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Radioactivity measurements by the 4πβ-γ anticoincidence spectroscopy method using a Ge(Li) detector
N U C L E A R I N S T R U M E N T S A N D M E T H O D S 78 0970)
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CO.
R A D I O A C T I V I T Y M E A S U R E M E N T S BY T H E 4n/~-y A N T I C O I N C I D E N C E S P E C T R O S C O P Y M E T H O D U S I N G A Ge(Li) D E T E C T O R Y. KAWADA, O. Y U R A and M. K I M U R A
Electrotechnical Laboratory, Tanashi-shi, Tokyo, Japan Received 5 August 1969 By the aid of a 4x[J-y anticoincidence set-up with a Ge(Li) detector, a method was developed which makes possible radioactivity measurements of some nuclides having complex decay schemes without requiring the decay scheme correction. The method employs the whole p-spectra in both the 7- and anticoineidencechannels, and the measurements are made according to the exact coincidence/anticoincidence principle. For examples of applica-
tion of the method, measurements of ~°Co, 11°mAg-ll°Ag and 134Cs were described and the results were compared with those obtained by other methods. Concerning the introduction of spectral information in the 4nfl-~ technique, the advantages of the anticoincidence technique over the coincidence are pointed out with special reference to accuracy and precision.
1. Introduction Among a variety of the methods available for radioactivity standardization, the 4n//-y coincidence method 1) is considered as one of the most accurate methods. This is especially true in the measurements of simple /3-7 nuclides, in which the method can be applied straightforward and an excellent accuracy can be established. However, when the method is applied to the measurements of nuclides having complex decay schemes, the decay scheme correction, which is required unless the efficiency of either the//- or y-detector is the same for each branch, becomes involved and hence the applicability of the method is somewhat restricted. In most cases, the correction might be determined with an adequate accuracy by using the coincidence-absorption method described by Williams and Campion2), but the procedures are rather laborious and troublesome, as it requires a series of coincidence measurements on sources with different/%efficiencies. In this paper, a modified method with the 4re//- 7 technique is described which permits measurements of some of nuclides with complex decay schemes without requiring the cumbrous correction. The proposed method follows the principle of anticoincidence rather than coincidence, and the spectral information of the signals from a high resolution 7-detector employed is introduced into both the 7- and anticoincidencechannels. In the following, the principle and procedures of the method will be presented in detail together with some typical examples of application.
channel measures the y-spectrum in coincidence with the //-signals. The fl-efficiencies are then calculated from the ratios of relevant photopeak-areas in the Yand coincidence-spectra. Another is the 47~//-y anticoincidence spectroscopy, in which the anticoincidence-channel measures the y-spectrum in anticoincidence with the//-signals. In this case, the//-inefficiencies are determined in a similar manner. In the present work, the latter method was used, since it seemed to be more advantageous than the former in the point of precision and accuracy. With our arrangement, the y-signals from a Ge(Li) detector, which is combined with a 47~//-y gas counter, are analyzed firstly by a multi-channel pulse height analyzer (PHA) to acquire the direct 7-spectrum. Then the anticoincidence signals are analyzed in succession by the same P H A to obtain the anticoincidence yspectrum. During the second analysis, the//-counting rate, np, is measured by a scaler. For a simple /3-7 emitter, the disintegration rate, no, may be then determined as no
= n p / [ l - ( n A*/ . , ) ]*,
(1)
• and n* are the counting rates corresponding where n7 to the photopeak-areas in the ?- and anticoincidencespectra, respectively. Here the asterisk represents that the pulse height analysis was made with the live time mode of operation of the PHA. The subtraction of the background spectrum is required only when the background has peaks at the region of interest. It is noted here that in the anticoincidence-spectrum the Compton continuum is also reduced considerably and the peak may be well separated from the continuum even when a source with a high/3-efficiency is measured. The simultaneous recording of the spectra in the yand anticoincidence-channels is desirable to obtain
2. Principle of the method 2.1. THE PRINCIPLE There are two possible ways to introduce the spectral information in the 4rr//-y experiments. One is the 4zc//-y coincidence spectroscopy, in which the coincidence77
78
v. KAWADA et al.
AX~
l----;i--I-.
/'~0 p,'/ PO"
I
\\~ [II,o, ~'
l~n-Ll
l(no,Fract ional Intensi ty: qno
..........
s,o,.,,,_,,
/ l~'k'l / J)'2,'Stcltel
AYz+I
Fig. 1. Generalized decay scheme offi- 7 emitting nuclide. better precisions. However, we are generally forced to make pulse height analyses in succession with a single multi-channel analyzer. Nevertheless, even for this case, the merit of the coincidence/anticoincidence measurements with a high efficiency/?-detector regarding the precision may be still held if the anticoincidence gating technique is used. The detailed discussion on this point will be made in the later section.
mined in the similar manner as in eq. (3) can be expressed as
[
qOkv= Pk+ i
s=k+l
qsk
Pk~k+ i
s=k+l
where ek is the r-counting efficiency for/?k" Considering the relation: k--1
i
v=0
s=k+l
£ qkv -= Pk -t-
2 . 2 . G E N E R A L ANTICOINCIDENCE EQUATION
The decay scheme of a /?-7 emitting nuclide may generally be represented as shown in fig. l, where /?k implies the/?-branch to the k-th excited state with the branching fraction of Pk- The ?,-transition from the k-th state to the v-th is denoted as 7kv. Its transition probability in terms of the fraction of disintegrations is denoted by qkv" In applying the method to the measurements of nuclides with complex decay, it is convenient to refer to the y-transitions which directly lead to the ground state, i.e. 7go. In such a case, the disintegration rate will be given by
}
(qskqg~k), (4)
qsk
(Kirchhoff's law), the following equation will be obtained from eq. (4): q 1o(Pl 0 + q20(,°20 -~-.. • + qkOq~kO
=
= plex -t- p 2 8 2 +
~
s=k+l
+ ...
-t-Pkgk-t-
(qsl~Osl+qs2~s2-~-"" +qsk~sk),
(5)
which leads to
k=l
(qko~Oko)+Poeo = ~ (Pkek). k=O
(6)
On the other hand, the/?-counting rate is expressed by
k=l
but ¢Pk0
=
1 --(nnko/nT~o). * *
(3)
Here n*Yko and n*ko represent the counting ratesin the photopeaks corresponding to 7go in the 7- and anticoincidence-spectra, respectively, and So r-counting efficiency for/?o-branch. Eq. (2) can be derived in the following way. Consider the ?-transition from the k-th state to the v-th. The apparent /?-efficiency, ~Okv, which is deter-
n# = no Z (Pkek)"
(7)
k=O
It will be seen from eqs. (6) and (7) that the disintegration rate can be expressed by eq. (2).
