optical discriminator is closely analogous to the use of a coiled spring to alter the detection efficiency in the TDCR method, described above But it is not completely clear that any further optical-discrimination correction for zero-detection probability needs to be made to the result obtained by coincidence counting In fact Fig. 3 of the Wu et al. paper for the activity of 14C, as measured by Wu et al. seems to confirm this in that a plot of N'N"/N,N, against X,/I shows N'N"/N,N, essentially This may be associated with the fact, equal to unity for values of I,/I between 1 and 6. term in Eq. 5-30 mentioned above, that between about 20 keV and 3.5 MeV the exponential Therefore, as indicated in the first sentence of differs but little from unity. 75.4.3.4.1, perturbations and counting losses due to zero detection become insignificant Thus the assay of 14C for B-particle emitters with maximum energies above about 150 keV. is a borderline case, and it would be of interest to apply the method of Wu et al to 'H for which the relative effect of zero-detection losses would be so much greater. 5.4.3.4.3.
Coincidence
counting
counter is very As with many other detectors of 4a geometry, the liquid-scintillation Frequently the well suited for use as the j3 detector in P-7 coincidence counting. The flat face of the scintillator source is contained in a cell of hemispherical geometry. re-entrant-well cell sits on the cathode end of the phototube, with a 4-cm or 5-cm-diameter
Radioactivity
866
measurements:
principles
and practice
An intercomparison of measurements of the activity NaI(T1) detector placed over the cell. of a 1%~ solution between four international laboratories using the method of 4*B(LS)-7 coincidence counting by efficiency variation is reported in BIPM (1980). The extreme limits to the range of 13 reported results was only 0.6 percent. 5.4.3.5.
Other
methods
"Dual-label" assays, especially of samples containing mixtures of 'H frequently made in laboratories making LX measurements in connection with applications in the life sciences. The method is described in NCRP (1985) the method used to make the necessary quench corrections. Other pairs of that may be assayed by this method are 3H and "S, 3H and 3zP, and l'+Cand 36C1.
and 14C, are radioactivity together with radionuclides
5.4.4. Many radionuclides such as 3H, r"C (as CO,), 37Ar and samples of other radioactive noble gases have been calibrated by the method of internal gas counting using a suitable proportional-counting gas such as methane containing a small but measured amount of the gas to be calibrated. This is a 4?r method that avoids the problem of source self-absorption. It was probably first described in 1947 by Miller and by Brown and Miller, using internal gas counters in the Geiger-Miiller region. Later, similar measurements were carried out by Engelkemeir and Libby (1950) using single counters that were cylindrical in form with an axial wire anode. As the length of the counter was usually much greater than the radius of its cylindrical cathode, there was a uniform electrical field strength between @ihe anode wire and the cylindrical cathode wall over much of its length. But at each end of the counter the electrical field would be distorted and end-effect corrections had to be made (see Fig. 5-14 and Spernol, 1967). For cylindrical counters of small diameter there might also be a significant correction needed because of the loss of radiation to the walls without creating one ion pair in the counting gas.
Schematic representation of the electric field strength Fig. 5-14 along the anode wire of a proportional counter for internal-gas counting (after Garfinkel et al., HN, 1973). A somewhat simpler method, but which eliminated the need to calculate end corrections was used in 1949 by Mann and Parkinson (also see S.B.Garfinkel et al., HN, 1973). This method was based on the use of two (and later, three) cylindrical gas counters of different as possible. lengths, but, in every respect other than length, constructed as indentically The anode-wire supports were precisely machined end plates so that (as illustrated schematically in Fig. 5-14) the difference in count rates between the two counters should give a count rate for an ideal counter with uniform electric field and needing no correction for the distortion of electric field at the anode-wire supports at each end of the counter. It was important, however, that the shorter counter should not be so short that the electric field should never attain a uniform value along the length (in the middle) of the counter. At the National Bureau of Standards two sets of three such compensated internal gas One set has cylindrical cathodes of copper counters have been in use for some 30 years. and the other set has smaller but similar cathodes of stainless steel. Any residual wall effect was eliminated by operating the counters at different to zero pressures, plotting count rate against the reciprocal pressure, and extrapolating In many cases such extrapolations the reciprocal pressure (i.e. to infinate pressure). possibly because ,9 showed no change in count rate as a function of inverse pressure, particles incident upon the wall induce the emission of secondary electrons that then reach Such an effect has been observed by De Roost et al. (1969) in the form of the anode. equally spaced afterpulses in a 4nfl proportional counter, the time interval between pulses corresponding to the time of transit between cathode and anode. Other configurations of internal gas counter have been designed by Spernol and Denecke (1964) and Olsson et al. (1962). The former consisted of a single cylindrical counter with specially designed guard electrodes to preserve the uniformity of the electrical field; the latter consisted of a single cylindrical counter with one end so constructed that it could NBS tritiated water standards be moved back and forth to alter the counter length. calibrated by the former (Spernol and Denecke) counters agreed with the NBS value to 0.2 In many ways the Olsson et al. design, although more percent (Mann and Spernol, 1964). complicated than the simple NBS design, should have an advantage in that their counter both configurations. Here in the long and short position has exactly the same end-support
Radioactivity
measurements:
principles
and practice
867
again, however, the NBS and Uppsala results for the half life of "C (Godwin, 1962) were in very close agreement. Internal gas counting systems must be equipped with suitable gas-handling and equipment pulse-shaping (for pressure, volume and temperature) and quantifying The NBS internal gas counters are provided with a cryogenic preamplifiers and amplifiers. filling and mixing system, and the count-rate data from the six counters are collected simultaneously on a minicomputer that can be operated, if required, as a multichannel analyzer (S.B. Garfinkel, et al., HN, 1973, p. 59). An ingenious method of position-sensitive internal gas-proportional counting in tubular counters with resistive axial anode wires or metal-coated glass fibres has been developed by Mori and colleagues, in order to eliminate the counter end corrections electronically. A paper (Mori et al., 1987) given at an ICRM seminar on Techniques in Radionulide Metrology held in Rome in 1987 describes the method and cites previous references, while a later twenty-year review of radioactivity measurements made at the 1987) gives a short but very Nagoya University Department of Engineering (Watanabe et al., comprehendible description of the method. Very briefly, the counter described by Mori et al. (1987) consists of a 95.cm-long and 20.pm-diameter nickel-chromium anode wire, with an electrical resistance of 2.09 kn, stretched along the axis of a 4-cm-diameter cylindrical stainless-steel cathode. Each end of the wire went through a lumped resistance and charge-sensitive amplifier to a "position processor". If, for convenience of presentation, we think of the cathode as being horizontal with a left (L) and right (R) end, then for a charge Q collected from an ionizing event occurring at a distance x from the left end of the anode wire of length y, the ratio of the charge outputs from each end of the anode wire is given by the simple expression QL/(QL + QR) = x/r. The authors estimate an overall uncertainty of fl.l% in their measurement of the activity of a sample of [r4C]-methane, but anticipate a lower uncertainty by making more precise measurements of the effective volume and by using a "partially resistive anode wire". 5.4.5. Direct activitv measurements with reentrant-well crystals 5.4.5.1. Introduction In 1963, Brinkman and Aten. described how a single NaI(T1) crystal could be used, in conjunction with a multichannel analyzer, to measure the activity of a radioactive source that decayed with no direct transitions to the ground state of the daughter nucleus, but that emitted two cascade photons in coincidence. This method of sum-peak coincidence counting can also be practiced with two shallow-well-type NaI(T1) crystals placed face-to-face in 4s-sr geometry, or in essentially Oa-sr geometry, within the reentrant cavity of a so-called well-type NaI(T1) crystal (see J.M.R. Hutchinson et al., HN, 1973, p, More recently "pin-well"-NaI(T1) crystals have been fabricated that have wells 187). measuring between 2 and 8 mm in diameter from which the geometrical escape window from the open end of the reentrant well is only of the order of one or two percent. Hutchinson and Mullen (1983) report experiments with an all-the-way-through "well" in which the geometrical escape factor is 1.296% of 4s. 5.4.5.2. Available types. applications and calibration A well-type photon detector is a right-circular cylindrical single crystal with a coaxial reentrant cylindrical hole (well) cut to a depth of about 0.5 to 0.6 times the height of the cylinder. It may also be cut, with greater accuracy, all the way through (see 75.4.5.1). The source to be measured is placed in the bottom of the well (or half-way through the bottomless well) so that the detector "views" the radiation from the source at the largest possible solid angle, of nearly 4rr sr. The detector material is most frequently thallium-activated sodium iodide, NaI(Tl), but cesium iodide, CsI(Tl), bismuth germanate. Bi,Ge,Olz (now, generally referred to as BGO), and cadmium tungstate, CdWO,, are also used (see y4.6.1 and p. 33 of NCRP, 1985). It should be noted that 99 percent of 200.keV photons are absorbed on traversing 34 mm of NaI(T1). For CsI(T1) and BGO the corresponding values are 23 mm and 9 mm, respectively. These figures help to choose the required crystal dimensions. Semiconducting crystals (Ge(Li)or HPGe) can also be used to construct well-type detectors (also see 7 5.4.5.5). Such detectors are very useful instruments for relative and direct ("absolute") measurements of activity or of photon-emission probabilities, because the detection efficiency is in general not too strongly dependent on source position or on photon energy. The measurements with large well-type detectors are much less time consuming than 4?r(PC)--, coincidence measurements and are often of comparable, if not superior, accuracy: the latter being the case for certain nuclides with complex -/-ray spectra. If a well-type
scintillation detector is to be used to calibrate a source of unknown
868
Radioactivity
measurements:
principles
and practice
activity, its detection efficiency for the radionuclide in question must be determined, either from calculation or by measurement. The calculation of the total efficiency is if accurate dimensions of the crystal and its housing are known and accurate possible attenuation coefficients are available (Mannhart and Vonach, 1976). Several corrections such as for scattering in the material surrounding the detector or in the lining of the well, for bremsstrahlung and source positioning have to be evaluated. Mannhart and Vonach (1978) have further reported a method for an experimental determination of total efficiency by measuring count rates using suitable single-T-ray sources the activities of which do not need to be known accurately. For these measurements the sources are placed either at the bottom of the well or in an exactly reproducible position outside, on the detector axis and some 10 cm away. By using an iterative procedure, they obtained efficiencies with uncertainties of 0.3% or less. For sources emitting coincident y rays, the uncertainties of the calculated efficiencies were even considerably lower. The important fact that efficiency calculations for radionuclides with complex r-ray spectra are often more accurate than those for single r-ray emitters can be understood from the following simple considerations. If two y rays in cascade are detected with efficiencies e, and ez, respectively, the probability of non-detection is l-e that is equal to (1-el)(l-ez). If the decay scheme comprises n independent branches with partial abundances, h,, and k, coincident transitions from each branch i, the total efficiency becomes e =
; h,[l - I?(1 - ei,)] i=l j=l
,
(5-32)
where eij is the efficiency of the jth coincident 7 ray from the ith branch. The inefficiencies, 1 - e,,, are already quite small and their products even much smaller. Therefore, in the case of complex decay, the calculation of the total efficiency can be highly accurate, even if the parameters of the decay scheme are not accurately known. For practical applications Eq. 5-32 may have to be completed in order to take into account the effects of bremsstrahlung, conversion electrons, characteristic x rays and of discrimination thresholds (see Winkle?? and Pavlik, 1983). Among the radionuclides for which Pavlik and Winkler (1983) could measure the activities with uncertainties between 0.1% and 0.7% the following multi---ray emitters should be noted: 56Co, '5Se, 82Br, 'lomAg, lzsSb, 13'Ba, 134Cs, 15'Eu, l"Ta, and "'Ir; and also some single---ray emitters such as ?Zr, 54Mn, "Sr and 13'Cs. Instead of using total efficiencies, the measurement of activities by photopeak analysis is sometimes preferred. But an experimental measurement of the photopeak efficiency is of limited accuracy because of uncertainties in the evaluation of peak areas, geometrical dimensions and of multiple scattering processes, and of attenuation coefficients (Fig.41 of NCRP, 1985). 5.4.5.3.
Detectors
and counter
construction
The crystals used for 4vr(NaI-Tl)7 measurements have typically a diameter and a thickness of 127 mm (5 inches) and are mounted as an integral unit on top of a suitable electron-multiplier phototube. More details on the systems used in five laboratories are presented in a review article by Ballaux (1983). Dimensions can be made to order and measured by the manufacturer to within 0.05 mm or better. The outer surface and the inside of the well must be covered with light-reflecting layers (e.g. Al,O, or TiO,). The reentrant well is usually lined with aluminium to protect the crystal surface and also to reflect emitted light. As an example, the NaI(T1) detector described by Mannhart and Vonach (1976) was placed inside a lead shield of 5-cm wall thickness and lined with graded layers of Cd, Cu and Al, in order to prevent x rays generated in each previous layer of Pb, Cd and Cu from reaching The background count rate thus obtained was about 33 5-l for a threshold the detector. energy of 22 keV. Legrand et al. (1975) employed a somewhat smaller NaI(T1) crystal (102 x 127 mm) with a 50.mm-deep well of 12.mm diameter. The inside of the well was covered with Al,O, paint (0.5-mm thick) and lined with 1 mm of Be. We may also mention the NBS sun-peak method that utilizes two 203 x 102.mm crystals that can be operated in the summing, coincidence and anticoincidence modes Hutchinson et al., HN, 1973, p. 187). 5.4.5.4.
Practical
urocedures.
The total -,-ray efficiency of a well-type crystal depends different behaviour: From about 60 keV better than 0.5%. and a accurate,
source Dreoaration
NaI(T1) (J.M.R.
and counting
(the ratio of the numbers of detected to emitted photons) There are three regions of rather on the photon energy.
to 200 keV, the efficiency is close to 100% and can be calculated to For energies above 200 keV the calculations are considerably less calibration by means of single-y-ray standard sources may be
Radioactivity
measurements:
principles
and practice
869
preferable. An uncertainty of between 0.5 and 2.0% may then be reached in the region below 1.25 MeV. At the latter value the efficiency is in general between 60 and 70%. In the region below 60 keV the efficiencies vary rapidly with energy. Moreover, there are not many reliable calibration energies in that region and efficiency uncertainties range from 5 to 15%. The influence of the material surrounding the scintillation crystal and of the source dimensions must also be measured if full advantage of this method is to be taken. If the crystal dimensions are not known accurately enough, an alternative method for measuring the detector efficiency and its energy dependence can be applied, as described by Mannhart and Vonach (1978). This method requires the measurements of count rates from the same uncalibrated sources inside and outside the well. By using either single-r-ray sources or sources emitting two coincident -y rays, an efficiency curve covering the energy interval from 480 keV to 1.84 MeV has been evaluated by these authors. The preparation of sources for 4?r7 counting does not involve the same regarding thickness of source and backing, as do sources for particle counting.
criteria, Very thin
sources and backings are needed only for nuclides emitting a large proportion of low-energy In most other cases the procedure consists of dispensing a weighed drop of the photons. After evaporation of radioactive solution on to a plastic foil (mylar, cellulose, etc.). the solvent, which may be accelerated by infrared heating, the source is covered by a similar foil and welded on to the first, thus forming a sandwich. It is possible to use liquid sources in thin-walled polyethylene tubes, or even very 1984), provided that adequate corrections are calculated. thick solid sources (Winkler, Marinelli beakers that contain bulk sources and surround a NaI(T1) crystal detector are very useful for the assay of environmental samples (see p. 270, NCRP, 1985). But the sources are, in An outstanding advantage of 4x7 counting is its simplicity. general, much weaker than for particle counting because pulse pile-up must be avoided and Count rates are generally not higher relatively long dead times (10 MS) have to be used. than about 5000 5-l , depending on the background count rate. The discrimination level should be kept as low as possible (10 to 25 keV), depending on the energy level of the background and electronic noise. The latter may correspond to less than 8 keV. 5.4.5.5.
Corrections,
evaluation.
accuracv
and testing
As a well-type detector can be used in a great variety of situations as to the source and the instrumental details, it is necessary to configuration), (type of nuclide, calculate or measure, in each case, a number of correction factors in order to make the Because the results of efficiency calculations are best use of its measuring capabilities. valid only for the naked crystal and for point-like sources, the influence of the material surrounding the detector and that of the light-reflection layers and linings inside the well must be taken into account by separate measurements or calculations. The same is true for corrections due to source position, geometry and thickness. Special radiation effects bremsstrahlung) as well as the influence of a finite (B rays, 7-7 angular correlations, discrimination threshold must also be taken into account. The Lining of the well diminishes the efficiency of a well-type crystal detector. But in the vicinity of the iodine absorption edge (32 keV) the absorption does not vary exponentially with photon energy. In that energy region the interactions are mostly by photoelectric effect in the innermost layers of the crystal well, from where more than 20% of the iodine x rays escape and are lost. Therefore, the choice of the discrimination threshold should represent a compromise between the effects of absorption of primary x rays and the escape of iodine x rays. Low-energy 7 or x rays may create some difficulties because of the presence of a finite discrimination threshold, which is always required to prevent interference from electronic noise. This is especially so if a considerable part of a peak lies below the threshold. This effect may be enhanced by low and unstable detector resolution. A low threshold may therefore be advantageous. On the other hand, it is possible to suppress the detection of the low-energy part of the spectrum by using an absorber (1 mm of perspex causes a reduction by a factor of 100 or more) and to take this into account by calculation. The corrections for the effects of extended and, or, thick samples are generally measured experimentally, but can also be calculated. It should be noted that, above 200 keV, thick samples feign a higher efficiency because Compton-scattered radiation in the source shifts the energy to values for which the efficiency is greater. From a practical standpoint, the central question is: how accurately can activities be measured? Several authors have measured sources of very well- known activity, such as those measured in international comparisons ((2.2.3), with their own well-type detectors, The differences were generally in the range of 0.1 to 1 percent (see Ballaux, 1983). As comparisons are more difficult to perform with thick and large-volume samples, there is not much information available on such measurements.
Radioactivity
870
5.4.5.6.
Applications.
examules
measurements:
and suecial
principles
and practice
systems
The use of 4sy measurements by large well-type detectors is a welcome alternative to 47r(PC)-7 coincidence counting, especially with nuclides decaying by electron capture and subsequent multiple-~-ray emission. In those cases the counting efficiency and hence the The simplicity and rapidity of 4lrr measurements predispose accuracy are particularly high. one to use this method for routine radioactivity assays of short-lived nuclides, such as used in medicine (?? ="'Tc, l'lIn, lZ31) 16gYband "lT1, which are being increasingly Vatin, 1983). The possibility of measuring thick sources of bulk samples with high accuracy offers sections of numerous advantages in measuring activation cross neutron-induced the A further interesting application has been reported for the measurement of reactions. counting. solution samples of g9Tc by bremsstrahlung A different concept of a 4x7 counter has been developed by Denecke (1984), in the form of a 4nCsI(Tl)-sandwich spectrometer. It consists of two crystals, each of 50.8-1~1 cavities of lo-mm diameter, machined in diameter and 25.4.mm thickness, with hemisepherical The sources are placed in the cavity centre of the the center front of each crystal. joined crystals. Thin hemispherical absorber shells of polyethylene were hot-pressed to fit in the cavities, in order to absorb particles but not photons. For this configuration, the photon-detection efficiency between 10 and 200 keV is practically 100% and highly accurate photon- emission rates can be measured. A still different type of solid 4x7 counter is the well-type Ge(Li) detector described by De Bruin et al. (1979). These authors used a cylindrical Ge(Li) crystal of 45.mm diameter and 62.mm height with a 46.mm deep well of 16-m width. Good energy resolution and relatively high detection efficiency, almost independent of sample dimensions are, by larger summation effects. however, counterbalanced The latter lead to sample-dependent distortions of the high-energy y-ray spectrum which had to be avoided by the use of absorbers of high-l. material. 5.4.6.
