Angular distributions of low-energy β-rays emitted from a sealed source

Appl. Radiat.ht. Vol. 45. No. 3, pp. 317-323,1994 Copyright c 1994 Elsevier Science Ltd Printed in Great Britain. All rights reserved 0969-8043/94 $6.00 + 0.00

Angular

HISAO

Distributions of Low-energy p-rays Emitted from a Sealed Source

YAMAMOTO’*.

TOSHIYUKI

NORIMURA’

and

AKIRA

KATASE’

‘Radioisotope Research Center, University of Occupational and Environmental Health, Kitakyushu 807. Japan, ‘Department of Radiation Biology and Health, University of Occupational and Environmental Health, Kitakyushu 807, Japan and ‘Tohwa Institute for Science, Tohwa University, Fukuoka 8 15, Japan

(Received 27 July 1993) Angular distributions of P-rays from a sealed standard source of “‘C are measured and found not to be isotropic. The anisotropy of the angular distribution is ascribed to the difference in the absorption of b-rays in the source, which depends on the angle of emission. A simple method is developed for calculating the angular distributions by using the logarithmic relationship of the transmission for b-rays against absorber thickness. The distributions obtained agree well with the experimental results.

work (Yamamoto et al., 1991). This work showed experimentally the anisotropic angular distribution of b-ray emission from the source due to the absorption in its sealing layer and estimated the resulting effect on the detection efficiency. However, more sophisticated experiments are required to make clear the effects of scattering and absorption of b-rays on the angular distributions. In the present work, detailed results are obtained by improving the methods of the measurement and the analysis of the angular distribution of P-rays for a sealed standard source of 14C.

1. Introduction In the measurement of the intensity of p-emitting radioisotopes, the absolute efficiency of a detector is obtained by using a standard /?-ray source of known activity. Standard sources are usually sealed by thin foils for soundness and easiness of handling. The path length of P-rays in the sealing materials varies depending on the emitting angle with respective to the normal to the plane of the source. Hence, the emission of the /?-rays from the source is not isotropic because of the difference in the absorption in the foils. In order to obtain the precise values of the detection efficiency, the effect of this anisotropy should be taken into account, particularly for the measurement of low energy P-ray sources. Kovarik (1910) first noticed the consequences of forward scattering of P-rays in the experiments to measure its absorption in thin foils. He found a rise in the initial portion of absorption curves and concluded that this rise was due to the forward scattering of p-rays. Angular distributions of the /?-ray emission were, however, not measured in his work. Recently, many studies have been made on the scattering and energy loss of monoenergetic electrons both theoretically (Liljequist et aI., 1978; Spalek, 1982; Spalek, 1988; Salvat et al., 1985; Proykova, 1980; Ismail and Liljequist, 1988) and experimentally (Ismail and Liljequist, 1988; Graham et al., 1963; BIverstam et al., 1973; Itoh et al., 1983). Conversion electron sources were used in these studies. So far as we know, no experiments of the above kind have been reported for b-ray sources, except our preliminary *Author

2. Experimental Method and Results A measurement system was composed of a Canberra 2lOOA preamplifier, a Canberra 2021 spectroscopy-amplifier and an EG&G Ortec 7100 multichannel analyzer. A semiconductor radiation detector fabricated from a commercial silicon photodiode (Yamamoto et al., 1989) was used for detection of b-rays. The active area of the detector was 13.2 mm* (4.1 mm dia) and the depth of the depletion layer was estimated to be about 100 pm. During the experiments, both the standard source and the detector were placed in an evacuated chamber (Canberra 7400). The interior dimensions of the chamber were 133 mm in diameter and 90 mm in depth, and the inside surface was lined by three kinds of materials as mentioned later. The detector was set at the point of half depth in the chamber. Its sensitive surface was placed at 33 mm away from the wall pointing towards the center of the chamber. The source was located at a distance of 58 mm from the detector surface on the

for correspondence. 317

HISAOYAMAMOTOet al.

318

length p and the angle 8 of P-ray emission with respect to the normal to the source surface is expressed by P’tl

(1)

cos 0 ‘Plastic Foil (t=6mglcm*)

Fig. 1. Schematic cross-sectional drawing of the principal part of ‘Y-source (not to scale).