3. Corrections and counting statistics 3.1. ACCIDENTAL LOSS OF ANTICOINCIDENCE-SIGNALS The most important correction involved in the proposed method might be that for the accidental losses
RADIOACTIVITY
of anticoincident pulses. In connection with radioactivity measurements by anticoincidence counting, Bryant has suggested that this type of correction can be reduced to a problem of the dead time correction if a special timing system is used3), but we deal straightforward with this problem from the viewpoint of accidental loss of anticoincidences. It is assumed that the pulse width, T, of the gating signals is equal to the dead time of the fl-channel, and the relative delay between the fl- and y-signals is D as schematically shown in fig. 2. When the live time mode of operation of the P H A is used for the analyses of the y- and anticoincidence-signals, we can regard the yand anticoincidence-channels as ideal ones which have no dead time. Under these conditions, the following three cases are supposed to have a chance to cause accidental losses in the case of measurements of a simple 13-7 emitter. a. After a disintegration is detected in the fl-channel, the successive disintegration occurs within duration of time ( T - D ) and is recorded in the y-channel, but not detected by the fl-counter intrinsically. In this case, the loss rate, n~, is given by
n i = n#n*(1-ep)(T--D),
(8)
where ep is the intrinsic efficiency of the/?-counter. b. The situations are the same as those in the case (a) except that the successive disintegration is not recorded in the//-channel due to the dead time. The loss rate, n~, for this case is ~¢ nztt = n#n,e#(TD).
(9)
It should be noted that this term is closely related with the dead time correction as will be described later. c. The first disintegration is detected in the y-channel, I
I
I
IReg oni RegionB Rag ion] '
I
c!
Ai
79
MEASUREMENTS
but not in the fl-channel. The anticoincidence-channel may miss to catch the true anticoincidence if the successive disintegration occurs within a delay of time D and is detected in the fl-channel. The loss rate, n;', for this case becomes
na" -= n~n~* (1-ep)D.
Therefore, the total accidental loss rate, nx, is given by the sum of these three components, and we obtain
nx = n#n, (T - e~D). Using the relation, e ~ ( 1 - n ~ T ) = 1-(n*+nx)/n*, ( l l ) can be rewritten in the form: n,~ = np
n*T(1--n#T)-- ny* D + n*D 1-n~(T+D)
! I
! d
Inhibiting
Gate Purse n
~D~i
,4
I
i
~ D ~,
--m
Fig. 2. Illustration of the t i m i n g relation o f pulses in the/J- a n d 7-channels.
(11) eq.
(12)
The Compton continuum may also be reduced by the accidental loss, but the resultant spectrum might be also continuum and the effects will be eliminated in the course of the determination of the photopeakareas in the anticoincidence spectrum. The above discussions can be therefore applied even to the measurements of nuclides having complex decay schemes if ~p is replaced by q~, and hence eq. (12) may be used for these cases. 3.2. T H E DEAD TIME CORRECTION
Usually a multi-channel pulse height analyzer has a dead time greater than the resolving time of the gating circuit, and the counts in the photopeaks are considerably smaller than those in the continuum area. However, the possible complexities due to these situations can be overcome if the 7- and anticoincidence-spectra are recorded with the live time mode, and the flcounts are registered with the real one. Neglecting the terms of higher order, the counting loss rate, n~, in the fl-channel due to the dead time is expressed as n~ = n~T. It is, however, convenient to give the expression in the following form:
n~ = n~ { ( T - D ) + D } . l~-Putse
(10)
(13)
When eq. (12) is used as the correction for the accidental loss of anticoincidences, the first term of eq. (13) will be compensated in the calculation of no. This is because the term in the case (b) in the preceding section may also be regarded as the correction for the dead time loss arising during a period of time ( T - D ) before the gating pulse falls down (region B in fig. 2). In the course of the calculation of no, the effects of the second term also may be cancelled out by the anticoincidence signals which are produced by the coin-
80
Y. K A W A D A e t al.
cident events within a period of time D after the gating pulse due to the preceding event has fallen down (region C in fig. 2). In the case of a simple/7-7 emitter, for example, the counting rates in each channels are given by np = nosn(1 - n o s J ) ,
(14)
H?* ~ /'/0By,
(15)
and
t
tit
na* = n o B , - nospS,(1 - nospO) - nx - n~.
(16)
It is seen from the above equations that the value of } becomes no, and no dead time correction is needed in the disintegration measurements by the proposed method.
n#d{1-(n*+nz)ln*
peak-areas depend upon the number of the data-points used for the interpolation, the shape and smoothness of the continuum and other several characters of the spectra. It is therefore difficult to give a general expression of the counting statistics in the measurements of no. So, in the following, only the case for simple fl-7 emitters will be considered. Supposing that the 7- and anticoincidence-spectra are recorded successively according to the procedures mentioned in the foregoing section and the fl-counts are registered during the second analysis, the fractional standard deviation, o-an,, in the measurements of no with the anticoincidence gating will be expressed as O'Anti=
N7
\
8/7 i
3.3. THE RESPONSE OF THE fl-COUNTER TO y-RAYS AND INTERNAL CONVERSION ELECTRONS
This method also involves the correction for the response of the fl-counter to y-rays and internal conversion electrons. The situations for this correction are the same as those in the 47rfl-7 coincidence measurement, and the correction can be expressed in the same form as given by Campion1). That is
where N~ and NA are the total counts in the photopeaks of the y- and anticoincidence-spectra, and Np is the total number of the/7-counts. I f the measurements are made by the coincidence gating technique, the fractional standard deviation, o-Co,,, will become o-Coin z
f _ (1-~0) 1 (c~G~+ss/,), ~p l+c~
(17)
where c¢ is the total internal conversion coefficient in the 7-t~ansition under consideration, Go is the counting efficiency of the/7-counter for the internal conversion electrons, and 8p~ is the sensitivity of the fl-counter to the y-rays. In eq. (3) ~o has already been defined. F r o m a simple analysis, it will be found that the correction for the response of the/7-counter to these events associated with other y-transitions is not required.
w h e r e Arc is the total counts in the photopeak in the
coincidence spectrum. This is because the second analysis can be considered as the y-efficiency measurement with the fractional standard deviation of [(1-e~)/Nc]" which is independent of the statistics in the 7-counts4). Since 1/N~ is small enough compared with other terms in eq. (18) and e~< 1, the ratio of the above two equations can be approximated as ~Anti ~ / f ( 2 - 8 ~ ) . ~
3.4. COUNTING STATISTICS The uncertainties in the determination of the photo,D.. ^--~ I. . . . . ~ ~ ]
I [
A,~ .... v,
N v -}-
(1-8~)
t
-/'
(20)
which gives, for example, aaotdCrco~.~ 0.25 in the case
n,~,, I "1 ~ , ' ~ 7
Inhibit j G ~
Biased AmpL~1024Channet[ ]_&Stretcherl I P.H.A. I
I( Cryost at I & Dewar) Fig. 3. Schematic diagram of the measuring arrangement.