4r ionization
5.4.6.1.
chambers
General
The basic facts about the ionization of gases have been described briefly in 74.4.1. Radionuclide metrology makes ample use of T-ray and P-ray ionization chambers operated more The main features of such activity measurements and or less in the saturation region. In the present section we their application to quality control are explained in 74.5.1. can therefore confine ourselves mainly to a discussion of practical aspects, i.e. of the Errors, corrections and equipment used and of the method of measuring ionization currents. will also be explanations concern calibration procedures considered. The r-ray but the measurements of p rays and other electrons are not fundamentally measurements, different, except for the much higher absorption. 5.4.6.2.
Ionization
chambers,
sources
and suworts
Among the numberless possibilities to arrange a pair of electrodes in a volume of gas, chambers are by far the most important ones. the parallel-plate and cylindrical For electrodes are best suited and will be radioactivity measurements coaxial cylindrical The source to be measured is introduced into a coaxial reentrant considered exclusively. The material and the shape of the electrodes have considerable tube, at ground potential. influence on the chamber response to ionizing radiations. The ideal ionization chamber would be one with a response varying linearly with the The former can be approximated in a of photon energy. source activity, and independently wide range of activity, whereas the latter is impossible. function may be Some calculations in order to improve the shape of the response successful, but the construction of a good ionization chamber will widely rest upon former Besides the geometrical dimensions, the nature and and trial and error. experience, electrode pressure of the gas filling, and the material and thickness of the collecting will influence the ionization current. With air at ambient (atmospheric) pressure, the chanber walls can be made very thin, but the sensitivity is low and depends considerably on Therefore, most chambers for activity measurement are filled with a pressure and humidity. dry, inert gas at a high pressure (1 to 2 MPa; 10 to 20 atm) and sealed, in order to keep Argon is preferred in many cases; nitrogen may give a better the mass of the gas constant. The higher sensitivity of pressurized linearity but a 2 to 3 times lower sensitivity. chambers must of course be purchased at the price of relatively thick walls of the chamber and the reentrant tube. The electrode arrangement of the chamber in use at the BIPM is shown in Fig. 5-15. The wall material is stainless steel, the electrodes are made of aluminium, and the chamber The insulators are of ceramic material, the sensitive is filled with nitrogen at 2 MPa. volume is 5.2 dm3.
Radioactivity measurements: principles and practice
H-V
Sectional view (schematic) of a pressurized, well-type Fig. 5-15 ionization chamber (after Rytz, 1983). The design and construction of a pressurized well-type ionization chamber is too delicate an undertaking, even for experienced metrologists, to give satisfactory results. Therefore, it is advisable to purchase one of the trustworthy products on the market (see Fig. 74, NCRP, 1985). If liquid samples are to be measured, these must be contained, as aqueous solutions, in flame-sealed standard ampoules of glass. If merely relative results are sought, e.g. for checking dilution factors, other vessels may be used provided two or more identical ones Solid samples of identical configuration can also be compared with each are available. other. Contamination of the chamber well must be strictly avoided. The ampoules for liquid samples must be considered as part of the ionization chamber, because they are involved in each single measurement in exactly the same way. However, as each time a different ampoule must be used, it is important to have available a large Thus, for the SIR as an number of completely equivalent and interchangeable ampoules. example, several thousands of ampoules are available that have been manufactured from the same glass melt, in order to assure the uniformity of the material (p. 220, NCRP, 1985). Moreover, the possible variations of the dimensions of 30 randomly chosen specimens have been checked with great care and expressed relatively in terms of apparent activity variations (see Rytz, 1983). The samples and the reference sources have their appropriate supports made of light chamber well. The material, e.g. perspex, and are introduced sequentially into the correct position in which the sources should be placed for measurement can be located by surveying the reentrant tube with a point source and observing the ionization current as The correct position is the point source is displaced laterally or axially in the tube. Further, it is important to check the defined by a minimum and a maximum, respectively. repeatability of the measurements when a reference source is measured many times and taken out of the chamber and of the support, each time. The preferred radionuclide for use as a reference source is ZZ6Ra because of its long Such sources must be manufactured by specially equipped and well-known half life. suppliers, and the radium salt must be densely packed in double-walled, arc-welded envelopes of Pt-Ir alloy, so as to be perfectly sealed. It is desirable to have available a set of sources covering the whole range of the high-precision measurements envisaged. The ratios of these sources must then be checked periodically, in order to verify their airtightness. The airtightness of the ionization chamber must also be tested by periodic measurements of the ionization current, each time with the same source and the same capacitor (see q5.4.6.3). 5.4.6.3. Ionization-current measurements Many
different
circuits
for highly precise measurements
of weak currents have been
Radioactivity
a72
measurements:
principles
and practice
described in the literature (H.-M. Weiss, HN, 1973, p. 291; K. Zstinszky, HN, 1973, p. 299; Blanchis, 1985). The Townsend balance with continuous or stepwise compensation (see Figs. 5-16 and 6-24) is often used in combination with preset voltage, charge or current. Other circuits measure the time average of the voltage drop across a high resistance (Walz and In all cases a highly sensitive Weiss, 1970), or they employ feedback-current integration. charge measurement is needed, often a vibrating-reed instrument for voltage or but it is no longer electrometer (e.g. Gary, of the Applied Physics Corporation, manufactured) or a digital voltmeter (e.g. Keithley, see 76.8.2.1) sometimes with feedback (76.8.2.2). The electric quantities measured (voltage, capacity, resistance) do not have to be known accurately. All that is needed is a highly stable current-measuring system and Santry et al. (1987b)have described the automatic-control and datareference source. of the National Research Council of processing equipment installed at the laboratories It comprises a Keithley Model 617 Programmable Electrometer and an IBM XT Personal Canada. and enables the activities of y-ray-emitting radionuclides to measured with Computer, reproducibilities of 0.05%.
Block diagram of a semi-automatic circuit for ionizationFig. 5-16 Townsend balance with stepwise compensation current measurements.
(after Rytz, 1983). In the operation of most ionization chambers the collecting electrode is kept close to ground potential. The high d.c. voltage to be applied to the high-voltage electrode is often taken from dry batteries, but these are, nowadays, being replaced, more and more, by Negative or positive potentials of low-noise electronic power supplies. highly-stabilized, several hundred volts, up to about 2000 V are usually applied. The capacitance of such ionization chambers is of the order of 50 pF, and that of the For most measurements it is cable to the collecting electrode may be of the same order. Some of the capacitor in parallel with the chamber. necessary to add an external commercially available products are more suitable and a careful selection as to temperature and leakage is important. The capacitance also varies considerably with dependence to arrange a set of such For high-precision work, it is therefore advantageous humidity. capacitors in an airtight box provided with high-quality insulators and containing a drying becomes very stable and After several weeks, the capacitance agent (e.g. silica gel). nearly insensitive to small temperature changes. Deformations of the cables may give rise to spurious charges and must be avoided. Rapid changes of the voltage applied to cables, capacitors or insulators may induce delayed variations that can be avoided by providing waiting periods of about 20 s after such changes (e.g. after the opening of the short circuit). 5.4.6.4.
Activity
measurements
The principal virtues of using well-type ionization chambers for the measurement of Although activity are the simplicity of operation and the high precision of the results. such measurements are necessarily indirect, i.e. related to standard sources via a stable in metrological work can hardly be overestimated. their importance reference source, of the high possible precision can only be taken if a number of However, full advantage The main facts concerning the precautions are observed and certain tests applied. measurement of an unknown source by means of a standard (and hence a calibration factor, K) have been explained in l/4.5.1. 5.4.6.5.
Efficiency
and efficiency
curves
is defined as the activity of a The equivalent activity, A, (see ~4.5.1.1.2), radionuclide sample that gives the same response as the long-lived reference source at time is t,; the reference times of all five "'Ra reference sources used in the SIR programme a relative efficiency of the ionization The reciprocal of A, represents 1976-01-01.
Radioactivity
chamber. A, chamber and measured by relation
principles
873
and practice
is thus a characteristic quantity for each radionuclide, in a given ionization the same geometrical environment, It can be that is independent of time. means of a previously, and directly, standardized source, according to the
A, = A[R + f(R - l)/(&, where
measurements:
-
f)l
exp(-&(t,
- Ql
exp[&(t,
- to)1
,
(5-33)
A is the certified activity of the national-laboratory standard source at a stated reference time t,; R = I,,/I, is the ratio of the responses to the BIPM "'Ra reference and nationallaboratory standard; f is the background-plus-leakage current; x S( X,, are the decay constants of the submitted radionuclide standard and of 226Ra,respectively; and tm is the mean, or otherwise stated, time of the BIPM measurements.
The background current, f, should be measured for about 60 minutes, both before and after measuring a source. In general, it does not vary much, especially if the chamber is mounted within a shield of lead bricks, about 5-cm thick. The plot of an x-y recorder gives, in addition, a valuable check of the performance of the measuring system. The quantity A, is identical to the "relative KR factor" Ks in Eq. 4.1 and can be used to establish an efficiency curve, either directly (see, e.g. Weiss, 1973) or in a more elaborate manner, as described for the SIR programme (Rytz, 1983). Such curves are very useful for interpolations and the evaluation of impurity corrections. A typical efficiency curve for a commercial radionuclide ("dose") calibrator is shown in Fig. 96 of NCRP (1985). 5.4.6.6.
Corrections
Corrections for r-ray-emitting impurities, present as impurities in a source to be measured, can easily be calculated if the amount of the impurity can be established. These corrections can be considerable for impurities emitting high-energy photons in a source: that emits only low-energy photons, as, for example, a "Co impurity in a 57Co source. Corrections may also be needed for bremsstrahlung, if the sample emits high-energy p rays and if the measurement involves the use of the y-ray efficiency curve. Beta-ray ray-bremsstrahlung efficiencies for some p-ray emitters have been measured at BIPM, and an efficiency curve determined. Corrections can easily be evaluated, and are small except in extreme cases, such as for '44(Ce+Pr). As saturation may not be achieved in the whole sensitive volume of the ionization chamber, recombination may occur and a correction for non-linear response may be necessary. Tests should be carried out using sources of different activities of the same radionuclide and for different l-ray energies. 5.4.6.7.
Uncertainties
As is well known, the precision of the measurements with a well-type ionization chamber is often higher than that of most direct methods. But this should not incline one from making a detailed analysis of the various uncertainty components, taking into account that they may depend on the photon energy. The components to be considered are l l l l l
uncertainty of the non-linearity correction, instability of the current-measuring system, statistics of ion collection, variations in ampoule dimensions, repeatability (standard deviation) of the mean
ionization-current
ratio
The influence of the ampoule walls is about twice as large at 60 keV (241Am) as it is at 1.25 MeV (?Zo). i.e. the sum For SIR measurements, the combined relative uncertainty, in quadrature of all these components at a level of one estimated standard deviation, is about 0.1% for *"IAm and 0.05% for 60Co. 5.5.
COINCIDENCE
COUNTING
5.5.1. General The measurement of activity by the method of coincidence counting involves the recording of individual emission rates of two simultaneous radiations from the same nuclear transition, in each of two separate detector channels, together with the rate of coincidence, in time, between them, provided that the second radiation does not arise from an interaction of the first radiation outside the decaying atom. Thus the coincidence method can be used to measure the activity of an amount of a radionuclide that decays by emitting a beta particle followed by a prompt gamma ray from the daughter nucleus. It cannot be used without serious complications in cases where two radiations associated with the decay consist, for example, of a beta particle and external bremsstrahlung, such as in the decay of 32P, Clearly, if the efficiency of each of the two detector channels was
Radioactivity
874
lOO%, then the coincidence
count
measurements:
principles
rate should be equal
and practice
to that in each channel
is one of the most powerful in the repertoire of The coincidence-counting method radionuclide metrology. H. Geiger and A. Werner first described its use, in 1924, to monitor the efficiencies of two observers recording the number of scintillations caused by alpha particles striking a given area of a ZnS(Ag) screen subtending a known solid angle to The principle of this experiment is illustrated in Fig. an alpha-particle-emitting source. of two detectors if but it is equally applicable to finding the efficiencies 5-17, different radiations emitted from a radioactive source. ""llt,me +
Observer
A (CAN,)
ObserverB
Cotncidences
or
N,=
(&,N,l
(E,EBN,)
Na.Na
number
of coincidences
-6X5 3 =10
The principle of activity measurement by coincidence counting. Fig. 5-17 As was done in the early days, each observer used a low-power telescope and recorded the occurence of a flash on the ZnS(Ag) screen by pressing a key that caused a needle to move across a strip of smoked paper. 5.5.2. Applications
to activitv
measurement
The application of the coincidence-counting method to the measurement of activity can perhaps be best illustrated by considering a specific example, namely that of the calibration of sources of a simple beta-gamma emitter such as 6oCo. This radionuclide decays by emission of a beta particle to the 2.5-MeV excited state of 60Ni whence it decays with a half life of the order of a picosecond, with the emission of two gamma rays in cascade to the ground state of 60Ni. In terms of such a short half life the emissions of the beta and gamma rays are essentially simultaneous. These radiations are then detected and counted by means of a p-7 coincidence-counting system, similar to the basic system shown in Fig. 5-18, that detects and records beta- and gamma-ray count rates and also the rate of coincidences between them. of the source, and Ng, N, and N, be the beta-channel, Let N, be the activity gamma-channel and coincidence count rates, respectively. Then ep, equal to Np/Nos and c., of the two detectors for their respective equal to N,/N,, will represent the efficiencies radiations. As was emphasized by P. J. Campion in 1959, it should be noted that these efficiencies include all effects that lead to count rates, in the respective beta and gamma channels, except those due to dead-time losses. In addition the respective count rates must
a75
Radioactivity measurements: principles and practice
Block diagram of the basic components of a typical 4n@-Y Fig. 5-18 coincidence-counting arrangement (after NCRP, 1985). have been corrected by subtracting the background count rates, and N, must be corrected for accidental coincidences arising from the fact that the coincidence gate is open for a finite time often of the order of one to ten microseconds, the latter, for example, being required in the case of a delayed gamma-ray emitter such as that of 1-ps half life in the 514-keV level in "Rb in the decay of "Sr. In terms of the beta-channel and gamma-channel efficiencies we can write down the coincidence equations, corresponding to those given in Fig. 5-17, for a simple beta-gamma emitter, namely: No
=
N,sa
p
N, = N, > ,
and
N,
=
N,c,+,
whence
N,
=
N$J,/N,
(5-34)
In addition, if a series of coincidence measurements is made over a period of time that is not short compared with the half life of the radionuclide being assayed, then the data may have to be normalized to a chosen fixed point in time. Such a normalization is usually referred to as a "decay correction" but it may seem somewhat inappropriate to refer to a law of nature such as the radioactive-decay law as a correction. A decay, or half-life, correction should actually refer to the updating of nuclear-decay data that must be made from time to time in the light of newly made evaluations. By no means do all radionuclides have decay schemes as simple as that of "Co which can be assayed using low-efficiency beta- particle detectors, with sufficiently high But the decay schemes of numerous beta-gamma emitters accuracy to meet many requirements. in common use are much more complex and involve further radiations such as conversion In such cases the use of a high-efficiency 4n electrons, x rays and Auger electrons. counter in the beta channel combined with the method of efficiency extrapolation to 100% beta- counting efficiency is mandatory (y5.5.3). But as A. P. Baerg points out in 73.2 of NCRP (1985) "there are cases in which low-efficiency beta-particle detectors may be advantageously used". He gives one such example provided by the assay of "'1 that decays by 100% beta-particle emission (Egmax= 153 keV) to the 39.58.keV excited state of lZgXe. This then decays promptly with the emission of 7.5% 39.58-keV gamma rays, plus conversion and Auger electrons, and some 70% of xenon x rays with energies between 29.5 and 33.6 keV. But these x rays can be used, together with the gamma rays, to signal the 39.58.keV xenon An lzsI source was standardized at the National transition in the gamma-ray channel. Bureau of Standards using a thin (0.25-mm thick) plastic-scintillator phototube assembly to detect the beta particles, and a thin (1.6.mm thick) NaI(Tl)-crystal phototube assembly to detect the photons. (Spernol et al., 1976). The thin plastic was very insensitive to photon interactions and any that could have interacted were excluded by pulse-height discrimination; and sufficient absorber was placed between the source and the detector to The NaI(T1) crystal was provided with a 0.13-mm-thick remove conversion electrons. beryllium window that, together with the air between it and the source, was sufficient to absorb all of the beta particles. Under these experimental conditions, the activity of the "'1 source could be measured by recording the count rates in the individual detector channels and the coincidence scaler, and substituting these into equation 5-34 to obtain N, (Mann and Hutchinson, 1976). Liquid-scintillation (LS) detectors have also been widely used in the beta channel, and are comparable with 4n,9 proportional counters with respect to their high detection An intercomparison between four national laboratories was organized by a efficiencies.