diagonal line of the chamber and separated by 42 mm from the wall surface. All the measurements were made at room temperature. The “C-source (LMRI EBU-3, 2552 P-rays per s) calibrated by the absolute measurement with a 4n proportional counter was used. Figure 1 shows schematically the cross section of the principal part of the source. The i4C itself is hot-sealed between two plastic (Mylar) foils coated by a gold layer. The area of activity deposited is about 3 mm in diameter. The thickness of the plastic foils is about 6 mg/cm* (LMRI, 1981), and that of the gold layer is less than 0.1 mg/ cm*. The b-rays emitted from 14C are, therefore, absorbed mainly in the plastic foil. The rate of absorption is dependent on the path length of b-rays in the plastic layer. The relation between the path

where t is the thickness of the sealing foils and is about 6mg/cm* in the present experiment. Figure 2 shows a typical pulse-height distribution measured for 1.5 x IO’s for b-rays from 14C at f3 = 0”. The dashed line in the figure represents the region of high background noise. The level of the discriminator was set at the minimum measurable energy (about 6 keV) over that of the highest noise. The effects of b-ray backscattering by the inner surface of evacuated chamber on the counting rate were examined by using three lining materials: copper (Z = 29) aluminium (Z = 13) and paper. The paper is mainly composed of cellulose. As described in Appendix, the effective atomic number Z, of a compound is obtained for the electron backscattering by the relation

where N, and Z, are the number of atoms and the atomic number, respectively, of the i-th element in the compound. From equation (2) the value of Z, is 6.35 for the paper. In Fig. 3 are shown the pulse-height distributions measured for 7.2 x 10’s for the lining material of paper at 8 = 0',20", 40”, 60” and 80”. With increasing 8, the height of the peak in the spectrum falls lower and the peak disappears finally. In Fig. 4 the variations of the counting rate are shown for the three

Paper

40 Fig. 2. Pulse-height

distribution

60 Channel

80 Number

100

120

140

of p-rays from 14C source. The source is sealed by two plastic about 6 mg/cm2 in thickness.

foils of

Angular distributions of p-rays

319

from a sealed source I

I

1

I

e=o’

0

Paper

0 8

q

A

Copper

0

Aluminum

0

Paper

20’ .5-

0

0

8 = 40’

A

8

A

8 = 80’

0 0

a.0 0

0

0

0

0

0

q

a

60’

0

8 0

.O-

a 8

0s

AA

‘AA A

A

08

a 0

1.5-

A OL

50

100

Channel

Number

8

Fig. 3. Pulse-height distributions of p-rays from “‘C source for a lining material of paper at various emission angles. The emission angle 0 is taken with respect to the normal to the surface of the source.

8

3. Analysis

and Discussion

3.1. Effects of the p-ray backscattering of chamber on the counting rate

by the wall

Figure 5 shows the variations of the counting rate A (0, Z) as a function of the atomic number Z of the lining materials for various values of 8. The straight lines are obtained by applying the least-squares method to the present experimental results for the respective angles 0. Within the statistical error, the values of A (0, Z ) increase almost linearly with those of Z for each angle. Furthermore, when A (0, Z ) for 0 = 90” is evaluated at Z = 0 by extrapolating the experimental results, the value is obtained to be approximately zero, agreeing with that expected from the geometry of the source and the detector. Hence, it appears that the corrections of the counting rates reasonably can be made for the effects of the backscattering by extrapolating A (0, Z) to Z = 0 for each angle of 0. In Fig. 6 the open circles are the results A (0) obtained after these corrections were accomplished. The values of A (0 ) decrease abruptly

A ;

20 lining materials of copper, aluminium and paper by open circles and closed circles, open triangles, respectively, as a function of the emission angle 0. The measured counting rates depend on the emission angle and also on the atomic number of the lining materials.

A

40 8 (Deg

60 1

80

Fig. 4. Variations of the counting rate for three lining materials as a function of the emission angle tI of /?-rays.

increasing 8. At 0 = 48” the value reduces approximately by half of that at 0 = 0”. Figure 7 gives the variation of the values of slopes dA/dZ of the straight lines obtained in Fig. S(a) and (b) as a function of 8. The solid line in Fig. 7 was drawn by connecting these values of dA/dZ smoothly. There are apparently two groups of dA/dZ: the low (e = 00 - 40”) and the high (0 = 70” _ 90’) values. with

3.2. Angular dependence of the counting rate A Monte Carlo simulation can generally be applied to estimate the angular dependence of the counting rate of p-rays on the thickness of sealing foil of the source. In the preliminary work (Yamamoto et al., 1991), we tried, however, to calculate the angular dependence by using a semiempirical method, where it was assumed that transmission curves always take a linear shape for monoenergetic electrons. In the present work, we propose a simpler method to estimate the angular distribution, as mentioned below. From experimental observations (Evans, 1955a), it is adequate to assume that a plot of logarithmic transmission for b-rays against absorber thickness generally has an almost linear shape. Namely, the transmission Y after passing through an absorber of

HISAOYAMAMOTO

320

et al.