RADIOACTIVITY
10s
173
MEASUREMENTS
8I
k 332
k
¥ c
o 2 _c 1 0 u m
o
°
~ ~ 10 ~
~z~D °
°"
° °'°®
~°
~'~*'° °° °° •
.
_//__l lOO
Anti-Coincidence...
150
~
":]
Gated • ~ . . . . .
I//
I
. ,°
200 Channel
I 300
/. "1 .... 350
f _ QI, .°. 40o
number
Fig. 4. y- and anticoincidence-spectra of 6°Co. that e# = 0.9. It will be expected that the counting statistics is considerably improved if the anticoincidence gating technique is used. The above discussions can be easily extended to the cases of complex fl-7 emitters, if effects of the statistics of the continuum are neglected. F r o m eq. (1), it may be seen that a fractional error, c5, in (n~/n*)produces a fractional error of {(1 -~#)/@}~5 in no. It is therefore expected in the anticoincidence spectroscopy that the effects of uncertainties in the determination of the photopeak-areas may also be diminished by a factor of (1-e#)/@. This is another reason why the technique of anticoincidence was used rather than coincidence. Nevertheless, the uncertainties in the determination of the photopeak-areas may still cause an appreciable error in the final result, and the precision obtainable of the method seems to be somewhat limited especially when a source with a greater value of (1-ca)/@ is measured.
4. Experimental arrangement The schematic diagram of the measuring system is shown in fig. 3. As the 7-detector, an Ortec 20 cc Ge(Li) detector (modified coaxial type) was used in conjunction with an Ortec model 118-A F E T preamplifier, and the amplified signals were fed to a model 409
linear gate through a variable delay line. The output was applied to a 1024 channel P H A (Nuclear Data 2200) via a biased amplifier and a pulse-stretcher. The energy resolution of the system was about 3.9 keV fwhm for the 1332 keV photons of 6°Co. The 4~zfl-counter is a rectangular box-shaped one, and positioned below the ,/-detector. Although, as for this set-up, the y-rays from the source enters into the Ge-erystal through the side wall of the cryostat of right angle type, the energy resolution did not deteriorate appreciably. The dimension of each half of the 4~zflcounter is 9.5 cm x 6.0 cm in area and 2.0 cm in depth. The/3-signals were amplified, discriminated and fed to an univibrator to produce the gating signals. The pulsewidth of the gating signals and the relative delay between the/3- and 7-signals were usually chosen as 4.8 #sec and 1.5 #sec, respectively.
5. Some examples of radioactivity measurements 6°Co: In order to confirm the validity of the method, measurements were made on several 6°Co sources prepared by the conventional procedures for 4n/3 counting. A typical example of the y- and anticoincidence-speetra is shown in fig. 4. Here the separation of the peaks from the continuum was made by graphical method, and both the peaks of 1173 keV and
82
Y. KAWADA et al.
~139
cM~°"L,
,
253d
i L
138 o
24.4s
~137 .£
~136 £3 I
I
t
|
1
2
3
4
I
I
5 Source Number
6
~,~o~.,~°~./ /
Fig. 5. Results of radioactivity measurements of 6~Co obtained by the proposed method (open circles) and by the 4~/~-7 coincidence counting method (closed circles).
2 8 70 k,82 °/,;
\ 110Cd
1332 keV were used for the determination of the #-efficiency. The results of the measurements are plotted in fig. 5 together with those obtained by the 4n#-y coincidence method. Although the results by the proposed method are subject to a slightly larger variation owing to the low v-efficiency of the Ge(Li) 10 4
Fig. 6. Decay scheme of 11°mAg-tl°Ag as quoted from ref.S). The numerical figures written above level-bars represent fractionay-intensities from a given excited state and differ from the notal tion q used in the text.
detector, they agree well with those by the 4nfl-y coincidence method. Other simple fl-V emitters such as 22Na, Z4Na, 46Sc, 82Br and a98Au are the subjects of the application of the method, but these nuclides can be measured with a sufficient accuracy by the convert-
658k
--
885k
706k 67 rk /1
/
937k
764 k
1384k
103 o
,
B1Bk E
1505k U uq C
(4°K) 1476k
U 10 2 • O I O
I
1565k
Coinci de'nce
Anti
°;
:%
°°
101
° °
°,°
•
°
°°
I
200
I
30Q
i
I
400 Channel
J
/ /
//
number
Fig. 7.7- and anticoincidence-spectra of lt°mAg-ll°Ag.
°
°
°
~
~°°
°
°, o
I
8OO
•
i
•
°oo°L ° * o 9OO
~
°.
~l,o
RADIOACTIVITY
1900, ~ 186 ~"184 ~i~8
c ounting
o_
~82 E ~186
...................