a76
Radioactivity measurements: principles and practice
BIPM working group in 1977 to compare results of 134Cs measurements obtained using the method of 4~p(LS)-r with efficiency extrapolation. The results, together with three in which 4a proportional or pressure proportional counters were used in the beta channel, are given, together with experimental details, in chapter VII of BIPM (1980). All of the sixteen reported results lie within a range of kO.5 percent. 5.5.2.1. Gamma-eamma coincidence counting This method involves the use of two photon-detector systems, and is not recommended as a method of choice except in special circumstances, It is discussed in some detail in NCRP is given, (1985), where the coincidence equation that is applicable to the assay of %o together with an indication of the difficulties involved and references to pertinent publications. The difficulties include: Effects due to possible angular correlation between two gamma rays; possible extra coincidences due to the Compton scattering of either gamma ray or photon from one detector into the other, and a need to know the relative effiencies of the two detectors to photons of different energy. Consequently, this method may be neither the least trouble-free nor the most accurate. It has, however, been rather fully discussed by Hayward et al. (1955) and Taylor (1967) in the respective applications to the standardization of "Co, and of lz51 and lQ:Hg. 5.5.2.2. Coincidence-countins
corrections
The principal corrections are for background, the loss of counts due to the dead time in each of the two single-radiation channels, and for accidental coincidences in the coincidence channel. For non-extending dead times r1 in channel "1" and r2 in channel "2", the corrected count rates are, respectively, N1/(l - N1rl) and N,/(l - N2~z), i.e. the number of counts recorded in a given "clocked" second of counting time divided by the actual live-time fraction of that second. Thus, if N counts per clocked second are recorded, the coincidence mixer will have been "dead" for a fraction NT and "live" for a fraction@ - Nr]of the clocked time. The dead-time corrections must, of course, be made before subtraction of the background count rates. In practice 'I and ~~ are usually equal. It is more difficult to calculate the dead-time correction for lost coincidences in the coincidence channel, because this depends on the single-channel dead times and the dead time and resolving time in the coincidence channel. It is also difficult to calculate the correction in the coincidence channel for "accidental" coincidences (i.e. unrelated coincidences occurring by chance between radiations from different decays). Many approximate formulae have been derived during the last two decades, mostly as single expressions for the activity, to take account of these corrections (e.g. Campion, 1959; Bryant, 1963; and Baerg,1973). Campion's and Bryant's formulae have been used frequently, although Bryant's formula is only valid for equal efficiencies in both channels (Smith, 1978). Today, the exact corrections derived by Cox and Isham (1977), or the extended or modified formulae of others (Smith, 1978, 1987; Funck, 1980) are mostly applied. A further improvement of the coincidence method may be obtained by the so-called computer discrimination as developed by Smith and Stewart (1975). In this technique, p-particle count raters are measured simultaneously, over a continuous range of p efficiencies, in coincidence with y pulses, using appropriate electronic equipment. Smith (1987) has extended this method to include simultaneous discrimination in both the 0 and 7 channels and has given explicit solutions based on the Cox-Isham formalism. These developments all pertain to non-extending dead times and, in general, to coincidence systems only. But developments in electronics now make possible the design of more sophisticated systems which have certain advantages, especially in lower uncertainties The in the corrections at high count rates, and other corrections may become necessary. use of extending dead times has also become common after its revival by Miiller (1973). The main features of some modern systems are: common dead times in all channels (J.E. De Carlos and C.E. Grenades, HN, 1973, p. 209; Bouchard and Vatin, 1977); live timing (Baerg er al., 1976; Chauvenet et al., 1987; Miyahara et al., 1987); use of very short pulses (Bouchard and Vatin, 1977; Gehrke and Johnson, 1982); use of extending dead times (Baerg et al., 1976; Bouchard and Vatin, 1977; Santry et al., 1987); variable (preset) dead and resolving times (Gostely and Noverraz, 1975); extrapolation techniques (75.5.2.3); anti-coincidence counting (75.5.3); and selective sampling (75.5.3.2). In addition to the above sources of error there is a further possible source that was pointed out by Gandy (1961), due to differences in the arrival times of channel "1" and Channel "2" pulses at the open gate of the coincidence mixer and to fluctuations in that difference. This effect, known as "jitter" may arise from electronic instability, from differences in the pulse-rise times, or from different electron-collection times in the two detectors, one of which might, for example, be a solid-state detector and the other a gas proportional counter the collection time in the latter detector critically depending, because of the lower ion mobilities, on the location of the initial ionization in the gas. The Gandy effect may, however, be reduced by adjusting the delay shown in Fig. S-18 so that there is a zero mean delay between the two channels (Williams and Campion, 1965; Special electronic circuits have also been Munzenmayer and Baerg,1969; Funck, 1980).
Radioactivity
measurements:
principles
designed to balance the delays automatically (Scheller can also be made for time jitter (Funck, 1981).
and practice
and
Seyfried,
1985).
077
A correction
In applications of the coincidence-counting method to the assay of p-y emitters using detectors that subtend relatively small solid angles to the source, it is necessary to correct for any angular correlation between the radiations emitted. But such a correction, SS well as other decay-scheme-dependent corrections, becomes unnecessary when either detector subtends an angle of 4s steradians to the source. This and its high efficiency, make the 4ap detector the instrument of choice in the standardization by coincidence counting of 8-7 emitters. Further refined corrections to provide greater accuracy for dead-time resolving-time effects in the coincidence channel, at high count rates or for long times, are briefly discussed and referenced in NCRP (1985). 5.5.2.3.
Coincidence
countine
with
efficiencv
and dead
extrauolation
The basic principle of the method of coincidence counting is that channels "1" and "2" shall respectively record radiations "1" and "2" only, and the coincidence scaler shall record the coincidences in time between the two radiations. But this is only feasible in the case of radionuclides that decay in a simple manner, as in the case of "Co where the simple Eqs. 5-34 apply. The decay of % is more complex, but the recording of the two separate radiations can be kept to the two separate channels by an appropriate choice and use of the two detectors. But the decay schemes of most beta-particle emitters are far more complex and frequently involve the prompt emission, from the daughter atom, of gamma rays, conversion electrons, x rays and Auger electrons. All of these can be detected by the beta detector, and, all but the gamma rays, can be detected with high efficiency if that detector is, as is no" often the case, a 47rp pressurized gas-proportional counter. This situation can, however, be turned to advantage by the method of efficiency extrapolation. If a is the internal conversion coefficient, and if cc0 and ep7 are the efficiencies for the detection in the 4sj3 counter of, respectively, conversion electrons and gamma rays, then Eqs. 5-34 can be rewritten as =EcB + C87 No
=
N,
=
l+a
NC = "here Lo is the probability ray being Compton-scattered
No Lea + (1 - sp)(
N, e,/(l N, [~p’,/(l
+ a)
)I
I
,
+ a) + (1 - rp)c,l
,
(5-35)
of observing spurious coincidences due, for example, to a gamma from one detector to the other, and being detected in both.
By inspection of Eqs. 5-35 it is seen that, for a S?rflcounter of high efficiency, the term (1 - ea) is small and tends to zero as eB tends to unity so that NJN, is still a very good approximation to co, and N, tends to Nfl,/N,. In practice the approximate values obtained for Na at values of co between, say, 0.7 and 0.95 are plotted against NJN, and then extrapolated to N,/N, equal to 1.00, or, alternatively, against to zero, to give, in both cases, the activity, N,, of the (1 - NC/N,), with extrapolation source. Initially the method of efficiency extrapolation utilized efficient 4r@ gas-flow proportional counters, operated at atmospheric pressure, and the beta-particle detection efficiency was changed by either dissolving the active source on its foil mount, adding carrier solution and redrying, or by adding very thin metal, or metallized, foils above and below the source. But more recently high-pressure 4np counters, operating at pressures up to 70 atmospheres (7 MPa), have been designed to enable the method of efficiency extrapolation to be effected simply by changing the discrimination level in the beta channel (Baerg et al. 1967; Baerg, p. 95, HN., 1973). As stated by these authors, the use of high-pressure counters is to prevent discrimination against higher-energy beta particles that may deposit only a small part of their energy in the detector's sensitive volume when operated at atmospheric pressure. In other words the efficiency extrapolation, of count rate against co or against (1 - ta) for low-energy events, must be monotonic. In practice this extrapolation can be made with a linear fit, or by means of a low-order polynomial. If several gamma rays of different energies, representative of beta branching in the parent nucleus, are emitted by the daughter nucleus, the efficiency extrapolation "as often carried out by selecting one suitable gamma ray and "gating" on to it. But the reliability of extrapolation procedures may be improved, where several beta branches are associated with promptly emitted gamma rays, by recording the count rates of two or more gamma rays at the same time ( Baerg, 1981; Smith, 1987). Appropriate equations have been developed to express N, as a linear function of the t"o or more NC/N7 ratios. These equations with decdils and references are given in NCRP (1985, 73.2.8.3).
a78
Radioactivity measurements: principles and practice
A further improvement of the coincidence method may be obtained by the so-called computer discrimination developed by Smith (1975). In this technique p-ray count rates in coincidence with -/-ray pulses, are measured over a continuous range of @ efficiencies using Smith (1987) has extended this method to include appropriate electronic equipment. simultaneous discrimination in both the B and 7 channels and has derived explicit solutions based on the Cox-Isham formalism. 5.5.2.4. Efficiencv tracing Coincidence counting has also been applied to the assay of pure beta emitters by compounding them with a beta-gamma emitter that has a simple decay scheme and a not-too-dissimilar beta-ray spectrum (Campion et al., 1960). Baerg et a1.(1964) made similar measurements by quantitatively mixing previously calibrated solutions of the pure beta emitter with the 8-7 tracer, instead of compounding the two radionuclides in the same molecule. Efficiency extrapolation to lOO-percent efficiency gives the total count rate of the mixture from which that of the tracer can be subtracted to give the activity concentration The report of a recent international comparison of of the traced radionuclide. 13'Cs-activity measurements using 134Cs as the tracer (Rytz, 1985) gives a full account of the formulae used. Electron-capture nuclides with moderate decay energies (e.g. 54Mn) have also been calibrated in this manner, the Auger-electron-x-ray shower, that is readily detected in the Further details and many references 4~8 counter, being treated as a single beta branch. can again be found in NCRP (1985). 5.5.3. Anticoincidence
counting
The method of anticoincidence counting, a complementary variant of coincidence But it has the vary great advantage of counting, was proposed by Bryant (1962). eliminating the need to correct for the Gandy effect, for accidental (random) coincidences, and for By, the spurious coincidences due to Compton scattering (see Eqs. 5-35). The only remaining corrections needed are those for dead-time losses and backgrounds. But one serious problem with the method is that the dead-time correction for the anticoincidence channel is difficult to derive. Bryant (1962) has, however, derived an approximate expression for the correction, which is also discussed in NCRP (1985). To understand the method it is convenient to consider again the case of simple 8-7 The principle of the method resides in also recording, in addition to coincident decay. gamma rays, gamma rays that are not associated with a recorded event in the beta-detector channel. This is accomplished by disabling the gamma channel for a sufficiently long time T before and after the beta particle has been detected. This is achieved by using the detected beta event to close a gate in the gamma channel for an extra time 2T and delaying all gamma signals by the time T. Thus only those gamma signals that precede or follow a recorded ,9 particle by more than T are accepted as anticoincident events. The value of T is chosen to exclude essentially all coincident gamma events, including those delayed by the Gandy effect. The total gamma-ray count rate is also recorded, and the difference between this total and the number per second of non-coincident gamma rays gives the rate of coincidences. The activity of the source can then be computed using the coincidence equation N, = N$,/N,. Another advantage, pointed out by Bryant (1962), is that the anticoincidence method, unlike its coincidence forebear, can be readily extended to measure the activities of radionuclides that decay to an isomeric state emitting delayed radiations, provided that the half life of the isomer is not too long. This can be achieved by increasing the extra time that the gamma-channel gate remains closed from 2T to 2T + r The time T + r is set equal to m half lives of the isomeric state, m being chosen so that the probability of recording an unwanted "coincidence", equal to 2-m, is as small as desired. Bryant describes the application of this method to measuring the activity of a s5Sr source using a 4x8 counter to detect the primary K x rays and Auger electrons from the 85Sr source, and a NaI(T1) crystal to detect the 0.514-MeV delayed gamma rays, with a half life of 0.9 ps, from "Rb. As Bryant (1962) further pointed out, the coincidence and anticoincidence measurements can also be carried out simultaneously and used to cross-check each other. The difficulty in deriving the dead-time correction in the gamma channel arises from the fact that there is already an inherent dead time, T,, that is generated following every anticoincident pulse, to which class of pulses the extra dead time 2T is not attached. The dead-time correction for the gamma channel must therefore incorporate both 2T, or 2T + r , and T,, that is generated. It is interesting to note that if Y is the anticoincidence corresponding to Eqs. 5-35 for the coincidence method is
count rate, the equation
Radioactivity measurements: principles and practice
Y =
=
N,
-
879
N,
N, (1 -
CT ca)
(5-36)
-
l+a' Two variants of the anticoincidence method have recently been great value, as they eliminate essentially all corrections due to They are the the live-timed anticoincidence-counting method of Baerg selective sampling method of Miiller (1981) that are described in the
developed that are of instrumental effects. et al. (1976) and the next sections.
But first it may be helpful to remember three principles of anticoincidence counting: (i) the final answer, namely the disintegration rate of the source is given by the are recorded in all channels by virtue coincidence equation N, = NC/N@'., (ii) count m of the set counting time or live-timer, even though it becomes habitual to refer to recording counts in each channel -- the insertion of artificial dead times in channels does not change the count rate exceDt that at very high counting rates a loss of a preponderance of very short-time sequential events may be lost thus disturbing the Poisson timedistribution; and (iii) the use of an extending dead time, of T + T /JS, in the beta or gamma channels means that m other pulse, either beta or gamma, can be recorded in the dead-time interval immediately preceeding that pulse. 5.5.3.1. Live-timed anticoincidence
counting
This method, that was proposed by Baerg et al. (1976), using extending dead times, eliminates essentially all remaining corrections for instrumental effects. (Also see, for Defining the anticoincidence count rate as Y, Baerg et al. example, Santry et a1.,1987a.) summarize the coincidence and anticoincidence equations, in forms suitable for efficiency extrapolation as follows: (a)
N, = F(N,/N,), tends to N, as
NC/N, + 1 ,
(b)
= N, + f(1 - NC/N,), tends to N,,as
(cl
= N, + f(Y/N,), tends to N, as Y + 0
(d)
= N, + g(Y), tends to
N, as
NC/N, + 1 ,
,
and
Y + 0
(5-37)
It enables the The circuit used by Baerg et al. (1976) is shown in Fig. 5-19. application of an extending dead time of the same duration T to both the beta and gamma By delaying the gamma pulse it is channels if an event is detected in either of them. assured that only beta and gamma events can be recorded that are totallv unassociated with any signal passing through the other channel. Referring to Fig. 5-19, any gamma-ray pulse will be delayed, by an amount of about 1 ps by the delay network, D,, to eliminate any Gandy-effect jitter. The beta- and gamma-channel signals are then routed through gates G, and G, to both their respective scalers and also to the delay network D, where they are The purpose of this delay is to enable first combined and then delayed by about 10 ns. either a beta or gamma pulse to be recorded before gates G, or G, are closed by activation of the extending dead-time circuit by the beta or gamma pulse.
Fig. 5-19 Baerg
Block diagram of a live-timed anticoincidence ci -uit (after 1976).
et al.,
This extending dead time must have a duration longer than any ,9-y jitter, and is usually not less than 2 P.S. At the same time the generated dead-time logic signal is applied through gates G, and G, to shut off the live timer for whatever the duration the extending dead time may last. The pulses recorded in the gamma-channel scaler are
Radioactivity
880
measurements:
principles
and practice
Therefore the antiscaler. uncorrelated with any events recorded by the beta-channel counts in the gamma-ray scaler coincidence count rate, Y, is given by the accumulated This briefly divided by the accumulated live time, the value of which is usually preset. The other and essentially describes the method of live-timed anticoincidence counting. gates shown in Fig. 5-19 are for second-order refinements that are described in Baerg et Much supplementary should be consulted for further details. al. (1976), which paper information may also be garnered from the sections in NCRP (1985, n3.2) that were written Baerg et al. also note that they extended to anticoincidence counting the by Dr Baerg. concept introduced by De Carlos and Granados (HN, 1973 p. 209) of pooling the beta- and These authors had also gamma-channel signals to generate a common, shared, dead time. pointed out its possible applicability to live timing in coincidence counting. of the activity of As a test of the method, Baerg et al (1976) compared measurements and anticoincidence counting. They three 60Co sources by both the methods of coincidence of beta detection by used the method of efficiency extrapolation varying the efficiency electronic discrimination, Their results are shown in Table 5-2, the uncertainties shown The results obtained by the two being standard deviations of type A (73.4.1.2) only. As the functions f and g go to methods also lie within a range of about 2 0.03 percent. zero when Y goes to zero, there is no need to know the count rate recorded by the gammaIt is, in general, only used to monitor the stability of that channel monitor (Fig. 5-19). channel. Table
5-2
and relative anticoincidence-counting results for different values of the extending dead time for 60~0 sources
Coincidence-
of different
activity
Extending dead time (w)
16,925 16,925 3,631 36,335 3,631 36,335 16,925 3,361 3,361
* Uncertainties Selective
et al.,
Coincidencecounting result (s-l)
3.5 5.4 5.4 13.4 13.4 53 53 134 265
5.5.3.2.
(from Baerg
in units
sampling
(5) (5) (1) (13) (1) (13) (5) (1) (1)
1976).
Relative anticoincidence-counting result
::
of the last digit(s)
0.99981 0.99977 0.99984 0.99967 1.00012 1.00015 0.99974 1.00030 0.99970
are shown
(46) (34) (39) (50) (42) (42) (32) (28) (24)
*
in parentheses
(SESAM)
This ingenious method, proposed by Miiller (1981) also selects non-beta-correlated signals in the gamma channel using the fact that, in a channel (here the p channel) with an extending dead time, T, no pulses can appear in a time interval T preceding the observed pulses (because, otherwise, the latter would have been lost) and therefore in this time interval pulses in the other, y, channel do not have a coincident partner ("anticoincident pulses"). The efficiency of @-ray detecti on can then be calculated from the ratio of the rates of coincident to anticoincident Y pLll*a*. The former arrive in time intervals of length T preceding 7 pulses, the latter in time intervals of more than T. This ratio will be essentially immune from the effect of radioactive decay, but the recorded beta count rate must be normalized for short half lives and both the beta and the gamma count rates must be corrected for background and dead-time losses. For high beta count rates the dead-time correction in that channel becomes more complicated, as does also the accumulation of the gamma-channel counting data. A simplified block circuit diagram is shown in Fig. 5-20. The extending (cumulative) dead time can, as suggested by Mtiller, be set at 25 @s and the gamma-channel delay at 60 On the detection of a beta particle the resulting pulse in the beta channel is used to ps. start a multichannel analyzer operating in the time mode to record the arrival times of pulses in the gamma channel with the introduced delay. For the first 35 p* it will record in its appropriate time-bins the times of arrival of all detected gamma rays, while in the second time interval of 25 ps it will record only those gamma-ray pulses that are uncorrelated with any beta-particle pulse. At the conclusion of the 25-p* extending dead time, the logic level of the dead-time gate will return to the "off" position, and the multichannel analyzer will turn off until the arrival of the next detected beta-particle pulse starts a new cycle of gamma-channel arrival-time storage. Thus the time-bins will continue filling up until an "arrival-time density spectrum" like that shown in Fig. 5-21 will be accumulated. The peak on the right represents the initiating beta pulse of coincident events, while the gamma-ray arrival times start 60 ps to the left because of the delay in the gamma-ray channel. After a sufficiently long counting time the registered counts in the two regions will fill up the respective time bins to average numbers of
881
Radioactivity measurements: principles and practice
Normalizing for the different receiving times in the G and g, in the two zones. two zones, in our example 35 and 25 ps, the count rates G and g are obtained. These, ignoring dead-time and background corrections, give
counts,
,
R, = g/G whence and
1 - R, = NC/N7
, (5-38)
N, = No/(1 - R,).