0.8

/so-

-0.6 In

a

/-O

”

al c

2 0.4

c” ._ 5

2

0.2 40' GAPP' 1.0 t

i Atomic

Number

jl

( Atomic

Number

Fig. 5. (a) and (b). Variations of the counting rate as a function of the atomic number of lining materials for various values of 19.The straight lines are fitted to the experimental results by the least-squares method.

thickness

x can be expressed

by

Y = Y,exp(-p.u)

(3)

where Y0 is the value of Y at x = 0 and p is the absorption coefficient for the absorber. The ratio Y/Y, of the transmission corresponds to the relative counting rate N of P-rays after passing through the absorber. The actual thickness of the absorber is related with the emission angle 0 of P-rays by equation (1). Thus, the value of N (0) for the B-rays emitted to the angle 0 is written by the equation (4)

8

Here, the absorption coefficient p depends not only on the maximum energy E, of [I-rays but also on the atomic number Z of the absorber materials. Baltakmens (1970) has obtained absorption curves for a wide range of the maximum energy with various absorber materials and proposed the following formula: (Deg)

Fig. 6. Counting rates as a function of 0 obtained after corrections for effects of the backscattering of /l-rays by the wall of the evacuated chamber (see text).

fl = 0,00*z 0.2XE$57 where Em is measured cm2/mg.

WlbOll

(5)

in MeV and p is given in

Angular

distributions

of b-rays

90

60

30 8

(Deg)

Fig. 7. Values of the slopes of the straight lines shown in Fig. 5 as a function through these values smoothly.

20 Fig. 8. Variations

321

from a sealed source

40 8 (Deg)

60

of 0. The solid line is drawn

60

of the angular distributions of the /?-rays with the thicknesses t of the sealing the source. The ordinate is normalized to unity at B =O”.

01.06----\

0

z

a ? ‘7

_

2 “0.5%

-

‘Z ‘Ir d

-

Measured

-

Calculated

_

foil of

t = 6 mglcm*

8

40 (Deg)

60

80

-

Fig. 9. Comparison of the angular distribution between the experimental and the calculated values. Open circles are the experimental results. Solid and broken lines show the results calculated for a sealing foil of 6 mg/cm2 in thickness without and with correction, respectively, for the effect of scattering in the foil.

HISAO YAMAMOTOet al.

322

The absorber material of the source was plastics (Mylar: polyethylene terephthalate). The effective atomic number Z was estimated to be 4.55 from the weighted mean of Z for constituent elements of this sealing material. From the values of Z and E,,, (0.156 MeV for 14C) and equation (5) p was evaluated to be 0.214cm2/mg. The values of N(0) were calculated from equation (4) for the various thicknesses of the sealing foil of the source as a function of the emission angle 8. Figure 8 shows the obtained results. The ordinate of the curves is normalized to unity at 0 = 0”. The increase of the thickness of foil makes the dependence of the relative counting rate on the emission angle 0 stronger. In Fig. 9, N (0 ) (solid line) for a foil of 6 mg/cm2 are compared with the present experimental values (open circles). In the region of 0 below 60” the agreement is reasonably good, whereas above 60” the difference increases with 0. This deviation is ascribed mainly to the scattering of P-rays in the sealing foil of the source. Although scattering is fundamentally a phenomenon in three dimensions, the scattering is assumed to take a Gaussian form as a function of the angle which is denoted by 4. Then, the relative counting rate No(0, 4) of the P-rays scattered to the angle fI from the original emission angle (0 + 4) is expressed by

N,(O, $I= where 0 is the standard deviation of the Gaussian distribution, and 10 + 4 1 the absolute value of (0 + 4). The whole counting rate N,(B ) is calculated from the formula NT(~)=

II No(R 4) d4. s -n

(7)

In Fig. 9 the values evaluated from equation (7) for u = 13” are represented by a broken line, which agrees well with the present experimental results (open circles). 4. Conclusions The angular distribution of P-rays was measured in the evacuated chamber. Effects of backscattering by the wall on the counting rates were examined by using three lining materials: paper, aluminum and copper. The This

backscattering increment grew

increased the almost linearly

number

Z of these

for

this

effect

counting

rate

to Z = 0.

The angular

distribution

source

of

could

14C was

lining

materials.

be made

not

The

corrections

by extrapolating

of p-rays isotropic

counting rate. with the atomic

from because

the

the sealed of

their

in the sealing layer. It was, therefore, necessary for the determination of detection efficiency to take into account the angular dependence of P-ray emission. A simple method for calculating the angular distributions was developed scattering

and

absorption

by using

the

for P-rays

against

distribution

relation

agreed

of

logarithmic

transmission

absorber

thickness.

The computed

with

the experimental

results.