Anti-Coincid ence Spectroscopy
178
oo
0'1 0'2 0'3 0'~ o's 0!6 0'7
0!8 019
~I0
Fig. 8. Results of radioactivity measurements of n°mAg-la°Ag. The open circles are the results by the proposed method and the dotted line their mean. The closed circles and the solid line show the results by the 4~/3-~,coincidence-absorption method. For the value of e# in the abscissa, mean/~-efficiency was taken in the proposed method, while apparent /~-efficiency was used in the 4~/3-7 coincidence-absorption method. tional 4n/?-7 coincidence method, and the proposed method is therefore of no importance. The proposed method can be applied most effectively to the measurements of complex /?-7 emitters having no or weak/3-branch which directly goes to the ground state, i.e. Po ~ 0. These are, for example, 56Mn, 59Fe, 9SZr-95Nb, lx°mAg-ll°Ag, 124Sb, 1311 and 134Cs, and examples of the measurements on some of these nuclides will be described in the following. ~°mAg-ll°Ag: The decay scheme of l~°mAg-ll°Ag as quoted from the Table of Isotopes 5) is shown in fig. 6. From the experimental results on the relative/3-intensities of ~°mAg-~a°Ag reported by Katho and Yoshizawa 6) and Daniel et al.7), the fractional/3-intensity of the 2870 keV //-branch is estimated to be 0.0155 (sum of the intensities of all fl-branches in l a°mAg-ll°Ag was taken as unity). Among a number of 7-transitions present, only two of them lead to the ground state directly. They are 658 keV and 1476 keV in energy. The fractional transition probabilities of them were calculated from the data in ref. s), and found to be 0.9466 and 0.0379, respectively. The sources were prepared by the deposition of 0.01 N nitric acid solution of Ag*NO3 on gold-coated V Y N S films, and treated with Ludox-SM. Fig. 7 is a typical display of the 7- and anticoincidence spectra of this isotope, where the q~-values were 0.707 for the 658 keV peak and 0.639 for the 1476 keV peak. The//-efficiency for the 2780 keV//-rays was taken to be unity. The error arising from doing so will be small enough,
MEASUREMENTS
83
since this/?-branch is weak and energetic enough. The internal conversion probabilities are very small in both transitions, but in the 116 keV isomeric transition from 11°mAg one can find a noticeable number of internal conversions which are not coincident with the 1lOAg/?-rays, and thus these will cause an overestimation in the final results. By using the published data: K / L / M / ( N + O) = = 2.04 ± 0.06/1/0.214 ± 0.008/0.036 ± 0.003 as reported by GeigerS), K/K(658 keV) = 3.0 by Katho and Yoshizawa 6) and K(658 k e V ) = 0.00264_+0.0001 by Newbolt and Hamiltong), the necessary correction is estimated to be 0.0127/%. Here the counting efficiency for the conversion electrons was taken to be unity1°). The results of the activity measurements after making the above correction are plotted in fig. 8 as a function of (1-ap)/%. The typical measuring time is 2000 sec for each of the two pulse height analyses. In this figure, the results obtained by the 4n/3-7 coincidence-absorption method z) are also plotted after making the correction described above, where a conventional 4nil-7 coincidence equipment using a NaI(T1) scintillation counter (?-window was set on the 658 keV photopeak) was employed. The agreement of these results is satisfactory. 134Cs: In the disintegration of ~34Cs, two transitions directly go to the ground state as shown in fig. 9, i.e., the dominant (98.5%) from the 605 keV, and the minor 0 . 5 % ) from the 1168 keV. Parts of the spectra of the 7- and anticoincidence-signals are shown in fig. 10. In this measurement, it might be advantageous to use the 563 keV peak instead of the 1167 keV in the
13~Cs
2.05y-,~~~_~ 89k27°/ox'~k~ ~iOkZs~ \ \ oo2.71%
~
\
2
u~
tD 9 o~ o ~-
1~
134Bo Fig. 9. Decay scheme of 134Cs as quoted from ref.5). For the numerical figures, see the caption of fig. 6.
84
Y. KAWADA et al.
605k
796k i l
10 ~
g J: <.
I1;t BO2k
c 102 0 ~Direct • .• .1., " •
"•
• Anti C o i n ~ Q t e d ~
10 ~ / 610 I I I , 100 80
,
,,
120
,
I
,
i
~
140 1(50 1 0 Channe[ number
//
,
400
,
i
420
,
,
440
i'4~i
460
Fig. 10.7- and ant•coincidence-spectra of 1~4Cs. determination of % since the 563 keV peak is more intensive and gives almost the same result in the determination of q). After making the correction for the internal conversions and ~,-sensitivity of the/~-counter, the results of the measurements are presented in fig. 11 together with those by the 4nil- 7 coincidence-absorption method (7-window was set on the 605 keV photopeak). As can be seen from the figure, the two results are in good agreement. Nuclides having flo branch: In the case that a fibranch decays to the ground state (/3o in fig. 1), the proposed method can not be applied directly, but in some cases the/%efficiency for rio may be estimated by the extrapolation of the data for other/q-branches. The disintegration rate then can be calculated according to eq. (2) with a reasonable accuracy. This procedure might be applied to the measurements of 4VCa-4~Sc, 199AH etc. For nuclides having a "triangle decay scheme" such as 42K, the method is of no use, and the measurements of these nuclides must be made by other methods.
6. Concluding remarks Although the present method has somewhat restricted applicability, it has been successfully applied to the measurements of some of nuclides having complex decay schemes. The method is rather troublesome in analyses of the spectra, but the measurement
itself is very simple in procedures, and the result can be obtained with only one source. In the present stage, the method requires a fairly long measuring time to get a satisfactory counting statistics owing to the low 7efficiency of the Ge(Li) detector, but this difficulty might be overcome by the use of a larger Ge-crystal, a thinner 4n/%counter and sources having better /%efficiencies. In connection with the proposed method, we have pointed out that the ant•coincidence technique has some substantial advantages in the coincidence/anticoincidence works using spectra. The similar technique 98 98 cm 97
~96 95 }9~ "~ ~5 93 92 0.0
nting
Anti-CoincidenceSpectroscopy
o!~
o!2
0%
I - E~ E~
Fig. 11. As for fig. 8, but of ta4Cs.
o!~
RADIOACTIVITY MEASUREMENTS may be applied to other experiments; for example, the efficiency tracing m e t h o d of measuring pure/?-emitters, subsidiary technique of the decay scheme studies, a n d the escape probability analyses offl-rays from a source in 4rcfl counting. This work was done as a part of the research programme supported by the Atomic Energy Bureau of Japan. The authors are indebted to Mr. M. Y a m a s h i t a for his useful discussions, and also to Drs. Y. I n o u e a n d M. K a n n o for their interests a n d e n c o u r a g e m e n t s in this work.
85
References 1) p. j. Campion, Intern. J. Appl. Radiation Isotopes 4 (1959) 232. z) A. Williams and P. J. Campion, Intern. J. Appl. Radiation Isotopes 14 (1963) 533. 3) j. Bryant, Intern. J. Appl. Radiation Isotopes 13 (1962) 273. 4) p. j. Campion and J. G. V. Taylor, Intern. J. Appl. Radiation Isotopes 10 (1961) 131. 5) C. M. Lederer, J. M. Hollander and I. Perlman, Table of isotopes, 6th ed. (Wiley, New York, 1967) p. 249. ~) T. Katho and Y. Yoshizawa, Nuel. Phys. 32 (1962) 5. 7) H. Daniel, O. Mehling and D. Shotte, Z. Physik 172 (1963) 2O2. s) j. S. Geiger, Nucl. Phys. 61 (1965) 264. a) W, B. Newbolt and J. H. Hamilton, Nucl. Phys. 53 (1964) 353. 10) y. Kawada, Intern. J. Appl. Radiation Isotopes 20 (1969) 413.