Schematic of the experimental arrangement used for the Fig. 5-20 selective-sampling method (after Mtiller, 1981). I number of registered gamma rays per channel
t
G
____
1
+T-(
I I .I I : ..........._. t ._^_...C._ ’ g
t
time (channel)
arrival of registered beta pulses
Selective sampling: measured frequency distribution of Y Fig. 5-21 pulses preceeding a registered ,9 pulse from a 60~0 source. The y pulses are recorded by repeated sampling, and their accumulation can be followed on the MCA screen. The time scale corresponds to 0.75 ps per channel (after Mfiller, 1981). Miiller (1981) remarks that most present-day multichannel analyzers are too slow, with channel-to-channel dead times of the order of 10 ps, to handle the count rate of a reasonably active source. He therefore used an electronic device called a "speed converter," with a resolution of some 50 ns per channel, that first stored the original sequence of arrival times and then transferred them to the multichannel analyzer at a lower speed (see BrBonce, 1976). This enables the transfer and storage of data in a time that is between 10 and 20 times slower than that required to record the pulses. For further information regarding the details and refinements of the method the Miiller's original paper (1981) should be consulted, together with a simplified version involving only time delays and gates (Miiller, 1985).
6.
ELECTRONIC INSTRUMENTS FOR RADIOACTIVITY MEASUREMENTS
6.1. INTRODUCTION In Chapter 4 various kinds of interaction between radiation and matter, as gas, liquid From such interactions there derive different methods of or solid, have been described. These detecting radiation, the principles underlying which have also been explained. interactions include gas ionization that finds application in the form of gas-ionization chambers, electrometers and electroscopes, and gas counters. Gas ionization also forms the basis for spark chambers and cloud chambers, that detect the tracks of ionizing particles, but which find their primary use in high-energy and particle physics rather than in the quantification of radioactivity. The rare, or noble, gases also act as scintillators when exposed to ionizing radiation, but detectors based on this principle are The interaction of radiation with liquids not common (see Knoll, 1979, for references). gives rise to the emission of photons that can be detected by the photocathodes of electron-multiplier phototubes, so that every radiation event in the liquid (above a certain threshold energy) can be detected individually by discrete pulses of electrons emitted by the last dynode of the phototube. ?erenkov radiation that arises from particles traversing a fluid with a velocity greater than that of light, can also be used for the detection of high-energy radiation, but is only rarely used to quantify it. Condensed rare gases can also be utilized as ionization chambers, but their use is still in the developmental stage. The potential use of liquefied xenon has, however, aroused considerable interest because of its high atomic number and of the fact that it should provide resolutions for gamma rays intermediate between those given by sodium iodide and germanium. (See Knoll, 1979, for some pertinent data and references.) In the case of solids, radiation interacts to produce ionization (electron-hole pairs), light and heat. Of these the first two properties are widely used for the detection and quantification of radiation (and, hence, radioactivity), but the last, as the basis of calorimetry finds use mainly in the assay of energetic alpha-particle or beta-particle emitters (e.g. 3zP, 63Ni, 226Ra+, and "special" nuclear materials). As will have been gathered from Chapter 4, the output of every detector in general used today is some kind of electrical signal. The simple electroscope, say quartz-fibre or gold-leaf, shows an electrostatic repulsion that decreases as the system is discharged by the radiation ionizing the surrounding gas. The ionization chamber gives rise to a steady current in the direct current mode, or a pulse of charge when it is operated in the pulse mode either as an ionization chamber or as a proportional or Geiger-Miiller counter. A scintillator emits prompt pulses of light, that are converted to pulses of electrical charge by means of a phototube. The phototube oc.tput may also in some cases be read as a direct current (see, e.g., 15.4.3.4.3). Semicondxtors when used as solid-state ionization detectors emit short pulses of negative and positive charge carriers (electrons and holes).
Typically the detection and quantification of radioactivity is accomplished by observing direct-current outputs, or counting pulse-output rates, of ionization devices. In either case the amounts of electricity to be measured are extremely small and are of the order of lo-' to lo-l5 A in the case of direct-current instruments and lo-" to lo-l5 C per detected event in the case of pulse detectors. The former used to be measured by means of electroscopes, string, quadrant, Lindemann-Ryersan, or vibrating-reed and Keithley electrometers, and the latter are usually measured by electrical-pulse techniques using integrated solid-state circuitry in the form of preamplifiers, amplifiers, multichannel analyzers, computers. and so forth. The many techniques used to acquire data about the properties of radiation emitted in the processes of nuclear and atomic decay, by recording the responses of various radiation detectors comprise the rapidly growing technology of nuclear electronic instrumentation - sometimes referred to as nucleonic instrumentation. The most widely used radiation detectors are the ionization chambers (and its radiopharmaceutically-oriented modification, the "dose" calibrator or radionuclide calibrator), the proportional counter, the sodium-iodide, thallium-activated, crystal, and the solidstate detectors. In North America the production of the high-purity germanium detector, HPGe, has almost entirely replaced that of the lithium-drifted germanium detector, Ge(Li), because the latter must be kept at cryogenic temperatures to inhibit the reversal of the drifting process, whereas the former can be maintained at ambient temperatures, and because the techniques of producing high-purity germanium crystals are now well established. We form of measure rators. ing and
thus see that not only do the most frequently used detectors give outputs in the short-duration low-amplitude pulses, but that pulse techniques can be used to the direct-current outputs of ionization chambers and radionuclide ("dose") calibIt is therefore important to gain some insight into the techniques of manipulatrecording small short pulses of electric charge.
Finally, it cannot be too strongly emphasized that, while this chapter attempts to outline the fundamental functions of electronic components. one no longer attempts to build
883
Radioactivity measurements: principles and practice
084
those components in the laboratory but, as often stated in earlier chapters, one now buys the component or function needed, or, at most, assembles it from integrated-circuit subcomponents. Thus any person who has been given the responsibility of selecting nucleonic equipment and, especially, solid-state detectors for a new regional radionuclide metrological laboratory would be well advised to consult the many excellent catalogues and brochures published by nuclear-instrument industry. Only in this way can one be sure of obtaining the most up-to-date equipment available in a rapidly developing art. 6.2.
PULSES
The average energy that must be expended in order to form one electron-ion pair in most gases is of the order of 30eV (ICRU, 1979a). Thus a 300-keV electron or a 3-MeV alpha-particle expending all their energy within an ionization chamber or a gas proportional counter will produce respectively lo4 or lo5 primary ion pairs. In the case of the proportional or Geiger-Miiller counter the number of ion pairs produced in this primary ionizing event will be further increased by the process of gas multiplication. An analogous process occurs in semiconductors, for which, however, the average energy expended to create an electron-hole pair is about 3 or 4 eV. Under the influence of an externally applied electric field to any "ionization" detector (gaseous or solid-state) the positive ions (gaseous) or holes (solid-state) move to the Electron and positive-ion drift velocities in most cathode and electrons to the anode. gases at typical pressures and applied voltages are respectively of the order of lo6 to 10' cm s-i (Bortner and Hurst, 1954) and lo2 to lo3 cm 5-l (Wilkinson, 1950). The respective collection times for electrons and positive ions are of the order of microseconds and milliseconds. In semiconducting crystals the electron and hole mobilities are not so disparate, and some can be found in which these mobilities are of the same order of magnitude. Thus Kittel (1971) quotes values for InAs of 77~10~ cm2V1.Y1 (electrons) and 1.25~10~ c&.~'s~~ (holes) at room temperature. Knoll (1979) also quotes mobilities for germanium at 300 K of 3.9X103 c&J-~s‘~ (electrons) and 1.9x103 cm'V_1s-r (holes); and at 77 K for germanium, 3.6~10~ cmzV-ls‘l (electrons) and 4.2~10 c&~~s~' (holes). (Also see Bertolini and Cache, 1968.) By way of example, for an applied electric field of 500 V cm-': A mobility of 77~10~ CII&.~~~~~would result in electron velocities of 38.5x106 cm s-1; and a mobility of 1.25~10~ ~rn*V~~s~' gives a hole velocity of 62.5~10~ cm 5-l. Corresponding collection times across a l-cm-thick semiconducting crystal would be 26.0 ns (electrons) and 1.6 /JS (holes). From these examples it can be seen that the output pulses from semiconducting crystals can be of very short duration. Considering both gas proportional counters and semiconducting detectors, it is clear that the electronic circuitry required to process and record numbers of detected events as a function of time must be able to handle output pulses that range from milliseconds to nanoseconds in duration. Ranges for current duration times in different types of detectors are: l
1 ns to 10 ns for scintillators semiconductors;
(liquid and plastic) and narrow depletion-depth
. 5 ns to 1.5 ps for pure or activated NaI and CsI scintillation detectors; . 0.01 ps to 5 ps for gas-filled detectors; Fairstein and Hahn (1965) emphasize that the instantaneous current in a detector is not proportional to the energy deposited in the detector; only the total charge or integral of the current with time are proportional. The pulse of charge generated in a proportional counter differs from the pulses generated in an ionization chamber or semiconducting crystal in that the anode of the counter is normally a fine wire that is used to produce in the adjacent gas a multiplication region of high electrical field, whereas ionization chambers and semiconductor detectors usually have parallel-plane or larger-diameter cylindrical electrodes. Taking into account the difference in the electronic and ionic mobilities in gases, the output pulses from a proportional counter or ionization chamber are somewhat more complex than those from semiconductor detectors. It is instructive to consider the sequence of events occurring in a proportional counter following the creation of a burst of ionization due to a primary ionizing event. purpose we will consider such a detector to which a suitable source of high For this voltage has been applied across the gas between the anode wire, or rod, and a cylindrical cathode. The electric field strength E, at a cylindrical surface in the gas, at a distance r from the axis of the counter, is given by V E=z
(6-l) L- In b/a
Radioactivity
measurements:
principles
and practice
885
where V is the applied voltage and b and a are respectively the cathode radius of the anode rod or wire. The value of E, therefore increases very value of r approaches that of a. As
soon
as
the
primary
ionizing
event
occurs
in
the
counter,
the
radius and the rapidly as the
electrons
formed
begin moving inward towards the anode and the positive ions outward to the cathode walls. Consequently an induced negative-voltage pulse begins to be generated in the anode by the The combined movements of the electrons towards it and of the positive ions away from it. electrons moving at velocities of the order of lo6 cm 5-l quickly reach the region of multiplication thus creating more ion pairs whose motions towards the anode and away from If there is a large residual resistance, R, it contribute further to the induced voltage. C, between the anode and cathode of the counter, then the negative pulse and capacitance, the product generated will be like that depicted in Fig. 4-4, for the case of RC large this figure The time scale of of R and C being the time constant of the simple circuit. both the movements of electrons that are is greatly distorted in that it illustrates accomplished in microseconds or less and the motions of positive ions that may take as long as several milliseconds to reach the cathode. the time taken for the primary The first interval of time, tI, shown represents electrons to reach the multiplication region which will be of 1 JLS duration, or less, if The next period of time, fZ the primary event occurs within 1 cm of the anode rod or wire. electrons generated in the multiplication region the time taken for the - Cl, represents The remaining growth of to reach the anode. This may be of the order of one nanosecond. the amplitude of the negative pulse is due to the much slower movement of the positive ions With mobilities of at least lo3 times less than those away from the multiplication region. of electrons this part of the pulse will take of the order of milliseconds to reach a in the unreal case of RC being infinite, the voltage on the anode, maximum. Thereafter, having reached a maximum asymptotically, would remain at that value. In real life, however, RC is not infinite and the pulse, having reached a maximum, will therefore slowly decay. In fact, in practice, the decay is hastened by incorporating C, into the circuit in the manner shown in Fig. 4-3. resistance, R, and capacitance, BY a careful choice of R and C, a pulse of adequate amplitude and of suitably short duration of This procedure for shortening the duration several microseconds can thereby be achieved. of the pulse is called "clipping". In the absence of clipping and at count rates in excess of a few hundred per second "pile-up" of the pulses from the detector will occur, giving rise to distorted pulses of increased amplitude, in the manner illustrated in Fig. 6-l. At higher rates of pile-up these increased amplitudes may exceed the dynamic ranges of subSuch clipping by means of an RC-decay circuit sequent amplifier stages and paralyze them. is known as RC differentiation, The rise time of such a pulse is defined as the time and the decay time is that required to go from 10 to 90 percent of the peak amplitude, required for the pulse to decay to l/e or 37 percent of the peak amplitude. The detectors described in Chapter 4 give output signals of from 10ml' to less than 10ml' coulomb per event. These pulses of charge give rise to small voltage pulses across The charge collected by the detector is the resistance R and capacitance C in Fig, 4-3. The amplitudes of the proportional to the radiation energy deposited in the detector. collected and the output voltage pulses are also approximately proportional to the charge radiation energy deposited. The purpose of all subsequent circuitry used to shape and amplify these pulses is to preserve such proportionality while giving them the power and characteristics compatible with the requirements of the analyzing systems, such as discriminators, counters, multichannel pulse-height analyzers, or computer-based programmable on-line analyzing systems.
@JLJLiS-
Pulse &apes from a typical radiation detector: a) at the Fig. 6-l 2mrJlifier input; b) after differentiation with a short time constant Note that the undershoot normally associated with the differRC. entiated pulses has been removed (after Mann ef al., 1980). 6.3. DIFFERENTIATING AND INTEGRATING NETWORKS The rise time of the negative pulse, in most detectors, ranges from 1 ns to the order of 5 /As, the latter being a rather large upper limit for most present-day detectors, The decay time of the pulse can range from nanoseconds, depending on the type of detector, to
a86 infinity
Radioactivity
depending
on the value
measurements:
of the decay
principles
constant,
RC,
and practice
of the external
circuit.
In Fig. 6-l the peaks of the pulses are depicted as a spike, or discontinuity. But it must be remembered that the time scale for the rise is of the order of nanoseconds whereas the decay takes of the order of a thousand times longer, i.e. microseconds or possibly, even, milliseconds. But whichever, the shape of the peak is still similar to those depicted in Figs. 4-4 and 6-1, and the differential quotient, dV/dt is a continuous function. Figure 6-2a represents a simple single RC-differentiation circuit in which the shape of the input voltage pulse, Vi, is again represented as a discontinuous function. The output voltage V, decays exponentially with the time constant R&, = 7, and falls to l/e (0.37) of its maximum value in time T. (The capacitance C, includes any residual capacitance, and may only comprise residual or parasitic capacitances.) This circuit is also used as a high-pass filter, derived from the fact that it attenuates low-frequency more than high-frequency signals (the impedance of a capacitance is inversely proportional to frequency). (For further details see Chiang, 1969.) Figure 6-2b shows a simple RC-integration circuit. The output of an uit is proportional to the integral of the input signal. The cirrcuit also time of the input pulse: The rise time of a pulse is defined as the time voltage to increase from 10% to 90% of Lts final value V,. This time is The integrating circuit is also used as a low-pass filter, because it frequency signals preferentially over low-frequency signals.
integrating circextends the rise required for the equal to 2.2 RC. attenuates high-
Fairstein and Hahn (1965-66) defined a differentiator as "a network in which the output signal approximates the mathematical derivative of the input signal," and an integrator as "a network in which the output signal approximates the mathematical integral of the input signal." The triangles shown in Figs. 6-2~ and 6-2d represent buffers (with unit gain) or amplifier-gain stages that provide electrical isolation between the different shaping circuits. The extra shaping circuit added to the output of the combined differentiationintegration network of Fig. 6-2~ to give the network shown in Fig. 6-2d simply serves to integrate the output pulse shown in Fig. 6-2~. The output pulse of the network shown in Fig. 6-?c is called a "unipolar pulse", and that from the network shown in Fig. 6-2d is called a "bipolar pulse". As there can be no net transfer of charge across the buffers, the areas of the positive and negative components of the bipolar output pulse be equal.
b) single RC shaping networks: a) single KC differentiation; Fig. 6-2 d) corn-KC integration; c) combined differentiation-integration; bined double differentiation-single integration. Vi = input Pulse, v,= output pulse, V,= maximum output pulse height (after Mann et al., 1980). Simple RC circuits do not give optimum pulse shapes either for reducing pile-up or for analyzing pulse amplitude. Modern circuits use complex, multipolar, active filters coupled with special d.c.-restoring circuits for improved performance. Thus while RC circuitry may be used in much of currently-operating nucleonic instrumentation, it is now being superceded by "Gaussian"or triangular-shaping circuitry or, in the case of scintillation detectors, by delay-line shaping. As noted in the preceding paragraph, the differentiation and integration of pulses can also be achieved by means of resistance-inductance (IX.) networks such as those shown in The time constant of the resistive-inductive circuit is equal to L/R, Figs. 6-3a and6-3b.
Radioactivity measurements: principles and practice
a87
where L is the inductance in henries and R is the resistance in ohms. As mentioned above in the case of RC circuits, the RL networks also do not give optimum pulse shapes for the reduction of pile-up or pulse-amplitude analysis.
Differentiation (a) or integration (b) of pulses by Fig. 6-3 resistance-inductance networks. Another network that is currently widely used to obtain a result similar to differentiation is that of the short-circuited delay line. A delay line in its most usual form consists of an inner conducting wire or rod running axially within an insulated outer concentric conductor. If the outer conductor is at ground potential and an electrical signal is impressed on the inner conductor of such a line that is of infinite length, the signal will travel along the inner conductor with a velocity that is inversely proportional to the square root of the dielectric constant of the material between the inner and outer conductors. If the dielectric is air, the propagation velocity of the signal will approximate that of the speed of light in a vacuum. The amplitude of the signal will, however, be attenuated because of energy losses, as it travels along the delay line. The ordinary coaxial cables that are used to connect various electronic components can also be used as delay lines. The higher dielectric constant of the insulation, used instead of air between the inner and outer conductors, gives rise to an increased delay, because of the lower velocity of propagation of the signal along the line. For an air-insulated delay line the signal is delayed by about 3.3 ns m-r. For most coaxial connecting cables the delay times will be approximately 5 ns m-l. (The characteristics of various coaxial cables and the velocities of signal propagation along them are given in Knoll, Table 16-l.) If a given length of a coaxial conductor is terminated by a short circuit at the end toward which the signal is travelling, the signal will be reflected with a 180" change in phase. It will then return to the input end of the line where the initial input signal and the delayed reflected signal, now of opposite polarity to give a shortene (clipped) pulse. The differentiating operation of a delay line is illustrated in Fig. 6-4 (a and b) for a step-function input pulse, in the ideal case where there is no attenuation in the delay line and the input resistance R, + R, is equal to the impedance Z,, of the delay line. In practice, there is attenuation and the amplitude of the reflected pulse would be less than that of the input signal. But modern good-quality d.c.-amplifiers are so designed that the base line remains at zero after the pulse has passed.
Delay-line differentiation: a) circuit with a single delay Fig. 6-4 line and a resistor, R b~~~~':~~~:e~~r~t:~~t~g~~~. equa1s the delay-line impedance; Double differentiation can also be carried out using two delay-line networks as illustrated in Fig. 6-5 with the resulting output pulse shown. For simplicity, the effect of RL decay has been omitted.