References Baltakmens T. (1970) A simple method for determining the maximum energy of beta emitters by absorption measurements. Nucl. Insrrum. Methods 82, 264. Baverstam U., Bohm C., Ringstrom B. and Ekdahl T. (1973) Depth selection by means of scattered electrons: A method to determine electron line profiles. Nut/. Imlrum. Methods

108, 439.

Evans R. D. (1955a) The Atomic Nucleus, p. 625. McGrawHill, New York. Evans R. D. (1955b) The Atomic Nucleus, p. 592. McGrawHill, New York. Evans R. D. (1955~) The Atomic Nucleus. p. 582. McGrawHill, New York. Graham R. L., Brown F., Davies J. A. and Pringle J. P. S. (1963) A new method for measuring the depths of embedded radiotracer atoms using a precision /I-ray spectrometer. Can. J. Phys. 41, 1686. Ismail M. and Liljequist D. (1988) Angular dependence of energy loss in a low energy internal conversion electron source. Nucl. Instrum. Methods A270, 520. Itoh J.. Toriyama T., Saneyoshi K. and Hisatake K. (1983) Energy distributions of 7.3 keV electrons passing through iron films for depth-selective Mossbauer spectroscopy. Nucl. Instrum. Methods 205, 279. Kovarik A. F. (1910) Absorption and reflexion of the /I-particles by matter. Phil. kag. 20, 849. Lilieauist D.. Ekdahl T. and Blverstam U. (1978) Analvsis _ . of the electron transport in conversion electron Mossbauer spectroscopy. Nurl. Instrum. Methods 155, 529. LMRI (Laboratoire de Metrologie des Rayonnements Ionisants. France) (1981) Standards of Radioocrrrir), [Catalogue]. p. 63. Proykova A. (1980) An analysis of scattering processes of conversion electrons in solid layers. J. Phys. D 13. 29 I. Salvat F., Mayo1 R., Martinez J. D. and Parellada J. (1985) Weight functions for integral conversion electron Miissbauer spectroscopy. Nucl. Instrum. Methods B6. 547. Spalek A. (1982) Energy and angular distributions of electrons emitted from spectrometer sources: Monte Carlo calculations. Nucl. Instrum. Methods 198. 399. Spalek A. (1988) Direct Monte Carlo simulation of scattering processes of keV conversion electrons in a radioactive source. Nucl. Insfrum. Methods A264, 410. Yamamoto H., Hatakeyama S.. Norimura T. and Tsuchiya T. (1989) Low-energy nuclear radiation detection with a silicon photodiode. Nucl. Instrum. Method.y A281. 128. Yamamoto H., Hatakeyama S., Norimura T.. Tsuchiya T. and Katase A. (1991) Anisotropic /l-ray emission from a standard source due to self-absorption. NW/. In.strum. Methods

B53,

178.

APPENDIX We consider at first the probability of backscattering of monoenergetic electrons by thick compound materials. This probability is assumed to be proportional to that of backscattering by nucleus that may happen along the electron path until they stop in the material. The latter probability per electron path length is given by the following formula (Evans, 1955b):

where N, and Z, are the number density and the atomic number of the ith atom, respectively, and c is the velocity

Angular

distributions

of b-rays

of light. The charge and mass of electron are denoted by c and nrO, respectively. The symbol /I expresses the ratio of electron velocity to that of light. On the other hand, the energy loss dT/ds by ionization per electron path length s is given by the relation (Evans, 195%) dT,ds

= [2ne4,(m,c’fi2)](~ x (h-$n0c2P ‘T/iI,;l -Kr(

\

N,Z,)

where S is the mean electron path length. Equation introduced into ds of the above equation. Thus, pGI=G(

zN,Z:)/(

~N,Z,)j;=atl

(A21

(A2) is

-Ir2YB2dT

=K,(f)cN,Zf (A41

where K2 and K,(.F) are constants, and Z, is the effective atomic number of the compound and is set as

//

where T is the total energy of electron, and I, is the geometrical mean ionization and excitation potential of the ith atom. The logarithmic term is approximated to be constant and is represented by K, including other constants. Then, the backscattering probability P(i) is given by integrating equation (Al) along the electron path as P(S)=

323

= K3 (S)Z, - /I’))] - p ‘)

ZN,Z,)/B2 fl

from a sealed source

-B2)/B’lds

(A31

Zc=(

zN,Zi)/(

FN,Z,)

(A51

When P(S) is averaged over the /l-spectrum, the backscattering probability P of /l-particles is given by P = K,Z,

(‘46)

where K, is a constant and an average value of K,(i). Therefore, the value of Z, for the whole b-spectrum is also evaluated from equation (AS).