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PUBLISHING
CO.
R A D I O A C T I V I T Y M E A S U R E M E N T S BY T H E 4n/~-y A N T I C O I N C I D E N C E S P E C T R O S C O P Y M E T H O D U S I N G A Ge(Li) D E T E C T O R Y. KAWADA, O. Y U R A and M. K I M U R A
Electrotechnical Laboratory, Tanashi-shi, Tokyo, Japan Received 5 August 1969 By the aid of a 4x[J-y anticoincidence set-up with a Ge(Li) detector, a method was developed which makes possible radioactivity measurements of some nuclides having complex decay schemes without requiring the decay scheme correction. The method employs the whole p-spectra in both the 7- and anticoineidencechannels, and the measurements are made according to the exact coincidence/anticoincidence principle. For examples of applica-
tion of the method, measurements of ~°Co, 11°mAg-ll°Ag and 134Cs were described and the results were compared with those obtained by other methods. Concerning the introduction of spectral information in the 4nfl-~ technique, the advantages of the anticoincidence technique over the coincidence are pointed out with special reference to accuracy and precision.
1. Introduction Among a variety of the methods available for radioactivity standardization, the 4n//-y coincidence method 1) is considered as one of the most accurate methods. This is especially true in the measurements of simple /3-7 nuclides, in which the method can be applied straightforward and an excellent accuracy can be established. However, when the method is applied to the measurements of nuclides having complex decay schemes, the decay scheme correction, which is required unless the efficiency of either the//- or y-detector is the same for each branch, becomes involved and hence the applicability of the method is somewhat restricted. In most cases, the correction might be determined with an adequate accuracy by using the coincidence-absorption method described by Williams and Campion2), but the procedures are rather laborious and troublesome, as it requires a series of coincidence measurements on sources with different/%efficiencies. In this paper, a modified method with the 4re//- 7 technique is described which permits measurements of some of nuclides with complex decay schemes without requiring the cumbrous correction. The proposed method follows the principle of anticoincidence rather than coincidence, and the spectral information of the signals from a high resolution 7-detector employed is introduced into both the 7- and anticoincidencechannels. In the following, the principle and procedures of the method will be presented in detail together with some typical examples of application.
channel measures the y-spectrum in coincidence with the //-signals. The fl-efficiencies are then calculated from the ratios of relevant photopeak-areas in the Yand coincidence-spectra. Another is the 47~//-y anticoincidence spectroscopy, in which the anticoincidence-channel measures the y-spectrum in anticoincidence with the//-signals. In this case, the//-inefficiencies are determined in a similar manner. In the present work, the latter method was used, since it seemed to be more advantageous than the former in the point of precision and accuracy. With our arrangement, the y-signals from a Ge(Li) detector, which is combined with a 47~//-y gas counter, are analyzed firstly by a multi-channel pulse height analyzer (PHA) to acquire the direct 7-spectrum. Then the anticoincidence signals are analyzed in succession by the same P H A to obtain the anticoincidence yspectrum. During the second analysis, the//-counting rate, np, is measured by a scaler. For a simple /3-7 emitter, the disintegration rate, no, may be then determined as no
= n p / [ l - ( n A*/ . , ) ]*,
(1)
• and n* are the counting rates corresponding where n7 to the photopeak-areas in the ?- and anticoincidencespectra, respectively. Here the asterisk represents that the pulse height analysis was made with the live time mode of operation of the PHA. The subtraction of the background spectrum is required only when the background has peaks at the region of interest. It is noted here that in the anticoincidence-spectrum the Compton continuum is also reduced considerably and the peak may be well separated from the continuum even when a source with a high/3-efficiency is measured. The simultaneous recording of the spectra in the yand anticoincidence-channels is desirable to obtain
2. Principle of the method 2.1. THE PRINCIPLE There are two possible ways to introduce the spectral information in the 4rr//-y experiments. One is the 4zc//-y coincidence spectroscopy, in which the coincidence77
78
v. KAWADA et al.
AX~
l----;i--I-.
/'~0 p,'/ PO"
I
\\~ [II,o, ~'
l~n-Ll
l(no,Fract ional Intensi ty: qno
..........
s,o,.,,,_,,
/ l~'k'l / J)'2,'Stcltel
AYz+I
Fig. 1. Generalized decay scheme offi- 7 emitting nuclide. better precisions. However, we are generally forced to make pulse height analyses in succession with a single multi-channel analyzer. Nevertheless, even for this case, the merit of the coincidence/anticoincidence measurements with a high efficiency/?-detector regarding the precision may be still held if the anticoincidence gating technique is used. The detailed discussion on this point will be made in the later section.
mined in the similar manner as in eq. (3) can be expressed as
[
qOkv= Pk+ i
s=k+l
qsk
Pk~k+ i
s=k+l
where ek is the r-counting efficiency for/?k" Considering the relation: k--1
i
v=0
s=k+l
£ qkv -= Pk -t-
2 . 2 . G E N E R A L ANTICOINCIDENCE EQUATION
The decay scheme of a /?-7 emitting nuclide may generally be represented as shown in fig. l, where /?k implies the/?-branch to the k-th excited state with the branching fraction of Pk- The ?,-transition from the k-th state to the v-th is denoted as 7kv. Its transition probability in terms of the fraction of disintegrations is denoted by qkv" In applying the method to the measurements of nuclides with complex decay, it is convenient to refer to the y-transitions which directly lead to the ground state, i.e. 7go. In such a case, the disintegration rate will be given by
}
(qskqg~k), (4)
qsk
(Kirchhoff's law), the following equation will be obtained from eq. (4): q 1o(Pl 0 + q20(,°20 -~-.. • + qkOq~kO
=
= plex -t- p 2 8 2 +
~
s=k+l
+ ...
-t-Pkgk-t-
(qsl~Osl+qs2~s2-~-"" +qsk~sk),
(5)
which leads to
k=l
(qko~Oko)+Poeo = ~ (Pkek). k=O
(6)
On the other hand, the/?-counting rate is expressed by
k=l
but ¢Pk0
=
1 --(nnko/nT~o). * *
(3)
Here n*Yko and n*ko represent the counting ratesin the photopeaks corresponding to 7go in the 7- and anticoincidence-spectra, respectively, and So r-counting efficiency for/?o-branch. Eq. (2) can be derived in the following way. Consider the ?-transition from the k-th state to the v-th. The apparent /?-efficiency, ~Okv, which is deter-
n# = no Z (Pkek)"
(7)
k=O
It will be seen from eqs. (6) and (7) that the disintegration rate can be expressed by eq. (2).