888
Radioactivity
Double
Fig. 6-5
works.
measurements:
differentiation
principles
and practice
by two ConseCUtiVe delay-line netRL decay on the Pulse shape
For simplicity the effect of
has been neglected. 6.4. AMPLIFIERS:
GENERAL
As has been indicated earlier, pulse-shaping circuits are essential for the purpose of reducing the tails of pulses generated in radiation detectors. Such radiation detectors may give pulses of charge with rise times of from nanoseconds to microseconds in duration, but with decay times of the order of milliseconds. Such slowly decaying tails limit the count rates that can be achieved to the order of one thousand per second if one wishes to preserve the proportionality between the measured amplitude of the pulse and the energy of the radiation detected. At higher count rates, unless the tails of pulses are clipped, the observed amplitudes will be larger because the recorded pulse is riding on the tail of a previous pulse. Such pile-up will cause distortion and, at higher count rates, may drive an amplifier into saturation. Pulse-integrating circuits also help to improve the signal-to-noise ratio in that, as "low-pass" networks, they also filter out higher frequencies. In order to operate scalers and other recording equipment it is often necessary to amplify, by many orders of magnitude, the voltage pulse derived from the small charge generzted in a detector. This is normally the function of a main amplifier with variable gain. But the main amplifier may be located some distance away from the detector, and the task of preserving the first feeble pulse from the detector is usually that of a small preamplifier that is located near to the detector, especially if it be a semiconductor. A preamplifier may be charge-sensitive, current-sensitive, or voltage-sensitive. The first of these three types is that which is appropriate to gaseous and semiconductor ionization-type detectors. If the charge generated in a detector were to be impressed upon a long cable having rather large capacitance, the voltage pulse that could be obtained from the initial charge would be insignificant. The charge-sensitive preamplifier should therefore be located as close as possible to the detector. Junction field-effect transistors (FET's) are used in the input stage of charge-sensitive pramplifiers, because they have have high input impedance and are significantly free from noise, especially when cooled to near liquid-nitrogen temperatures. Pulse-shaping is also necessary in order to optimize the signal-to-noise ratio and to provide the shape of pulse required by the pulse-height analyzer. Manufacturers will normally specify the input pulse-shape required by any given analyzer. The preamplifier should, in all cases, be placed as close to the detector as feasible. Preamplifiers should also be capable of driving the connecting cable to the main amplifier. This cable's impedance is commonly 50 ohms,and it must be terminated by its characteristic impedance at the input terminal of the main amplifier, either internally or externally, in order to eliminate reflections produced by mistermination. The charge generated in a gaseous or solid-state ionization detector is usually impressed across a resistance R and capacitance C, as shown in Fig. 4-3. The output-voltage-pulse amplitude is inversely proportional to the capacitance C, which, however, includes any stray, and possibly changing, capacitances associated with the detector. The stability of the output-voltage amplitude will therefore be very dependent on ambient factors such as temperature afid pressure. Such possible sources of instability have, however, been greatly reduced by using negative feedback preamplifiers, in which the value of the output-voltage amplitude depends principally on the value of a low-capacitance, stable feedback capacitor. The feedback-loop principle is also used in all types of operational amplifiers in order to improve their temperature stability, linearity, and rise-time characteristics. The output from the preamplifier is usually in the form of a tail pulse (Fig. 6-2a) that must therefore be reshaped at various stages in the main amplifier. 6.4.1.
Preamplifier
feedback
loop
The circuit of an a.c.-coupled charge-sensitive preamplifier is shown diagrammatically in Fig. 6-6. The feedback loop is shown through the capacitance C, and resistance R,. The test input is provided in order to introduce an external voltage tail pulse for testing the performance of the preamplifier or the entire electronic system, without the detector itself.
Radioactivity
measurements:
principles
889
and practice
Bias voltage
Q ’
CC(‘nF) -
-Low
noise
Driver
Voltage -
input stage
input
gain
low
c,
with
impedance output
high and
-
Impedance
4
93n
Series twminator resistance to match g3-ohm coaxial cable
(1pF)
II
CT{=1
pF)
R (son)
Block Fig. 6-6 preamplifier
diagram of a typical low-noise (after Ayers, 1973).
charge-.sensitive
--L ~x--t~R~~~-:;
Fig. 6-7 loop.
et al.,
&sic preamplifier-circuit diagram with negative-feedback A test pulse may be applied through R ,CT (after Mann 1980).
For the the basic
purpose of understanding the operation of the feedback circuit diagram, shown in Fig. 6-7, of the block diagram
loop, we will in Fig. 6-6.
consider In this
simplified basic diagram the three separate blocks are represented by a single triangle. Such symbols have already been used in Figs. 6-2 and 6-5 for an isolation stage or buffer. But they only represent the various functions performed by different electronic components be that normally commercially, and may selected from manufacturers' are available catalogues. to the preamplifier (triangle) are shown, the upper one In Fig. 6-7 two inputs The former noninverting (NI), and the lower one, which is here grounded, inverting (I). transmits the input signal through the preamplifier without inversion (without change in phase), and the latter input terminal gives an inverted output signal, as their names The "-A" in the b o d y of the triangle means that a negative input pulse exits as a imply. The capacitance C, and resistance R, positive output pulse with amplification equal to A. across the input and output of the preamplifier complete the negative feedback loop. A preamplifier with negative feedback operates in such a way as to reduce the input signal. In this mode of operation, which is also termed "closed loop", a fraction, f, of the negative output voltage is fed back and subtracted from the positive input signal (or positive output from negative input). The fraction f is determined by the feedback element. Suppose that the detector produces a total charge Qi, then this will give rise, in the open-loop mode, to an input voltage Vl to the preamplifier that is equal to QJC,, where C, is the "open-loop" capacitance, which is the sum of the detector capacitance and any stray capacitances, i.e. V, = -QJCF
(6-2)
preamplifier Therefore, with negative feedback, the voltage gain of a charge-sensitive becomes virtually independent of the gain of the preamplifier itself, and of the detector To a very good approximation the gain is dependcapacitance and stray input capacitances. ent only on the value of the feedback capacitance, C,, that can be exceedingly stable with respect to time and temperature. A resistance RF connected in parallel with the feedback capacitance discharges it and determines the discharge time constant, R,C,, of the preamplifier output pulse. reference may be made to Chiang (1969), Ayers (1973), For more detailed information, Knoll (1979), Fredericksen (1984) and, or, to the texts listed in 76-10. Very informative and up-to-date literature can also be obtained from the manufacturers of nucleonic equipment.
Radioactivity
890
6.4.2. Main
amolifier
and feedback
measurements:
principles
and practice
loon
partly-shaped detector function is to take the amplified, The linear amplifier's signals from the preamplifier and to amplify and shape them further until they are suitable As can be seen from Fig. 6-8, the for final pulse analysis or for count-rate measurements. linear amplifier consists of a number of amplifier stages, with feedback loops, coupled The shape of the final output pulse must be such as to together by shaping networks. optimize the signal-to-noise ratio and also to be compatible with the equipment used for Improvement of the signal-to-noise ratio is now achieved by the use the data processing. of complex bandpass filters to shape the pulse, and a "Gaussian" pulse shape is often By increasing the duration of the rise time of the pulse, and decreasing that of realized. A "Gaussianits time of fall narrower and more symmetrical pulses will be obtained. shaped" pulse is the limiting result obtained by an infinite number of integrating stages close to of differentiation although a pulse with a shape very following one stage stages of The approximately four integration. can be produced with "Gaussian" and the (CR) attenuates low-frequency components (e.g. hum) differentiating stage integrating stage (RC), which is, however, rarely used, attenuates those of high frequency The optimum noise reduction is generally obtained when the RC time constants (see 76.3). of the differentiating circuits are equal, but there is always a conflict between circuit noise, detector noise and pulse pile-up. One has to choose the optimum pulse shape for It should be realized, however, that minimum noise while retaining spectral information. superior, and complex, filters are used in modern amplifiers. 21 Fl.9,
SW0"d
0 "nlpolar out
Simplified diagram of a typical linear nuclear pulse amplifier with RC integration and both single and double differentiation of the output signal (after Mann et al., 1980).
Fig. 6-8
A primary requirement for a linear amplifier in a radiation-measuring system is possibly be affected by instability in the voltage stability. Its gain could, however, But, as in the case of the supplies, by aging of components and by temperature changes. charge-sensitive preamplifier the effects of such instabilities can be minimized by the application of the principle of negative feedback. As indicated in each of the amplifier stages A,, A, and A,, shown in Fig. 6-8, this is provided by the feedback resistors RF1, Considering one such stage, if, in the absence of feedback, the amplifier has R,, and R,, a gain equal to A, then the amplitude of the output signal V, for an input signal of If a fraction, f, of the output amplitude amplitude V, would be AV,. is applied to the inverting input terminal of the amplifier stage it will be subtracted from Vi, so that V, = A(V, - fVO)
V, = AV,/(l + fA)
or
Thus
,
the closed-loop
gain
V,/V,= compared
with
(6-3)
is
the open-loop
A/(1 + fA)
,
(b-4)
gain A
Af >> 1, so that the 1n general, however, such an amplifier will be designed with But the value of f is set closed-loop gain will be, with good approximation, equal to l/f. by the value of the feedback resistance, R, which can be made to remain constant with time and to be highly insensitive to temperature change, with the result that the closed-loop gain will be equally stable. There are many other circuit functions of the linear amplifier, not shown in Fig. 6-3, that provide for its overall adjustment. These may include, for example, variable-gain pulse-shaping time constants (often by switch settings), baseline restoration controls,
(q.v.),
etc.
An amplifier should have good overload characteristics in order to handle input pulses counter is used to of greatly different amplitudes, as, for example, when a proportional register a spectrum of beta particles. A linear amplifier with a gain of, say, lo3 that produces a maximum output pulse of 10 V will overload for input pulses greater than 10 mV For input signals having amplitudes much greater than 10 mV the from the preamplifier.
Radioactivity measurements: principles and practice
891
tens of microseconds, main amplifier can be driven into saturation and be paralyzed for thereby introducing "dead times" during which it is unable to process further input A wide selection of amplifiers with so-called good overload characteristics is, signals. however, available commercially. Other problems arise in handling the unipolar tail output pulses from preamplifiers. discussed in connection with the need for pulse shaping. This problem has been briefly Fig. 6-8 illustrates the kind of relationship between the signal that is generated across the output terminals of a gas-ionization detector and the output-voltage tail pulse from In this figure the tail-pulse duration is of the order of one-third of a the preamplifier. millisecond. If the pulses were arriving at constant frequency, the preamplifier could not handLe more than the order of 3,000 to 4,000 a second without overlap and consequent distortion; but it could also not handle more than about 1,000 5-l randomly distributed If, in pulses, such as those arising from radioactive decay, without risk of distortion. addition, these events arose from monoenergetic gamma rays interacting with, for example, a solid-state detector, then such distortion would give rise to a broadening of the finally observed gamma-ray peak by the addition of pulses to its high-energy side. Another source of distortion of unipolar pulses passing through a chain of shaping and feedback stages is caused by their depositing short-lived charges of the same sign on the These charges will be dissipated in various coupling and bypass capacitors in the chain. times governed by the various RC time constants of the capacitors in the chain. But these accumulated charges will cause distortion in an amplifier system at high count rates, One way to avoid such charge deposition unless some form of compensation is employed. leave no net charge, the positive and negative would be to use bipolar pulses which would lobes being of equal area. a differentiating Any coupling capacitor with resistance to ground will act as network and convert a unipolar pulse to a bipolar pulse with an undershoot of long Unipolar peaks with long overshoots can be converted by RC differentiation to duration. bipolar peaks, the second lobe of which is an undershoot of equal area to the first. And long undershoots can be removed or turned into undershoots of very short duration by the of pole-zero cancellation and baseline restoration, that are methods, respectively, described in the next section. Where an overshoot or an undershoot of, say, 300 ps would limit pulse-processing rates to the order of 1,000 s-l, an undershoot of the order of 10 ps would permit pulse-processing rates, without serious distortion, of the order of 30,000 s-1. 4.4.3. Pole-zero cancellation and baseline restoration The output pulse from a preamplifier is a tail pulse similar to that shown in Fig. Normally this tail pulse will traverse a coaxial cable to be processed by the input coupling differentiator of the first stage of a linear amplifier (Fig.6-8), from which it will emerge as a bipolar pulse similar to that shown in Fig. 6-9b. The undershoot of this This is achieved by pulse can then be removed by the process of pole-zero cancellation. adding a portion of the original tail pulse to the undershoot by means of a variable The resistor placed across the capacitor C,, (Fig. 6-8), as illustrated in Fig. 6-9c. variable resistor is adjusted, while observing the output pulses from stage A, (Fig. 6-8) on an oscilloscope, until suitable unipolar pulses of short duration (Fig. 6-9d) are obtained. 6-9a.
Time
Pole zero compensation of differential pulse undershoot; Fig. 6-9 a) original tail pulse; b) after passing through a coupling network of short time constant (differentiator); c) dashed line is portion of signal to be added back in; d) resultant pole zero compensated pulse (after Hatch, 1973). Baseline restoration, in its simplest form, is achieved by means of the biased-diodeInitially the diode in this cicuit is biased to be restorer circuit shown in Fig. 6-10. But when a bipolar pulse arrives at the input of this circuit the first non-conducting. lobe will be transmitted and the second will drive the diode into conduction, and the remainder of the signal will be short-circuited to ground, with the undershoot returning rapidly to the baseline, as illustrated in Fig. 6-11. A residual undershoot of much shorter duration survives, but the time during which there is a possibility of pile-up on the undershoot is reduced by a factor equal, in this illustration, to about six This type of restorer does, however, distort low-amplitude pulses. Where such pulses are likely to be present it is necessary to use an amplifier-diode-restorer circuit known as an "active restorer'.
Radioactivity
a92
measurements:
A
I
and practice
AV
Biased-diode restorer Fig. 6-10 (after Hatch, 1973).
I
principles
circuit
I
for baseline
,
I
80
0
Fig. 6-11 Pulse shape, a) before and b) after (after Hatch, 1973).
restoration
T
100 ps
baseline
restoration
6.5. MICROELECTRONICS Three or four decades ago in order to establish a function, such as transmitting or not transmitting a signal above or below a certain amplitude, a function known as "discrimination", one adopted a suitable design, purchased the necessary electronic components such as vacuum tubes, resistors and capacitors, and then assembled the circuit which would perform that function. Now, one normally purchases a completely assembled discriminator from a commercial supplier. Following the development of solid-state-diode detectors described in Chapter 4, complete integrated circuits (IC) can now be created on silicon wafers by the deposition or implantation of appropriate dopants and suitable metallic contacts and connectors. The procedures of modern microelectronic technology permits an electronic component such as a transistor to have dimensions of the order of micrometers, and enable as many as half-a-million transistors to be located on a six-inch-diameter silicon disc, and megabit "chips" may be expected to be in production soon, if not already (see C. Seitz and J. Matisoo, Physics Today, May,1984). Already by 1984, integrated circuits had reached such a degree of excellence that a complete charge-sensitive preamplifier could be purchased as a single module measuring about 3 x 1 x 0.25 cm (advertisement in Physics Today, May, 1984), and pens and pencils are available, containing a small fragment of quartz and single integrated circuits of many components, that give the calendar date, time of day and seconds in a small liquid-crystal digital display. This microelectronic revolution is having a profound effect on both the size and reliability of contemporary multichannel analyzers and other nuclear data-processing equipment, and it therefore behooves the planners of new radionuclide metrological laboratories to take careful note of the free publications of the nuclear industry. The recommended texts must be read to give the principles, but the industrial publications will inform one of their latest applications. It should perhaps be noted that, because a chip complete integrated circuit, the term "chip" is "integrated circuit".
6.6. COINCIDENCE
AND ANTICOINCIDENCE
LOGIC
of a silicon wafer often contains a frequently used synonymously with
CIRCUITS
Two of the most powerful methods for the direct measurement of activity are those of coincidence and anticoincidence counting. Pulse-height analyses by single-channel and multichannel analyzers (SCA and MCA, respectively) also involve the use of anti-coincidence logic circuits. A process
double-coincidence-counting circuit comprises two main detector channels that pulses from two separate detectors (one, for example, of 0 particles and the other
Radioactivity
measurements:
principles
and practice
893
of
A so-called "coincidence mixer" receives inputs from both and records them. 7 rays), channels and registers the number of times that events in each channel are coincident in The principles of coincidence and anticoincidence counting are discussed in Chapter time. 5, but in practice the method requires that the coincidence-mixing circuit shall put out a standard logic signal every time that the signal pulses from the beta and gamma channels as the coincidence to within a controllably short interval of time, known coincide, In the case of the anticoincidence logic circuit it is required that it resolving time. put out a logic signal whenever it receives a signal pulse from the beta-channel input or the gamma-channel input, but never when the two are in coincidence. circuit, coincidence and As with so much else in this age of the integrated anticoincidence circuits are not only available commercially, but they can be obtained with more than two inputs in order to provide an output logic signal when the signals to all Such circuits would be required to inputs are in coincidence, or, in anticoincidence. But in the implement the triple-to-double coincidence method described in 75.4.3.4.2. coincidence and anticoincidence circuits following two sections only simple, two-input, will be described - without any of the embellishments that can be obtained on commercially available models, such as variable resolving times and pulse shapes. 6.6.1.
Standard
loeic uulses
A standard logic pulse is one that conveys the message "yes" (or "1") or "no" (or "O"), as illustrated diagrammatically in the upper part of Fig. 6-12. The corresponding voltage levels of the "yes" and "no" pulses are designated V(1) and V(O), respectively. These pulses are square, and often of the order of 0,5 to 5 ps in duration. The three most important common logic systems are named, respectively, Transistor-Transistor Logic (ECL). Logic (TTL), the Nuclear Instrument Module system (NIM), and Emitter-Coupled Approximate unterminated signal levels in volts for each of these systems areshown in the lower part of Fig. 6-12. These are only approximate ranges as it is, for one thing, necessary that the range of output voltage should be greater than that required to drive If the signal terminates in a characteristic impedance of 50 the input of the next stage. For those who need more definitive information ohms, the levels are specified in amperes. about logic-system specifications, reference may be made, for example, to AEC (1974) or ANSI/IEEE (1982a).
I-----“,o,l 1 1
V(1)
l--
TTL
0
A0
1.8to5V
Coincidence
“No”
or”0” level
NlM;y:;;;;y
EC'dr::a"l;a;
to o.sv
Fig. 6-12 6.6.2.
“Yes” orl'l" level
I----------
Diagram
of a standard
logic
pulse.
or "AND" loeic circuit
diode-logic coincidence circuit (an AND gate) is shown A simple two-input In this figure logic signal pulses are shown arriving at diagrammatically in Fig. 6-13. the two inputs A and B. They could equally well be signal output pulses from two Some will, however, amplifiers and they are arriving at channels A and B randomly in time. arrive coincidentally. +pv(>W
Fig. 6-13
Coincidence
or "AND" logic circuit
(after Chiang,
1969).
If a moment be considered when the whole system is In Fig. 6-13, V(1) > V(O). then the quiescent, with no pulses arriving at A or B and both at the "NO" voltage V(O), If diodes D, and D, will be conducting and the output voltage will be maintained at V(0). a single pulse of amplitude V(1) were now to arrive at either channel A or channel B, the diode in the other channel will continue to conduct and the output of the system will at channels A But if positive logic pulses, V(l), arrive simultaneously remain at V(0). and B then the voltages across both D, and D, will fall to zero and neither diode will A logic pulse of amplitude V(1) will now be generated at the output of the conduct. circuit, indicating that a coincidence has been detected. When the input of either channel voltage will drop back to V(O),and remain so for as A or B drops back to V(0) the output long as either of the diodes D, or D, remains conducting.
Radioactivity measurements: principles and practice
094
A coincidence logic circuit can also be assembled using transistors instead of diodes (see Chiang, 1969). 6.6.3. The "OR" logic circuit The coincidence circuit described above enables an output logic pulse to be generated whenever two input pulses are impressed simultaneously upon channels A and B. An "OR" circuit (an OR gate) gives an output logic pulse whenever a signal pulse arrives at either channel A a channel B. This can also be achieved by means of a simple diode or transistor circuit. The diode circuit for positive input pulses is shown diagrammatically in Fig. 6-14.
IA
-VC
"OR" logic circuit. Fig. 6-14 The diode circuit shown in Fig. 6-14 is similar to the coincidence circuit of Fig. 6-13, but with the diodes reversed and the output biased at V(0) through the resistance R. In fact, if we were considering negative instead of positive input pulses, this OR circuit would act as a coincidence circuit, and the coincidence circuit of Fig. 6-13 would act as an OR circuit for negative pulses. non-conducting, and both In the quiescent state the diodes shown in Fig. 6-14 are If a positive signal V(1) appears at the input of inputs remain at the potential V(0). either channel A or channel B, diode D, or D,, respectively, becomes conducting and a positive logic pulse of amplitude V(1) is generated at the output of the circuit, indicating that non-coincident pulses have arrived at the inputs of channel A or channel B. arrive in In addition, however, an output logic pulse will be generated if signals coincidence at channels A and B. Strictly, therefore, the circuit shown in Fig.6-14, and which is known as an "OR" circuit, is an "and, or" circuit! Both the AND and OR logic circuits shown respectively in Figs. 6-13 and6-14, can be expanded to any number of input channels A, 8, C,..... .N, in parallel (see Chiang, 1969). 5 6 4
The "NOT" ionic sate
The NOT gate gives an output logic pulse that is the inverse of the input signal. Thus if the input signal is a positive pulse V(1) the output signal will be a negative pulse of amplitude V(1). This logic can be achieved for positive input signals by means of the transistor circuit shown diagrammatically in Fig. 6-15.
"NOT" or "NAND" logic gate (after Chiang, 1969). Fig. 6-15 then the transistor is cut off and the If the input to channel A is at voltage V(O), If, however, the input suddenly switches to V(l), then output will be at the level V(1). This is a somewhat the transistor saturates and the output level changes to V(0). simplified presentation of this logic function and for a more detailed description with suggested values for the various components Chiang (1969) should be consulted. 6.6.5. Anticoincidence
loeic circuit
The logic of a two-input anticoincidence circuit is designed so that an output logic pulse is generated only when a signal is received at input A and none simultaneously at input B, m when a signal is received at input B and none at input A. We have seen that this logic was almost achieved by the "OR" circuit described in 76.6.3 above; but, as was pointed out, the "OR" gate did not exclude coincident input signals and could be more The logic circuit required in order to circuit. strictly described as an "and, Or” identify only those signals in two channels that are not coincident in time is known as an "EXCLUSIVE OR gate" (Chiang, 1969); one such circuit is shown as a block diagram in Fig. 6-16 and incorporates one OR gate, one NOT gate and one AND gate.
Radioactivity measurements: principles and practice
a95
"EXCLUSIVE OR" gate (after Chiang, 1969). Fig. 6-16 The symbol for a NOT, or NAND gate comprises that for an AND gate with a small contiguous circle at its output. The special geometrical shapes used to symbolize the AND, OR and NAND (NOT) gates should also be noted as these are in constant use - just as a triangle is used in circuit diagrams to denote an amplifier or buffer. diagram are these symbols labelled as they have been in Fig.6-16.
Nor in a circuit
From Fig. 6-16 it will be seen that the OR gate will transmit logic pulses to the second AND gate for all coincident and anticoincident signals or logic pulses received by the OR gate. But the positive coincident logic pulses received at the second AND gate will be cancelled by the inverted coincidence logic pulses received simultaneously from the first AND gate. 6.7.
DISCRIMINATORS AND OTHER PULSE- AND DATA-PROCESSING EQUIPMENT
Discriminators permit the selection of amplitude voltages above or below which pulses can be either accepted for further processing for data collection, or rejected. Integral discrimators accept all pulses above a selected amplitude and are used in most electronic systems to exclude amplifier or other low-amplitude "noise". Differential discriminators select, for further processing, pulses in a range of amplitude, or u heipht, which is often limited to a small range of interestAV, e.g. a single gamma-ray peak in a gamma-ray spectrum. By the judicious use of one differential discriminator or of very many of them, one can design, respectively, either a single-channel analyzer (SCA), or a multichannel analyzer (MCA) that are used, especially the latter, in almost every branch of radionuclide metrology. 6.7.1. Inteeral discriminator A single discriminator circuit is one that is biased by an external threshold voltage in such a manner as to eliminate all input signal pulses below a selected amplitude or pulse height. The threshold voltage, V,, may be provided by means of the variable potentiometer P. This information is then used to select those incoming signals, with amplitudes greater than V,, for further processing. This circuit, which is illustrated in Fig.6-17, is called an "integral discriminator", and is chiefly used to eliminate unwanted pulses, including noise.
Simple integral-discriminator circuit; a) and b) show the Fig. 6-17 relationship between input pulse amplitude 4, threshold setting K, and discriminator output signal Vo. When Vi>/Vt, Voremains in the "yes" state (after Mann et al., 1980). 6.7.2. Differential discriminatororsinele-channel A
differential
discriminator,
or
analyzer
single-channel
analyzer,
consists
of
a
circuit
Radioactivity
896
network between
measurements:
principles
and practice
that identifies only those signal pulses with amplitudes in a lower threshold V,, and an upper limit VtY, so that AV = V,,
a narrow V,,.
range,AV,
one a lower-level (LLD) and This is accomplished by using two integral discriminators, the other an upper-level discriminator (ULD), in parallel in the manner shown in Fig. 6-18 so that the input signal of amplitude V, from the main amplifier, or other component is fed The output signal from each discriminator is fed to an to both discriminators. anticoincidence logic gate that will generate an output logic pulse a if an output logic pulses, V,, and V,, are received h pulse is received from LLD or ULD, but none if signal coincidence from LLD and LJLD.
v, Time __t
a) Block diagram of a basic singla-channel analyzer; Fig. 6-18 b) operation of the circuit for pulses below, between and above both the lower, VI, and upper, V2, level discriminator thresholdYland V2 in b) are equivalent to l'tl and vt, voltage settings. in a) (after Mann et al., 1980). respectively,
,
Thus the small first pulse shown in Fig. 6-18 will pass neither discriminator; the second pulse will generate an anticoincidence output logic pulse; and the third pulse generates output pulses from both discriminators in coincidence that will therefore be rejected by the anticoincidence circuit. The anticoincidence-output-logic used to permit the further processing amplitude between V,, and V,“. 6.7.3.
Scalers
(Pulse-countinn
pulse generated in the second example can then be and recording of the second signal pulse, V,, with
circuits)
Activity, the amount of a radionuclide is a rate of the quantity that specifies disintegration. After the pulses of electrical charge generated by an ionization type of detector of the radiation from a radioactive source have been processed it is necessary, in order to quantify the amount of radioactivity to measure the rate at which they are being produced. This rate serves as a relative measure of the activity of the source. The same necessity to count electrical output pulses occurring in a given time arises in the case of electron-multiplier phototubes used to detect the light output from scintillation detectors. In the 1930's when low-activity sources were measured at relatively low count rates it was usual to count the number of output pulses from the last stage of the electronic the relays of which circuitry using electromechanical registers required a fairly substantial pulse to operate satisfactorily. As the activities of sources to be measured to reduce increased and the speed of the electronics became greater, it became necessary the rate at which the electromechanical registers were driven in order to avoid overloading to the point of failure. This was accomplished by introducing a binary scaler between the or discrimination and the electro-mechanical register to scale last stage of amplification, The scaling down the pulse output rate to a level that was acceptable to the register. factor was equal to 2" where n could be chosen so as not to exceed the input capacity of Such registers also operated in conjunction with a series the electromechanical register. of neon or incandescent pilot lights that indicated the number of counts stll resident in the scaler when at the end of the chosen duration of the counting run the scaler was switched off.
Radioactivity
measurements:
principles
and practice
a97
In the present era of solid-state light-emitting diodes (LED's) and integrated These circuitry, scalers read out directly in the decimal system, in Arabic numerals. counts numerals are assembled from seven small elongated rectangularly shaped LED's such as digital watches and in many and various instruments are used nowadays in hand calculators, initially Nevertheless, with digital displays. the incoming signal pulses are still stored in a binary scaler and then decoded by means of a binary-coded decimal (BCD) decoder in order to activate the approriate segments of the LED displays to give the Arabic numerals that indicate the number of counts that have been accumulated. Any number Two decades of such a decade-scaler circuit are illustrated in Fig. 6-19. BCD-to-sevensegment decoders that are now of decade stages can be assembled from available commercially as integrated circuits.
Circuit of n-decade scaler with visual display and BCD Fig. 6-19 When a decade-counter stage has already accumuldigital output. ated nine counts, the arrival of another signal pulse causes the BCD to reset to zero and an overflow pulse is transmitted to the The count-enable gate allows the counts next higher decade stage. The reset is to be collected for, usually, a preset selected time. to return all stages to zero before starting counting (after Mann et al., 1980). 6.7.4. Multichannel
pulse-heivht
another
interval
of
analyzers
We have seen that an integral discriminator or a single-channel analyzer can be useful in excluding low-energy noise and, in the case of the single-channel analyzer, for defining a "window" of energy,AV, which will accept, for further processing, only those signals with pulse heights within the amplitude range lying between V and V + AV. Such a capability is very useful when one wishes to quantify a sample that is known to contain radioactivity that emits monoenergetic radiation, as noise and background radiation with energies lying below or above the "window" will be eliminated. Very frequently, however, it is necessary to record a whole spectrum of radiation energy from a single radionuclide, or a mixture of radionuclides, or when testing a special sample for radionuclidic purity. It is also very desirable in cases involving weak sources requiring Long counting times to record a whole spectrum simultaneously in order to minimize the effects of component instability. For this purpose, and in the early days after world-war II, crude multichannel pulse-height analyzers (MCA) were assembled using a series of integral discriminators to divide a given range of energy into a series of adjacent energy "windows", in exactly the same way as two integral discriminators had been used to define a single "window" with a limited range of energy. Thus lo- and ZO-channel pulse-height analyzers were assembled, respectively, from 11 and 21 integral discriminators. Each channel was provided with a scaler and register to record the number of pulses of each given increment of energy. Some of these early MCA's, particularly in Canada and the United Kingdom, were named "kick-sorters", and when they operated with their 11, 21, or more electromechanical registers at full cry, the less interested spectators would rarely prolong their visits. These MCA's were adequate for the detectors of their time, but with the advent of high-resolution solid-state detectors it has been necessary, in order to exploit their resolution, to develop MCA's of much higher resolution and greater storage capacity. Today MCA's can be produced, using integrated circuits and a different technique of pulse-height analysers, with 8192 channels or more. The then new technique was devised by Wilkinson (1950) in 1949, and it involved stretching the signal pulse as it entered the analyser so that the pulse was held st its maximum value during an interval of time during which it was used to charge a capacitor to a voltage equal to the amplitude of the pulse, V, After reaching the voltage V, the capacitor was discharged linearly by means of a source of constant current, and the time required so to discharge it was measured by means of a constant-frequency oscillator built into the MCA. These measured numbers of oscillations were then proportional to the
898
Radioactivity measurements: principles and practice
This technique is known as analogue-to-digital pulse heights of the input-signal pulses. conversion (ADC), "analogue-to-digital" signifying that the energy of the detected event that was initially proportional to a voltage had been converted to proportionality to a number. These whole numbers - the numbers of oscillations proportional to the various pulse heights - are then used to choose their appropriate sequential position in a computer-type Each such location is called a "bin". Thus an memory, known as "addressing the memory". input pulse that generated, say, n oscillations, which might be proportional to a pulse height of V,, would be addressed to the n-th bin and be stored. A second and then a third pulse of the same amplitude would be addressed to the same bin and stored, and so on for But a pulse, say, of amplitude V,,, would be addressed all pulses of the same amplitude. to the (n + 1) bin and stored there, as would also be all subsequently arriving pulses of that amplitude. Thus, as an experiment proceeds, all incoming pulses are assigned to the appropriate to the magnitudes of their respective pulse heights, and the energy bins spectrum of the detected radiation is accumulated. At the end of the experiment the memory is "read" by conventional computer techniques and the energy spectrum can be displayed on the computer-type screen, or a plot of it can be printed, in the form of incoming pulse rate as a function of energy, or channel (i.e. bin) number This type of MCA is also provided, now almost invariably, with a so-called "live timer" because of the long times involved in first converting and then storing large The pulses of greatest amplitude will clearly numbers of pulses of different amplitudes. take the longest time to sort by the Wilkinson method as they will generate the greatest number of oscillations. A loo-MHz oscillator will generate one oscillation every ten This interval of time will therefore approximately represent the shortest nanoseconds. interval of time reqired to increment the analyzer from one bin, or channel, to the next, i.e. one lo-ns pulse will address the first bin, two the second, and so on. Thus it will take about 8.2 /IS to send an event to channel 8192, or to the overflow where the record of stored as one single number, equal to the sum of all all higher-energy events will be events beyond the energy range of the MCA. In addition another 5 to 10 j~s will be needed to store the pulse in its appropriate channel. During this time of from 5 to 18 ps, known as the dead time the MCA will be unable to receive or to process any further pulse. Hence the need for the live timer, or clock, which at the conclusion of an experiment provides the time during which the MCA has been receptive to incoming pulses; and this is the time that must be used in order to calculate the count rate of incoming events. The live-timer circuit is provided with timing pulses from the MCA's constant-frequency oscillator, and the circuit is used to operate a gate that is closed to incoming signal pulses for the time during which the MCA is processing its last input pulse. A typical pulse-height spectrum obtained by a multichannel pulse-height analyzer at the National Bureau of Standards of one of its mixed radionuclide multi-gamma-ray standards Such spectra are usually collected over a measured live time. is shown in Fig. 6-20.
Channel
number
-
Gamma-ray spectra of a mixed radionuclide source consisting Fig. 6-20 of 5 ml of solution in a glass ampoule. Upper spectrum obtained with the source within a 12.7-cm diameter NaI(T1) well crystal. Lower spectrum obtained with the source at the face of a 60-cm3 Ge(Li) detector (from NCRP, 1985). Multichannel pulse-height analyzers now combine so many format-selection functions, such as, for example, linear or logarithmic ordinate (number of events) scale, isolation of a selected energy range, and summation of counts between two selected energies, to name but a few, that most MCA's begin to resemble and begin to perform many of the functions of a modern computer. It is not, therefore, wholly surprising to find that commercial suppliers of nucleonic instruments are now developing ADC's and buffer memories (packaged for compatibility with the NIM standard system) and interfaced, with appropriate programming provided, so that they may be used with several personal computers.
899
Radioactivity measurements: principles and practice
The fastest analyzers in use today use the method of successive aaoroximation to This method is based on building up a "comparison" measure the final output-pulse height. amplitude by means of very fast binary increments and comparing this, and other successive artificially-created amplitudes (when necessary), with the actual output-pulse amplitude, The great advantage of this method is that the time required to using a comparator. process a pulse is independent of its amplitude. Digital buffers that are now available enable one to store the processed pulseamplitude data that can then be transferred by means of a built-in and suitable interface to commercially-available microcomputers. developing era of Once again it must be emphasized that, in this explosively microelectronics and integrated circuits, it is useless to try to give within the limited description of the very complex scope of this report a full and comprehensive pulse-processing equipment now available. As was pointed out in 16.5, at the present time one selects the appropriate function and then aspires to acquire it. To choose an everyday example, few can afford the time to build a radio or a television; except for fun.
For further information and references on the operation and uses pulse-height analyzers, an article by Ross (1973) could be consulted.
of multichannel
6.7.5. Dead-time losses and gates As with MCA's, other pulse-handling electronic equipment and, indeed, the radiation detector itself are unable properly to process incoming signal pulses while they are still engaged in processing an earlier signal. As mentioned in 76.2 and illustrated in Fig. 6-2, an incoming pulse will be distorted if it rides on the tail of a previous pulse, and the pulse height of the riding pulse will no longer be proportional to the energy deposited in the detector by the primary ionizing event. It should also be remembered that, with the various stages of amplification, in a counting system, the time interval from the beginning to the end of the pulse varies from stage to stage. It is therefore of the greatest importance to be sure that all further input pulses are excluded from the system for the longest time that any one component takes to process an incoming pulse. The minimum time required for the whole system to accept a new pulse and to handle it without distortion is In general the dead time of the system will be the called the dead time of the system. dead time of its slowest stage. In order to be sure that no such distortion occurs it is customary to insert an electronic stage that imposes a dead time on the whole system. It is possible, but not always assured, that one of the other components has a dead time that is stable and independent of pulse rate and amplitude, but in lack of such assurance it is prudent to have an independent dead-time gate. Also this gate should be placed as early as possible in the electronic-processing sequence, otherwise pile-up and distortion may have already occurred in an earlier stage. But it is not practical to place the dead-time gate before the preamplifier that should be as close to the detector as possible. Dead-time gates are also extendable or nonextendable. The former occurs when the dead-time gate activates to prevent the processing of further signal pulses for, say a time T , every time that it senses a new pulse. Thus if two input pulses happen to be overlapping in time then the dead-time gate will close on the arrival of the first pulse, and then remain closed for a time T after the arrival of the second. A nonextendable dead-time gate closes on the arrival of a pulse and opens again after a time 'T, irrespective of how many events may have been detected during the period T that the gate was closed. The difference between these two modes of operation of a dead-time gate are A simple circuit used at the National Bureau of Standards to illustrated in Fig. 6-21. provide a nonextendable dead time is shown diagrammatically in Fig.6-22. This dead-time gate uses a retriggerable-monostable-multivibrator integrated circuit SN74122 (see Texas Instruments, 1976). circuit provides an output pulse of fixed, This but adjustable, duration whenever it is triggered by an input event. This pulse is used to block the input for the duration of the output pulse by feeding one of the outputs, ?j, back to the input. Just as in the case of the MCA the existence of dead time in a counting circuit has the effect of decreasing real counting time of an experiment. The end product sought in counting is almost always, one way or another, a count rate. h measurement of time is even explicit in the spectra of Fig. 6-20, and is indeed required if the spectrum has been taken in conjunction with a measurement, say, of nuclear-reaction rates or yields. In the case of an ordinary single-channel count-rate measurement it is also necessary to make a dead-time correction to the count rate. In essence, such a correction is based on using the measured dead time and count rate to calculate the real live time of the experiment. These corrections have been discussed in (3.4.3.5, and also, very fully by J. G. V. Taylor, in 72.7 of NCRP (1985).