3. Corrections and counting statistics 3.1. ACCIDENTAL LOSS OF ANTICOINCIDENCE-SIGNALS The most important correction involved in the proposed method might be that for the accidental losses
RADIOACTIVITY
of anticoincident pulses. In connection with radioactivity measurements by anticoincidence counting, Bryant has suggested that this type of correction can be reduced to a problem of the dead time correction if a special timing system is used3), but we deal straightforward with this problem from the viewpoint of accidental loss of anticoincidences. It is assumed that the pulse width, T, of the gating signals is equal to the dead time of the fl-channel, and the relative delay between the fl- and y-signals is D as schematically shown in fig. 2. When the live time mode of operation of the P H A is used for the analyses of the y- and anticoincidence-signals, we can regard the yand anticoincidence-channels as ideal ones which have no dead time. Under these conditions, the following three cases are supposed to have a chance to cause accidental losses in the case of measurements of a simple 13-7 emitter. a. After a disintegration is detected in the fl-channel, the successive disintegration occurs within duration of time ( T - D ) and is recorded in the y-channel, but not detected by the fl-counter intrinsically. In this case, the loss rate, n~, is given by
n i = n#n*(1-ep)(T--D),
(8)
where ep is the intrinsic efficiency of the/?-counter. b. The situations are the same as those in the case (a) except that the successive disintegration is not recorded in the//-channel due to the dead time. The loss rate, n~, for this case is ~¢ nztt = n#n,e#(TD).
(9)
It should be noted that this term is closely related with the dead time correction as will be described later. c. The first disintegration is detected in the y-channel, I
I
I
IReg oni RegionB Rag ion] '
I
c!
Ai
79
MEASUREMENTS
but not in the fl-channel. The anticoincidence-channel may miss to catch the true anticoincidence if the successive disintegration occurs within a delay of time D and is detected in the fl-channel. The loss rate, n;', for this case becomes
na" -= n~n~* (1-ep)D.
Therefore, the total accidental loss rate, nx, is given by the sum of these three components, and we obtain
nx = n#n, (T - e~D). Using the relation, e ~ ( 1 - n ~ T ) = 1-(n*+nx)/n*, ( l l ) can be rewritten in the form: n,~ = np
n*T(1--n#T)-- ny* D + n*D 1-n~(T+D)
! I
! d
Inhibiting
Gate Purse n
~D~i
,4
I
i
~ D ~,
--m
Fig. 2. Illustration of the t i m i n g relation o f pulses in the/J- a n d 7-channels.
(11) eq.
(12)
The Compton continuum may also be reduced by the accidental loss, but the resultant spectrum might be also continuum and the effects will be eliminated in the course of the determination of the photopeakareas in the anticoincidence spectrum. The above discussions can be therefore applied even to the measurements of nuclides having complex decay schemes if ~p is replaced by q~, and hence eq. (12) may be used for these cases. 3.2. T H E DEAD TIME CORRECTION
Usually a multi-channel pulse height analyzer has a dead time greater than the resolving time of the gating circuit, and the counts in the photopeaks are considerably smaller than those in the continuum area. However, the possible complexities due to these situations can be overcome if the 7- and anticoincidence-spectra are recorded with the live time mode, and the flcounts are registered with the real one. Neglecting the terms of higher order, the counting loss rate, n~, in the fl-channel due to the dead time is expressed as n~ = n~T. It is, however, convenient to give the expression in the following form:
n~ = n~ { ( T - D ) + D } . l~-Putse
(10)
(13)
When eq. (12) is used as the correction for the accidental loss of anticoincidences, the first term of eq. (13) will be compensated in the calculation of no. This is because the term in the case (b) in the preceding section may also be regarded as the correction for the dead time loss arising during a period of time ( T - D ) before the gating pulse falls down (region B in fig. 2). In the course of the calculation of no, the effects of the second term also may be cancelled out by the anticoincidence signals which are produced by the coin-
80
Y. K A W A D A e t al.
cident events within a period of time D after the gating pulse due to the preceding event has fallen down (region C in fig. 2). In the case of a simple/7-7 emitter, for example, the counting rates in each channels are given by np = nosn(1 - n o s J ) ,
(14)
H?* ~ /'/0By,
(15)
and
t
tit
na* = n o B , - nospS,(1 - nospO) - nx - n~.
(16)
It is seen from the above equations that the value of } becomes no, and no dead time correction is needed in the disintegration measurements by the proposed method.
n#d{1-(n*+nz)ln*
peak-areas depend upon the number of the data-points used for the interpolation, the shape and smoothness of the continuum and other several characters of the spectra. It is therefore difficult to give a general expression of the counting statistics in the measurements of no. So, in the following, only the case for simple fl-7 emitters will be considered. Supposing that the 7- and anticoincidence-spectra are recorded successively according to the procedures mentioned in the foregoing section and the fl-counts are registered during the second analysis, the fractional standard deviation, o-an,, in the measurements of no with the anticoincidence gating will be expressed as O'Anti=
N7
\
8/7 i
3.3. THE RESPONSE OF THE fl-COUNTER TO y-RAYS AND INTERNAL CONVERSION ELECTRONS
This method also involves the correction for the response of the fl-counter to y-rays and internal conversion electrons. The situations for this correction are the same as those in the 47rfl-7 coincidence measurement, and the correction can be expressed in the same form as given by Campion1). That is
where N~ and NA are the total counts in the photopeaks of the y- and anticoincidence-spectra, and Np is the total number of the/7-counts. I f the measurements are made by the coincidence gating technique, the fractional standard deviation, o-Co,,, will become o-Coin z
f _ (1-~0) 1 (c~G~+ss/,), ~p l+c~
(17)
where c¢ is the total internal conversion coefficient in the 7-t~ansition under consideration, Go is the counting efficiency of the/7-counter for the internal conversion electrons, and 8p~ is the sensitivity of the fl-counter to the y-rays. In eq. (3) ~o has already been defined. F r o m a simple analysis, it will be found that the correction for the response of the/7-counter to these events associated with other y-transitions is not required.
w h e r e Arc is the total counts in the photopeak in the
coincidence spectrum. This is because the second analysis can be considered as the y-efficiency measurement with the fractional standard deviation of [(1-e~)/Nc]" which is independent of the statistics in the 7-counts4). Since 1/N~ is small enough compared with other terms in eq. (18) and e~< 1, the ratio of the above two equations can be approximated as ~Anti ~ / f ( 2 - 8 ~ ) . ~
3.4. COUNTING STATISTICS The uncertainties in the determination of the photo,D.. ^--~ I. . . . . ~ ~ ]
I [
A,~ .... v,
N v -}-
(1-8~)
t
-/'
(20)
which gives, for example, aaotdCrco~.~ 0.25 in the case
n,~,, I "1 ~ , ' ~ 7
Inhibit j G ~
Biased AmpL~1024Channet[ ]_&Stretcherl I P.H.A. I
I( Cryost at I & Dewar) Fig. 3. Schematic diagram of the measuring arrangement.