Radioactivity measurements: principles and practice
900
ON,i
1
2
NZT
3
4
NT-~--
Relationship between input (N) and output (n) events for Fig. 6-21 systems with nonextendable and extendable dead times. For the system with nonextendable dead time T , events 3 and 6 are lost but events 2. 4. 5 and 7 are recorded because thev are seoarated in time by more than the dead-time interval T from the last preceding event to produce an output. For the system with an extendable dead time, event 4 is also lost because it is seoarated bv less than T from event 3, which extended the dead-time interval initiated by event 2. For extendable dead times all pulses that are not separated by at least the interval T from the preceding event whether this event is recorded or not, are lost (after NCRP, 1985).
Fig
6-22 Nonextendable dead-time circuit based on a single SN 74122 oneshot retriggerable-monostable-multivibrator integrated circuit. The IC itself is shown within the dashed lines with appropriate external connections outside the dashed lines (after Mann et al., 1980). 6.7.6. Count ratemeters Dosimeters used by health physicists to obtain d.c. readings as a measure of exposure in radiation fields are designed to give an instantaneous average reading of the exposure, whether it be from a photon source, or from w or p-particle sources the last two possibly arising from surfaces accidentally contaminated by such sources. A ratemeter usually comprises two stages, namely an input pulse-shaping stage and an output averaging stage. A simple "pump" ratemeter circuit is shown diagrammatically in Fig. 6-23. The input pulses may be logic pulses produced by the last stage of a detector pulse-processing system. The average voltage developed across R, for C,<
Radioactivity
measurements:
principles
and practice
Ratemeter circuit; BJ is the width in units Fig. 6-23 input pulse (after Mann and Garfinkel, 1966). 6.8.
LOW-LEVEL-CURRENT
901
of time of the
MEASUREMENTS
Ionization currents generated in ionization chambers can vary in magnitude from lo-'A to 10-13A. But a current sensitivity of 10 -i5A is desirable because background and leakage currents may be one or two orders of magnitude less than the ionization current due to a radioactive source. Two excellent reviews of the methods available for measuring such small currents,byH: were published in the Proceedings of the First International M. Weiss and K. Zsdanszky, Herceg Novi (1973, pp. 291 and 299). A Summer School on Radionuclide Metrology, held in description of the ionization chamber and associated electronic system used at the Bureau A new edition International des Poids et Mesures has also been published by Rytz (1983). has also been "Electrometer Measurements" (2nd ed., 1977) of Keithley Instruments recently published under the title "Low Level Measurements" (Keithley, 1984). 6.8.1. Townsend
induction
balance
especially at national laboratories, are often made Ionization-chamber measurements, In this method, using some kind of automated version of the Townsend induction balance. the ionization current charges one plate of a capacitor the increase in voltage on which is compensated by maintaining an approximately equal and opposite potential on the other plate This was originally done manually using a potentiometer and some kind of the capacitor. of electrometer to sense whether the potential of the capacitance was departing substantially from zero, but this is now usually achieved by the use of differential-voltagesensing and automatic-compensating systems. If the combined compensating voltage cv/t.
capacitance of the chamber is increased to V in time
output and external capacitor then the ionization current
t,
is C, and the I is equal to
devices earliest differential-voltage-sensing was the one of the types of vibrating-reed electrometer (VRE), which with many refinements is still in use. In a VRE, one plate of a capacitor (the reed) vibrates and thereby generates an a.c.-voltage output voltage input. If the VRE is connected across the from a constant or slowly increasing capacitance C, the output-voltage amplitude is proportional to the out-of-balance potential across the capacitance C. (See, for example, Fig.6-24.)
Fig. 6-24 Townsend balance HN, 1973). The VRE output pulses can next be amplitudes exceed a specified value they and used, by various means, to provide a
with stepwise
compensation
(after Weiss,
fed to an integral discriminator, and when their will be transmitted by the integral discriminator compensating voltage to the capacitor C.
One of the earliest automatic Townsend-balance systems was described by Garfinkel in 1959; its operation is illustrated in Fig. 6-24. As soon as the voltage on the integral discriminator D, reached about 12 mV the timer T was started. When the integral
Radioactivity
902
measurements:
principles
and practice
and -100 mV was supplied to the discriminator D, reached 50 mV, a relay was closed This could be capacitor plate that is shown connected to ground through the resistance R. repeated a selected number of times up to 15, after which the tFmer T was stopped as discriminator D, again started to detect and transmit pulses having an amplitude of 15 mV. several other current-measuring devices for use with Details of the operation of together with information on their efficiency calibration and their ionization chambers, precision of measurement have been given by Weiss (HN., 1973) and ZsdAnszky (HN., 1973) For more recent information, Rytz (1983) and along with references to other publications. Keithley (1984) should be consulted. 6.8.2.
Electrometer
amplifiers
of very There are two types of electrometer amplifier available for the measurement picoammeters", and the small currents, namely the shunt type also known as electrometer coulombmeters". capacitance type also known as "current integrators", or "electrometer There are also two principal types of each, and all four employ the principle of inverse amplifiers have also been developed with input-stage MOS-FET electrometer feedback. resistances of the order of IO'* ohms and voltage gains of about 50,000 (Zsdanszky, HN., 1973). 6.8.2.1.
Electrometer
oicoammeters
in Figs. 6-25 and 6-26, and is This type of electrometer amplifier is illustrated That shown in Fig. 6-25 is described in detail by Zsadnszky (1973) and in Keithley (1984). and that in Fig. 6-26 as the "feedback-type picoammeter", known as the "shunt-type amplifFers picoammeter", although, as mentioned earlier, all four of these electrometer resistance of the shunt type is R, and that of the The input employ inverse feedback. The input voltage V, of the latter configuration is equal to I,R,. feedback type R,/A. Some further details are given in Mann et al. The shunt type is not, however, often used. (1980) and Keithley (1983).
Fig. 6-25
Electrometer
picoamperemeter-shunt
Electrometer Fig. 6-26 Keithley, 1984).
type (after Keithley,
picoamperemeter-feedback
Current integrator Fig. 6-27 Keithley, 1977).
or coulombmeter-shunt
1984).
type (after
type
(after
Radioactivity
measurements:
principles
and practice
903
T
Current integrator Fig. 6-28 Keithley, 1977). 6.8.2.2.
Electrometer
coulombmeters
or coulombmeter-feedback
type (after
or inteerators
In the electrometer coulombmeters illustrated in Figs. 6-27 and6-28, the integration is achieved by charging a capacitor, C, in the former and C, in the latter. The current I, from the ionization chamber is essentially constant when measuring a long-lived source so that in time t the capacitance charges to a voltage V, equal to I,t/C,. As mentioned earlier, an amplifier with inverse feedback operates in such a manner as to reduce the So, for V, tending to be reduced to zero, V, = V, - V, or amplitude of the input signal. v, = -v,. Hence I, = -VOCf/t. "Dose" calibrators
6.8.3.
"DOSI?" calibrators, more known as also properly "activity calibrators" or "radionuclide calibrators", are usually gas-ionization chambers, many types of which are filled with argon at a pressure of about 2 MPa (20 atm). They have a reentrant well that is large enough to accommodate samples of gamma-ray-emitting radiopharmaceuticals in solution, contained in ampoules or serum vials. One type of radionuclide calibrator comprises a large plastic scintillator with a reentrant well. The instrument is usually set for the radionuclide to be checked by means of a selector switch or, sometimes, by means of plug-in resistance modules. Such calibrators, for the convenience of hospital personnel, usually read out the activity of the sample measured in switch-selectable ranges of, say, 0 to 1 mCi, 0 to 10 mCi, 0 to 100 mCi and so on up to perhaps 0 to 10 Ci; but many models can, by means of a two-way switch, also display the measured total activity of the solution in the container in either curies or becquerels. Further, rather clear and detailed, information regarding the principles and operation of such instruments can be found in NCRP (1980, p. 291). 6.9. STANDARDIZATION 6.9.1.
OF NUCLEAR
INSTRUMENTATION
General
Nuclear measuring instruments consist in general of parts which perform well defined separated functions, such as amplific ation or discrimination. This makes it possible also to subdivide nuclear instruments into separate modular subunits, according to their separate electronic functions. if such units can be For general use, it is convenient interchanged between different electronic systems either within a laboratory or between different laboratories. Thus, over the last two or three decades there has been an international effort to standardize all nuclear instrument modules, hence the name of the system, “NIH”, and that of one of its component parts, the "NIMBIN". For many purposes, however, compact instruments are needed, such as for monitoring or field measurements. And with the availability of cheap complex microprocessors, storage discs, and other miniaturized components, it may be less expensive to acquire certain compact, but complex nuclear instruments rather than to use modular systems; although, even with such compact some useful standardization of parts is still possible, equipment especially of connectors, cables and subunits. However, the intrinsic advantages of standardized modular systems are still valid, especially in the case of larger laboratories. These advantages include interchangeability of subunits, ease of servicing, flexibility and easy updating and reuse, availability of a wide range of modules, and so forth. Two standard systems of nuclear electronics are widely in use, firstly NIM, referred to above and which mainly applies to smaller stand-alone instruments, and secondly that for computer automated measurment and control (CAMAC), that applies mainly, as its name implies, to computer-controlled NIM was developed systems. primarily as an analogue-oriented system although it is being increasingly used for digital circuitry. inception, been computer-oriented. CAMAC has, from its Both NIM and sources throughout 6.9.2. Nuclear The
CAMAC instruments and the industrial world.
instrument
specifications
AHI 39/8-M
modules for
the
components
are
widely
modular
system
of
available
from
commercial
(NIM1 standard
nuclear
electronics
NIM
was
Radioactivity
904
measurements:
principles
and practice
produced by the NIM committee (US National Instrumentation Methods Committee), supported by the US Department of Energy and associated with the National Bureau of Standards (AEC, 1974). The NIM system is in widespread use throughout the world. Earlier systems, such for example, the NIM-compatible ESONE (European Standard on Nuclear Electronics) had, as, for example, found only limited acceptance. The NIM specifications pertain to the mechanical dimensions, the electrical power supply and the electrical signals, and were designed to overcome the situation illustrated in Fig. 6-29. Figure 6-30 shows a solution to the problem, namely a typical NIM/CAMAC crate (standard bin and chassis) which houses 12 single modules (or 24 half-width modules), or correspondingly less if double, triple, or more, modules are used. The total width of the standard bin is 19 inches (482.6 mm), the width of a standard module is such that a standard bin will accommodate 12 single-width modules, 6 double-width modules, or 6 single-width and 3 double-width modules, and so on. The height of the bins is 8 3/4 inch (222 mm).
Fig. 6-29 The problem. At the rear of the modules, plug-in units are coupled by a 42.pin connector to the Several power supplies are available with all or some of common power supply of the bins. the standard voltages, such as f 6V, ? 12V and ? 24V. Connections between modules are made through coaxial connectors at the front panels. Detailed recommendations Some fixed connections can also be made via the rear connectors. are made in NIM for logic signals ("O"/"l"), for the transmission of "slow" digital data, for fast logic signals and for linear analogue signals (0 to10V). NIM systems can be easily connected to computers via individual, task-oriented can then be sent automatically to the The collected data (e.g. spectra) interfaces. central computer for further treatment (e.g. peak-area evaluation). 6.9.3.
Cornouter automated
measurement
and control
(CAMACL
The CAMAC specifications (ANSI/IEEE, 1982a, b, c; CAMAC, 1973) for a standardized computer-automated modular nuclear-instrumentation system with digital data handling has been produced by a group of European laboratories organized by the European Standard on Nuclear Electronics (ESONE) Committee, the US NIM Committee, and some other standardization organisations. The mechanical format of the NIM and except that the minimum width of the single NIM module.
CAMAC crates and plug-in units module is 17 mm, half the width
is the same, of the single
Radioactivity
measurements:
principles
and practice
905
Radioactivity
906
measurements:
principles
and practice
CAMAC modules are connected at the rear via 86-contact connectors to a multiwire data latter is part of the crate and carries data, control bus (highway), the "Dataway". The It has a minimum cycle time of 1 ps and is interfaced by the crate signals and power. controller to the input-output (I/O) port of the computer. Up to 7 crates can be interconnected using a branch parallel highway and branch driver (ANSI/IEEE, 1982~). Larger assemblies with up to 62 crates can be combined using a serial highway and serial highway drive with appropriate crate controllers (ANSI/IEEE, 1982b). All operations of a CAMAC system are controlled by the central computer. This must be Standard software routines for CAMAC programmed using the appropriate computer language. are available in different languages (ANSI/IEEE, 1979). 6.9.4.
EASTBUS
A new modular system for data acquisition and control, designated "FASTBUS", has recently been developed by the NIM Committee with the collaboration of the ESONE Committee. Though This system is extremely fast and versatile with very great addressing capability. designed to meet the needs of the high-energy physics community, its superior characteristics make it attractive for many other applications. It is now a standard of the Institute of Electrical and Electronics Engineers and the American National Standards Institute to be published also as standards of ESONE and the (ANSI/IEEE, 1985), and is expected The development of FASTBUS was initially International Electrotechnical Commission (IEC). undertaken to meet the needs posed by the world-wide advent of a new generation of accelerhaving detector outputs numbering up to the ators (e.g. CERN, KEK, SLAC and FERMILAB), Some FASTBUS system currently in operation have data-transfer rates of order of 5 x 105. 160 megabytes per second (Dawson et al., 1985). which operate independently but which A FASTBUS system consists of bus segments dynamically link together as needed for operation passing. FASTBUS is a standardized Its versatility, modular data-bus system for data acquisition and control applications. addressing capability make it attractive for use in a wide variety of and speed consists of bus Segments which operate independently but A FASTBUS system disciplines. dynamically link together as needed for operation passing. This parallel processing feature accounts to a great extent for the high throughput of FASTBUS in multisegment Master modules compete for single or multiple segment control through a bus systems. arbitration scheme using assigned priorities. System speed is limited solely by propagatation and logic delays. . The principal
features
. High
typically
speed -
. Large
address
bus -
. Versatile
multiple
System-wide
Uniform,
l
Arbitration
6.10. FURTHER
parallel master
include:
than 10 MHz;
(32 bits):
processing: capability;
communication:
. Block transfers synchronous); l
greater
and data fields
. Segmented
l
of FASTBUS
-
system-wide
with
and
without
"handshake"
(i.e.
synchronous
or non-
protocol;
and interrupt
features.
READING
in addition to those already referenced in this chapter, There are many publications, that could usefully be available in a nucleonics laboratory for those who wish to study the Among these, in order of date of publication, are subject in somewhat greater depth. (McGraw Hill Publishing Electronic Devices and Circuits, by J. Millman and C.C. Halkias Electronics for Scientists: Principles and Experiments for Those Company, New York, 1967); and E. C. Toren (W. A. Benjamin, Inc, who use Instruments, by H. V. Malmstadt, C. G. Enke PLll.Se, Digital and Switching Waveforms: Devices and Circuits for their New York, 1973); by J. Millman and H. Taub (McGraw Hill Book Company, New York, Generation and Processing, Techniques in Instrumentation, by Ralph Morison (John Grounding and Shielding 1965); Operational Amplifiers: Design and Application, Wiley & Sons, Inc., New York, 1967); edited by G. E. Tobey, J.G. Graeme and L.P. Huelsman (McGraw Hill Book Company, New York, Applications of Operational Amplifiers; Third-Generation Techniques, by J.G. Graeme 1971; Company, New York, 1973). in the Burr-Brown Electronic Series (McGraw Hill Book Further good coverage of the subject may be found in Nuclear ELectronics, by E. Nuclear Electronics, by Kowalski (Springer-Verlag. Berlin, Heidelberg, New York, 1970); P.W. Nicholson (John Wiley & Sons, London, New York, Sydney, Toronto, 1974); and The Art of Electronics by P. Horowitz and W. Hill (Cambridge University Press, Cambridge, London, New York, New Rochelle, Melbourne, Sydney, 1980).
Radioactivity measurements: principles and practice
907
Reference could also be made to the integrated-circuit data sheets and applications literature available from various semiconductor companies such as Fairchild, Harris, Motorola, RCA, Signetics and Texas Instruments.
REFERENCES FOR 76.9. AEC, 1974. "Standard Nuclear Instrument Modules(NIM)," Energy Report TID 20893, 4th revn. (Washington, D.C).
AEC NIM Committee,
US Dept. of
ANSI/IEEE, 1979. "IEEE Subroutines for CAMAC," ANSI/IEEE Std. 758-1981, ESONE Report SR/Ol (1981), IEC Pub1.713 (1981) (Institute of Electrical and Electronic Engineers, Inc., New York). ANSI/IEEE, 1982a. "CAMAC Specifications," ANSI/IEEE Std. 583-1982, CEC Publ. EUR 4100 (1972), IEC Publ. 516 (1975) (Institute of Electrical Engineers, Inc., NewYork).
and Electronic
ANSI/IEEE, 1982b. "CAMAC Serial Highway," ANSI/IEEE Std. 595-1982, CEC Publ. EUR 6100 (1977). IEC Publ. 640 (1979) (Institute of Electrical and Electronic Engineers, Inc., New York). ANSI/IEEE, 1982~. "CAMAC Branch (Parallel) Highway," ANSI/IEEE Std. 596-1982, CEC Publ. EUR 4600 (1972), IEC Publ. 552 (1977) (Institute of Electrical and Electronic Engineers, Inc., New York). ANSI/IEEE, 1985. "FASTBUS," ANSI/IEEE Electronic Engineers,Inc., New York). CAMAC,
1973.
"CAMAC Tutorial
Papers,"
Std.
960-1985
(Institute
of
Electrical
and
IEEE Trans. on Nucl. Science N-20, No. 2, April
1973. Dawson, U.K., Costrell, Louis, Hirokazu Ikeda, Ponting, J. and Walz, H.V., Trans. on Nucl. Science NS-32, No. 5, October 1985, pages 2089 -2091.
IEEE
7.
RADIOACTIVITY
CALIBRATION
LABORATORY:
SCCPE.
STAFF AND EQUIPMENT
7.1. GENERAL All radioactivity measurements consist essentially of two basic operations, namely (i) the quantitative preparation of a suitable radioactive source, or sources, for making a The measurement in specific measurement, and (ii) the carrying out of that measurement. question may relate to any of a large number of different quantities such as activity, (Iparticle, B-ray or photon energies, the interactions of radiation with matter, the detectthe probabilities for the occurrence of ion and identification of radioactive impurities, in the environment, uptakes of different radioactive decay modes, amounts of radioactivity radiopharmaceuticals in animal organs, and so on. And a diversity of applications requires, in turn, a diversity of source forms and of Thus the quantitative preparation of sources almost invariably measuring instruments. films to thick source mounts, and dispensers requires a sensitive balance, "weightless" ranging from approximately Z-ml plastic pycnometers (baby-doll feeding bottles) to electromagnetic mass, or isotope, separators. Radiation-measuring devices range from simple, small, quartz-fibre pocket ionization chambers or very small in viva intercavitary detectors to the 2,300-kg CERN detector system mentioned in Chapter 4.