RADIOACTIVITY
10s
173
MEASUREMENTS
8I
k 332
k
¥ c
o 2 _c 1 0 u m
o
°
~ ~ 10 ~
~z~D °
°"
° °'°®
~°
~'~*'° °° °° •
.
_//__l lOO
Anti-Coincidence...
150
~
":]
Gated • ~ . . . . .
I//
I
. ,°
200 Channel
I 300
/. "1 .... 350
f _ QI, .°. 40o
number
Fig. 4. y- and anticoincidence-spectra of 6°Co. that e# = 0.9. It will be expected that the counting statistics is considerably improved if the anticoincidence gating technique is used. The above discussions can be easily extended to the cases of complex fl-7 emitters, if effects of the statistics of the continuum are neglected. F r o m eq. (1), it may be seen that a fractional error, c5, in (n~/n*)produces a fractional error of {(1 -~#)/@}~5 in no. It is therefore expected in the anticoincidence spectroscopy that the effects of uncertainties in the determination of the photopeak-areas may also be diminished by a factor of (1-e#)/@. This is another reason why the technique of anticoincidence was used rather than coincidence. Nevertheless, the uncertainties in the determination of the photopeak-areas may still cause an appreciable error in the final result, and the precision obtainable of the method seems to be somewhat limited especially when a source with a greater value of (1-ca)/@ is measured.
4. Experimental arrangement The schematic diagram of the measuring system is shown in fig. 3. As the 7-detector, an Ortec 20 cc Ge(Li) detector (modified coaxial type) was used in conjunction with an Ortec model 118-A F E T preamplifier, and the amplified signals were fed to a model 409
linear gate through a variable delay line. The output was applied to a 1024 channel P H A (Nuclear Data 2200) via a biased amplifier and a pulse-stretcher. The energy resolution of the system was about 3.9 keV fwhm for the 1332 keV photons of 6°Co. The 4~zfl-counter is a rectangular box-shaped one, and positioned below the ,/-detector. Although, as for this set-up, the y-rays from the source enters into the Ge-erystal through the side wall of the cryostat of right angle type, the energy resolution did not deteriorate appreciably. The dimension of each half of the 4~zflcounter is 9.5 cm x 6.0 cm in area and 2.0 cm in depth. The/3-signals were amplified, discriminated and fed to an univibrator to produce the gating signals. The pulsewidth of the gating signals and the relative delay between the/3- and 7-signals were usually chosen as 4.8 #sec and 1.5 #sec, respectively.
5. Some examples of radioactivity measurements 6°Co: In order to confirm the validity of the method, measurements were made on several 6°Co sources prepared by the conventional procedures for 4n/3 counting. A typical example of the y- and anticoincidence-speetra is shown in fig. 4. Here the separation of the peaks from the continuum was made by graphical method, and both the peaks of 1173 keV and
82
Y. KAWADA et al.
~139
cM~°"L,
,
253d
i L
138 o
24.4s
~137 .£
~136 £3 I
I
t
|
1
2
3
4
I
I
5 Source Number
6
~,~o~.,~°~./ /
Fig. 5. Results of radioactivity measurements of 6~Co obtained by the proposed method (open circles) and by the 4~/~-7 coincidence counting method (closed circles).
2 8 70 k,82 °/,;
\ 110Cd
1332 keV were used for the determination of the #-efficiency. The results of the measurements are plotted in fig. 5 together with those obtained by the 4n#-y coincidence method. Although the results by the proposed method are subject to a slightly larger variation owing to the low v-efficiency of the Ge(Li) 10 4
Fig. 6. Decay scheme of 11°mAg-tl°Ag as quoted from ref.S). The numerical figures written above level-bars represent fractionay-intensities from a given excited state and differ from the notal tion q used in the text.
detector, they agree well with those by the 4nfl-y coincidence method. Other simple fl-V emitters such as 22Na, Z4Na, 46Sc, 82Br and a98Au are the subjects of the application of the method, but these nuclides can be measured with a sufficient accuracy by the convert-
658k
--
885k
706k 67 rk /1
/
937k
764 k
1384k
103 o
,
B1Bk E
1505k U uq C
(4°K) 1476k
U 10 2 • O I O
I
1565k
Coinci de'nce
Anti
°;
:%
°°
101
° °
°,°
•
°
°°
I
200
I
30Q
i
I
400 Channel
J
/ /
//
number
Fig. 7.7- and anticoincidence-spectra of lt°mAg-ll°Ag.
°
°
°
~
~°°
°
°, o
I
8OO
•
i
•
°oo°L ° * o 9OO
~
°.
~l,o
RADIOACTIVITY
1900, ~ 186 ~"184 ~i~8
c ounting
o_
~82 E ~186
...................