Fig. 7-l Hoods designed for use in radiochemistry laboratories, actually located in cold-chemistry laboratory as shown above. hoods can be jacked up slightly to take the load and the legs removed so that floor tiles may be replaced in the event of a active spill. Hemispherical source support in nearer hood is evaporation of metal films on to VYNS source mounts (National of Standards, Gaithersburg, Maryland. U.S.A.).
909
but These radiofor Bureau
Radioactivity
910
measurements:
principles
and practice
In general, these two basic operations result in a radionuclide-metrology establishment being functionally divided into high- and low-level source-preparation laboratories and into counting laboratories, often located in separate wings of one building or in separate buildings in order to reduce the possibility of cross-contamination between radioactive sources. The source-preparation laboratories consist of storage rooms, equipped with lead, steel, mercury, or concrete shields, temperature- and humidity-controlled draught-free weighing rooms, and "hot" (radioactive) and "cold" (non-radioactive) chemistry laboratories. The radiochemistry laboratories may be equipped with hoods and work benches, similar to those shown in Fig. 7-1, that have been specially designed by one of the authors to facilitate the clean-up of radioactive contamination underneath them in the event of an accidental spill; mercifully a contingency that has not yet arisen to test their design. The counting laboratories consist of well-ventillated rooms, preferably air-conditionto accommodate detecting or counting systems such as ionization ad, that are designed chambers, Geiger-Miiller and proportional counters, solid-state detectors, liquid-scintillation detectors, and so on, each with its own appropriate electronic current-measuring, pulse-processing, or data-handling systems. All of these laboratories should be kept scrupulously clean at all times, and regularly monitored for stray radioactive contaminatand the health-physics staff. ion, both by the working personnel Bench-top and hood working areas in the source-preparation laboratories should preferably be of stainless steel which should be protected when in use, if not at all times, with clean double-layerSuch covering is commercially available in ad, absorbent paper on plastic, cover sheets. rolls of about l-m width from which strips of the requisite length may be cut. After use, these absorbent-paper on plastic sheets may be disposed of as radioactive waste, if they have been contaminated with any radioactive material. But some discrimination should be shown in distinguishing between high-, low-, and zero-radioactive contamination in order to avoid overloading the world's capacity for radioactive-waste disposal. Radioactive materials should not, in general, be stored in counting laboratories. The exceptions are well-sealed sources for monitoring instrument performance, such as, for These should be stored between use in a well-shielded and example, Ra and its daughters. permanent location to avoid causing fluctuations in the background count rates of detecting systems. In this respect it is also wise, if building low-level counting laboratories below ground, to check for radon in ambient ground water and (whether above or below ground) for radioactivity in the aggregate used in the adjacent structural concrete. In the construction of new counting laboratories and in the installation of new equipment one For extremely low-level radioactivity measurements it may must be wary of many pitfalls. also be essential to remove radon from the air being circulated in the counting room. A couple of examples of unexpected problems that were encountered at NBS may serve as a Initially inexplicable background changes (attributed at first to some cautionary tale: positron emitter in a mercury shield) were traced, after drawn-out and tedious investigation, to s5Kr lingering in a preamplifier diode that had been leak-tested with that gas; and and on another occasion strange fluctuations in counting rate were found to be caused by an elevator counterweight passing up and down the other side of the laboratory wall. Further details can also be found in 813.2.3 and 3.2.4 of this report. 7.2. SCOPE The scope and dictated by several
size of a radioactivity standardizing considerations, such as, for example:
laboratory
will,
of
course,
be
or perhaps population density, of the region; (ii) the extent to which (i) The population, radioactive materials are used in the region for research in physics or medicine; (iii) the to the environment by the mining or the of radioactivity magnitude of the release of power from processing and refining of uranium or thorium ores, by the generation to coal-powered plants or nuclear reactors, or by the controlled release of radioactivity laboratorthe environment from, for example, hospital and industrial radiopharmaceutical ies, or by nearby nuclear tests; (iv) the degree to which accuracy of radioactivity measuror less in research to flO% in medicine to ments is essential, e.g., from the order of U% perhaps +20% in environmental measurements; (v) the extent to which high-quality industrial support is available in the production and distribution of accurately-calibrated measuring instruments such as radionuclide calibrators; (vi) the extent to which these industrial radioactive materials, producers can also supply adequately pure, well-characterized and radioactivity standards, and, therefore the degree to including radiopharmaceuticals which such industrial producers participate in traceability exercises linking them to the regional and international radioactivity standards; and so on. In a predominantly agricultural area or nation there may be but a limited need for but in those nations that are using radioactivity techniques or radionuclide metrology, In this respect, nuclear power extensively there will be a correspondingly greater demand. Atomic Energy Agency's Table 7-1, from the February 1, 1988, issue of the International The need for radioactivity IAEA Newsbriefs No. 22 (Vol. 3, No. 1) is very informative. standards must, to a great extent, be correlated with the magnitude of a country's nuclearpower program and its consequent ability to produce radioactive materials, including radioThe IAEA also gives the in support of its industry and medical services. pharmaceuticals, reactors were newly connected to interesting statistic that, in 1987, 23 nuclear-power electricity grids, and that nuclear power now supplies more than 26% of the world's electricity.
Radioactivity
measurements:
principle*
and practice
From Table 7-l it is readily seen which areas of the world are nuclear-power rich and a new and those that are not. The nuclear-power rich, in order of "watts-electric", Europe and North America at about 110 and 105 GW, potential measure of wealth, are: The respectively, followed by the USSR and Japan with, respectively, about 33 and 27 GW. less nuclear-power-rich parts of the world appear to be South America, the Middle East, But many countries that are Africa, and South-West and South-East Asia, apart from Japan. not yet committed to nuclear power have swimming-pool or equivalent reactors that produce Howsufficient quantities of radioactive materials for medical applications and research. ever, given the present climate of public opinion, it is not surprising to find a trend toThus Canada has recently announced the availability of a new wards smaller reactors. generation of CANDU reactors, the CANDU-300, rated at 320 to 375 MU(e), about one-third the rated power of the CANDU-900 and one-half of that of the CANDU-600, but keeping the safety In Sweden, ASEA-ATOM has designed, using refuelling-under-power features of its ancestors. "SECURE" (fail-safe) reactor rated at 300 a very interesting new principle,* so-called The new principle is that of controlling the criticality and level of power by m(e). adjusting the level of boric acid in the water circulating in the reactor core. But there is also a pool of highly borated water around the reactor core, but separated only by a gas lock that allows the highly borated water to flood the core in the event of a decrease in There are no valves in this svstem within thereactor the flow-rate of the orimarv coolant. itself, so that this automatic shut-down is based only on the laws of physics.
TABLE
7-l Reactors/ total net MWe
Argentina Belgium Brazil Bulgaria Canada Czechoslovakia Finland France German Democratic Rep. Germany, Fed. Rep. of Hungary India Italy World
total:
2 7 1 1; 8 4 53 5 21 4 6 3
417 reactors
7.3. SIZE OF LABORATORY
(935) (5477) (626) (2585) (12 142) (3207) (2310) (49 378) (1694) (18 947) (1645) (1154) (1273)
Reactors/ total net MWe Japan Korea, Rep. of Netherlands Pakistan South Africa Spain Sweden Switzerland Taiwan, China United Kingdom United States USSR Yugoslavia
36 7 2 1 2 9 12 5 6 38 106 55 1
(26 877) (5380) (507) (125) (1842) (6529) (9646) (2932) (4918) (10 214) (92 982) (32 919) (632)
296 876 megawatts-electric (MWe) total net capacity.
AND NUMBER
OF STAFF
7.3.1. General Quite clearly, the magnitude of the effort needed to meet the metrological needs of any given region of the world in the field of radioactivity depends on the extent to which has become involved in its many applications. The needs may also be met by the joint efforts in varying proportions of a strictly standardizing laboratory and of commercial laboratories; and the proportions may change as the development proceeds. Thus the Canadian National Research Council (NRC) started a small radioactivity standardizing laboratory at their nuclear research laboratory at Chalk River in, about, 1946. Initially this standardizing laboratory had about three rooms accommodating one physicist, one chemist, and two technicians, to whom secretarial help was also available when needed. This effort "as continued at Chalk River when Atomic Energy of Canada Limited (AECL) took standardizing group in over the laboratories, but NRC also set up a small radioactivity their Ottawa laboratories. In recent years, however, both activities have declined as the Commercial Products Division of AECL has increased its distribution of calibrated samples, including radiopharmaceuticals, the "traceability" of which to the international reference system is maintained by AECL Commercial Products Division participating in the Atomic Industrial Forum (AIF) and National Bureau of Standards traceability programme. That part of AIF that supported this program has now become the United States Council for Energy Awareness (USCFA), and the name of the NBS/AIF programme changed accordingly. (NCRP, 1985, Chapter 8 may be consulted for information, with references, about this programme.) Radioactivity standardization in the United States since about 1940 "as the responsibility of the NBS Radioactivity Section (now the Radioactivity Group), but the measurement of large numbers of radium needles for medical use dated back, at least, to 1913 when Mme Marie Curie brought the first radium standard, certified by the International Radium Standards Commission, to the U.S. But it "as not until after the nuclear age began in the early 1940's that NBS became involved in the calibration of uranium-bearing ores and artificially-produced radionuclides. It may be instructive to follow the involvement of
911
Radioactivity
912
measurements:
principles
NBS in radioactivity standardization in terms of the size radionuclides were from about 1946, when reactor-produced present time.
and practice
of its becoming
Radioactivity Section available, until the
In 1946 or 1947 the NBS section comprised 9 scientists, 1 technician, and 1 secretary. that for a small radioactivity standardizing laboratory It might be noted, in passing, limited perhaps to one or two professionals and one or twd technicians, the best kind of professional to appoint to the first position filled would probably be a radiochemist. This is so because a well-trained radiochemist would be competent both in source preparation and in the assay of the sources. But it should also be emphasized that the next staff member appointed should probably be a technician. At the present time when personnelhiring ceilings are so often imposed, the staff patterns in so many laboratories become badly out of balance because of the tendency to hire a doctoral research graduate instead of a well-trained and competent technician. Shortly after 1965, at the time NBS moved to new laboratories in Maryland, the section numbered about 20 (including two secretaries), frequently with the addition of one or more long-term (6 to 12 month) visitors from abroad, wishing to gain additional experience before returning to his or her own national laboratory. At this time the numbers programs being carried out in were alSO swollen because of extensive "traceability" partnership with industrial and hospital laboratories, and with environmental monitoring laboratories of the federal government (Mann et al., 1981; NCRP, 1985). At the present time the full-time staff is 10 (including two secretaries), but is supplemented by two part-time retirees (one aging and the other more alert) and an occasional visit from a radiochemist or physicist from abroad under the aegis of international exchange programs. to sharpen our perspectives. In its new location in Maryland the section (group) occupies some 30 laboratories and offices, although only a fraction may be occupied at the same time because many of the laboratories are dedicated to specific activities, such as, high- and low-level radiochemistry and source-preparation laboratories, high- and low-level counting rooms, different kinds of detectors (such as a, j3, and photon), nucleonics (including microprocessing), and so on. For the first few years after 1946 greater numbers of a greater variety of radionuclides were being produced and put to use in scientific and medical research, so that there was an ever increasing demand for standards of these radionuclides. Concurrently more commercial houses became involved in the distribution of radioactive substances, including labelled compounds, and calibrated radioactivity samples, the calibrations of which were not always consistent between the different producers. Thus around 1970 medical laboratories, commercial producers, and regulatory agencies of the federal government started to organize traceability programs with NBS. The best known of such programs, which is still extant, is the NBS-AIF program referred to above, which comprises NBS, the Federal Drug Administration, and from six to eight commercial producers (the number has fluctuated during the years). These traceability programs are carried out monthly between NBS and the other participants. in general use reaches saturation and But, naturally, as the numbers of radionuclides as their producers and users become more skilled in making accurate calibrations, the numbers of standards required from the national laboratory should begin to decrease. Thus any regional radioactivity calibration laboratory that does its job well, may live to see that its services are not so urgently needed with the passage of time, with the advent of a more widely-distributed competence and expertise, and with the almost unlimited availabilility of radioactive materials and calibrated sources from the nuclear-power-rich countries of the world. in the nuclearNor, indeed, is this index of the passage of time without significance world where nuclear measurements have not only become simpler with the power-rich increasing availability of computers and microelectronics, but where the "fashion" has Radiopharmaceutmoved from nuclear physics to molecular biology and genetic engineering. icals do not have to be calibrated to tenths of a percent, and dosimetry, at present or indeed at any future time, probably needs to be accurate to only 10 or 20% in order to match the certainty with which we can predict physiological response. The one thing against which the nuclear-power-rich world has still to be on guard is the occurrence of another Windscale, Three Mile Island or Chernobyl; and it will need to maintain the resources to deal with it, It is now no longer feasible to take such precautions against the devastation of a large nuclear war; but sufficient resources are probably now available to cope with a small one. 7.3.2. A small
radioactivity
laboratory
In a region where there is not even a small reactor or accelerator, or even where a power reactor is coming into operation, radioactive research materials, radiopharmaceuticals, or environmental radioactivity standards may be imported from elsewhere, If this external supplier has a well-organized quality-control and traceability program in place, it may be in a position to supply reliable standards, free of impurity, to the region that is coming into operation. In such
an event,
the monitoring
laboratory
in the
starting
region
might
consist
of
Radioactivity
measurements:
principles
and practice
913
an activitylaboratory, one radiochemist and three rooms, namely a source-preparation This would certainly constitute the minimum calibration laboratory and an office. viable configuration, inclusive of staff! The minimum equipment needed microbalance, suitable glassware bottles.
for and
the source-preparation including dispensers,
laboratory would be a good "baby-doll" small plastic
radionuclide The equipment for the counting room could be at least a commercial one that had been calibrated by a laboratory that was calibrator (9.v.); and preferably Then a NaI(T1) well-crystal directly or indirectly traceable to the international system. detector system would be most desirable for use in both gamma-ray assays and in crude testing for the presence of impurity radionuclides which could also be accomplished, in longer term, by half-life measurements. If funds permitted, a commercial liquid scintilemitters would be a very great lation counter for the relative assay a- and B-particle, asset. If funds did not permit, a resourceful scientist could try his hand at constructing a Lauritsen-type electrometer, which is illustrated in Fig. 4-1, but which is no longer available commercially; a do-it-yourself sketch (without the aluminium enclosure) is also shown in Strong (1940, p. 229; a Later 1946 edition may still also have this sketch). Calibrated a, p or photon (including x-ray) sources on solid mounts can, under the best be calibrated to better than 2% (estimated standard deviation) using this conditions, simple ionization-chamber device. With the addition of a plastic ampoule holder that can be located at any of a variety of fixed distances from the electrometer chamber many photon-emitting nuclides in solution in standard glass ampoules can be assayed by comparison with calibrated sources of the same nuclides in the e.ame geometry. NCRP Report "General-Purpose ories."
No. 58 (NCRP, 1978 and 1985, Section 6.5) has Equipment" and "Minimum Instrument Requirements
useful information on both for Some Specific Laborat-
Most gamma-ray solution standards are distributed in lo-ml or 15.ml glass ampoules, Both the and many radiopharmaceuticals are dispensed in a variety of bottle shapes. standards and radiopharmaceuticals must, before measurement in a radionuclide calibrator, be transferred to a bottle having the same configuration as that for which the instrument was calibrated, or a correction factor must be determined. (See NCRP, 1978 or 1985). Such a laboratory would be able to check prepared Sources for maintenance of quality in a region where there was, initially, a fairly low demand, and its operations would increase as the use of radioactive materials increased. It could also rely on traceable longer-lived standards from other regions, but as its operations expanded it should have adjoining space into which its equipment and staff can expand. 7.3.3. A laree radioactivity
laboratory
In a burgeoning region the growth of a laboratory might approximate the case history, described briefly above, of the National Bureau of Standards, Radioactivity Section. As mentioned, various perturbations arise from the concomitant activities of other metrological laboratories in universities (e.g.. Lawrence Berkeley Laboratory), groups of universities (e.g., Oak Ridge National Laboratory), medical laboratories, and industry. In France there is a strong central standardizing and distributing laboratory, the Laboratoire de Metrologie des Rayonnements Ionisants (UiRI) in the Office des Rayonnements Ionisants, reporting to the Commissariat a 1'Energie Atomique and the Bureau National de Metrologie. IMRI has extensive calibration and production facilities. In the United Kingdom the National Physical Laboratory's (NPL) Acoustic and Radiation Division a group about the same size as that at NBS is responsible for radioactivity measurements, including the acquisition of nuclear-decay data, but the large-scale production of radioactivity standards in the United Kingdom is handled by Amersham International. The monitoring of quality, including that of personnel engaged in calibration functions, is performed by the British Calibration Services. Thus it would seem that there are too many variables, involved in the interplay between national, industrial, and university services in a region, to do more than hazard to fulfill the functions of any regional an estimate of the size and scope required radioactivity standardizing laboratory. A reasonable estimate might be six scientists (physicists and radiochemists) including the head of the laboratory, six technicians, one nucleonics and micro-processing expert, one mechanic, and one secretary, for a total of 15 persons. The ratio of scientists to technicians may be high, as many of the source-preparation and counting operations can nowadays be handled by skilled technicians. 10 technical staff will need nearly twice that number of Judging from experience, rooms. This ratio of rooms to people is not extravagant because, as mentioned earlier, the number of rooms is dictated by the number of "functions" but this ratio should decrease with any increase in the numbers of staff, because many of the "functions" will probably not need to be increased. Thus there will be "hot , ” medium-level and low-level radiochemistry Laboratories, one "cold" chemistry laboratory, perhaps two, or possibly a so-called "white" room. In addition there should be a draught-free humidityand room, one special low-level temperature-controlled balance room, a source-preparation counting room built from monitored activity-free material with circulated radon-free air,
914
Radioactivity
measurements:
principles
and practice
and probably at least three other counting rooms. one computer room, three or four offices for the six scientists and one secretary, a source-storage room, and a workshop, or access As eating and drinking is normally prohibited from radiation to one, will also be needed. areas, a tea rcmmor enlarged area in a "non-active" hallway, with a coffee maker and food At least one secretary is absolutely essential in order to take dispenser may be required. and publications of the group, but also the care, not only the routine correspondence business of ordering materials and dealing with inquiries about calibration services, and The occasional services of a skilled machinist, or access to a orders for standards. nearby machine shop is also almost essential. The equipment needed in any regional laboratory will depend upon the special As already mentioned, section 76.5 activities peculiar to that region and its priorities. of NCRP (1978 or 1985) may help as a guide, as should chapters 3 to 6 of this report.
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