Anti-Coincid ence Spectroscopy
178
oo
0'1 0'2 0'3 0'~ o's 0!6 0'7
0!8 019
~I0
Fig. 8. Results of radioactivity measurements of n°mAg-la°Ag. The open circles are the results by the proposed method and the dotted line their mean. The closed circles and the solid line show the results by the 4~/3-~,coincidence-absorption method. For the value of e# in the abscissa, mean/~-efficiency was taken in the proposed method, while apparent /~-efficiency was used in the 4~/3-7 coincidence-absorption method. tional 4n/?-7 coincidence method, and the proposed method is therefore of no importance. The proposed method can be applied most effectively to the measurements of complex /?-7 emitters having no or weak/3-branch which directly goes to the ground state, i.e. Po ~ 0. These are, for example, 56Mn, 59Fe, 9SZr-95Nb, lx°mAg-ll°Ag, 124Sb, 1311 and 134Cs, and examples of the measurements on some of these nuclides will be described in the following. ~°mAg-ll°Ag: The decay scheme of l~°mAg-ll°Ag as quoted from the Table of Isotopes 5) is shown in fig. 6. From the experimental results on the relative/3-intensities of ~°mAg-~a°Ag reported by Katho and Yoshizawa 6) and Daniel et al.7), the fractional/3-intensity of the 2870 keV //-branch is estimated to be 0.0155 (sum of the intensities of all fl-branches in l a°mAg-ll°Ag was taken as unity). Among a number of 7-transitions present, only two of them lead to the ground state directly. They are 658 keV and 1476 keV in energy. The fractional transition probabilities of them were calculated from the data in ref. s), and found to be 0.9466 and 0.0379, respectively. The sources were prepared by the deposition of 0.01 N nitric acid solution of Ag*NO3 on gold-coated V Y N S films, and treated with Ludox-SM. Fig. 7 is a typical display of the 7- and anticoincidence spectra of this isotope, where the q~-values were 0.707 for the 658 keV peak and 0.639 for the 1476 keV peak. The//-efficiency for the 2780 keV//-rays was taken to be unity. The error arising from doing so will be small enough,
MEASUREMENTS
83
since this/?-branch is weak and energetic enough. The internal conversion probabilities are very small in both transitions, but in the 116 keV isomeric transition from 11°mAg one can find a noticeable number of internal conversions which are not coincident with the 1lOAg/?-rays, and thus these will cause an overestimation in the final results. By using the published data: K / L / M / ( N + O) = = 2.04 ± 0.06/1/0.214 ± 0.008/0.036 ± 0.003 as reported by GeigerS), K/K(658 keV) = 3.0 by Katho and Yoshizawa 6) and K(658 k e V ) = 0.00264_+0.0001 by Newbolt and Hamiltong), the necessary correction is estimated to be 0.0127/%. Here the counting efficiency for the conversion electrons was taken to be unity1°). The results of the activity measurements after making the above correction are plotted in fig. 8 as a function of (1-ap)/%. The typical measuring time is 2000 sec for each of the two pulse height analyses. In this figure, the results obtained by the 4n/3-7 coincidence-absorption method z) are also plotted after making the correction described above, where a conventional 4nil-7 coincidence equipment using a NaI(T1) scintillation counter (?-window was set on the 658 keV photopeak) was employed. The agreement of these results is satisfactory. 134Cs: In the disintegration of ~34Cs, two transitions directly go to the ground state as shown in fig. 9, i.e., the dominant (98.5%) from the 605 keV, and the minor 0 . 5 % ) from the 1168 keV. Parts of the spectra of the 7- and anticoincidence-signals are shown in fig. 10. In this measurement, it might be advantageous to use the 563 keV peak instead of the 1167 keV in the
13~Cs
2.05y-,~~~_~ 89k27°/ox'~k~ ~iOkZs~ \ \ oo2.71%
~
\
2
u~
tD 9 o~ o ~-
1~
134Bo Fig. 9. Decay scheme of 134Cs as quoted from ref.5). For the numerical figures, see the caption of fig. 6.
84
Y. KAWADA et al.
605k
796k i l
10 ~
g J: <.
I1;t BO2k
c 102 0 ~Direct • .• .1., " •
"•
• Anti C o i n ~ Q t e d ~
10 ~ / 610 I I I , 100 80
,
,,
120
,
I
,
i
~
140 1(50 1 0 Channe[ number
//
,
400
,
i
420
,
,
440
i'4~i
460
Fig. 10.7- and ant•coincidence-spectra of 1~4Cs. determination of % since the 563 keV peak is more intensive and gives almost the same result in the determination of q). After making the correction for the internal conversions and ~,-sensitivity of the/~-counter, the results of the measurements are presented in fig. 11 together with those by the 4nil- 7 coincidence-absorption method (7-window was set on the 605 keV photopeak). As can be seen from the figure, the two results are in good agreement. Nuclides having flo branch: In the case that a fibranch decays to the ground state (/3o in fig. 1), the proposed method can not be applied directly, but in some cases the/%efficiency for rio may be estimated by the extrapolation of the data for other/q-branches. The disintegration rate then can be calculated according to eq. (2) with a reasonable accuracy. This procedure might be applied to the measurements of 4VCa-4~Sc, 199AH etc. For nuclides having a "triangle decay scheme" such as 42K, the method is of no use, and the measurements of these nuclides must be made by other methods.
6. Concluding remarks Although the present method has somewhat restricted applicability, it has been successfully applied to the measurements of some of nuclides having complex decay schemes. The method is rather troublesome in analyses of the spectra, but the measurement
itself is very simple in procedures, and the result can be obtained with only one source. In the present stage, the method requires a fairly long measuring time to get a satisfactory counting statistics owing to the low 7efficiency of the Ge(Li) detector, but this difficulty might be overcome by the use of a larger Ge-crystal, a thinner 4n/%counter and sources having better /%efficiencies. In connection with the proposed method, we have pointed out that the ant•coincidence technique has some substantial advantages in the coincidence/anticoincidence works using spectra. The similar technique 98 98 cm 97
~96 95 }9~ "~ ~5 93 92 0.0
nting
Anti-CoincidenceSpectroscopy
o!~
o!2
0%
I - E~ E~
Fig. 11. As for fig. 8, but of ta4Cs.
o!~
RADIOACTIVITY MEASUREMENTS may be applied to other experiments; for example, the efficiency tracing m e t h o d of measuring pure/?-emitters, subsidiary technique of the decay scheme studies, a n d the escape probability analyses offl-rays from a source in 4rcfl counting. This work was done as a part of the research programme supported by the Atomic Energy Bureau of Japan. The authors are indebted to Mr. M. Y a m a s h i t a for his useful discussions, and also to Drs. Y. I n o u e a n d M. K a n n o for their interests a n d e n c o u r a g e m e n t s in this work.
85
References 1) p. j. Campion, Intern. J. Appl. Radiation Isotopes 4 (1959) 232. z) A. Williams and P. J. Campion, Intern. J. Appl. Radiation Isotopes 14 (1963) 533. 3) j. Bryant, Intern. J. Appl. Radiation Isotopes 13 (1962) 273. 4) p. j. Campion and J. G. V. Taylor, Intern. J. Appl. Radiation Isotopes 10 (1961) 131. 5) C. M. Lederer, J. M. Hollander and I. Perlman, Table of isotopes, 6th ed. (Wiley, New York, 1967) p. 249. ~) T. Katho and Y. Yoshizawa, Nuel. Phys. 32 (1962) 5. 7) H. Daniel, O. Mehling and D. Shotte, Z. Physik 172 (1963) 2O2. s) j. S. Geiger, Nucl. Phys. 61 (1965) 264. a) W, B. Newbolt and J. H. Hamilton, Nucl. Phys. 53 (1964) 353. 10) y. Kawada, Intern. J. Appl. Radiation Isotopes 20 (1969) 413.