Minimizing the contribution of external bremsstrahhlung in internal bremsstrahlung spectra

Nuclear Instruments and Methods in Physics Research A245 (1986) 495-499 North-Holland, Amsterdam

495

M I N I M I Z I N G T H E C O N T R I B U T I O N O F E X T E R N A L B R E M S S T R A H L U N G IN I N T E R N A L BREMSSTRAHLUNG SPECTRA Shetha S e l m a n A L - D A R G A Z E L L I a n d M a z i n M a n u e l E L I A S

Physics Department, College of Science, Baghdad University, Jadriah, Baghdad, Iraq Received 23 August 1985 and in revised form 8 January 1986

A minimizing method for the contribution of external bremsstrahlung (EB) in internal bremsstrahlung (IB) spectra is described. It depends mainly on a good geometry arrangement of the detector chamber, choosing a low atomic number beta-stopper, and reducing the solid angle of EB relative to that of lB. A minimum value of the NEB/NIB ratio is achievable for a fixed source-detector distance. This method lowered this ratio by 37.8 times that of bad geometry leading to a minimum NEB/NIB ratio of 0.67% in one of the experimental arrangements used in this work.

1. Introduction Bremsstrahlung is a weak, continuous, electromagnetic radiation. It is classified into two types; internal bremsstrahlung (IB), which is produced due to change in dipole moment of the atom during the emission of any charged particle from the nuclei (mainly beta emission), and external bremsstrahlung (EB), which is produced due to the deflection of charged particles in the electrostatic field of a nucleus other than its own. IB spectra accompanying beta decay has been widely investigated since 1927 until the present time [1]. The disagreement among various experimental results as well as between experimental and theoretical predictions still appear in various ways. There are many factors which contribute to widen the gap between experimental and theoretical results. Experimentalists usually calculate or estimate these factors, which leads to unprecise results. This work is concerned with studying one of the important factors which affects IB spectra, namely EB. Minimizing the EB contribution to the IB spectrum decreases the gap between experimental and theoretical results of lB. The main source of EB in IB spectra is the absorber used to stop all beta particles from reaching the detector. The radioactive beta source also emits EB nonisotropically as well as all surrounding materials but with lower extent. The method depends mainly on choosing a low Z beta stopper, as well as reducing the solid angle of EB relative to that of IB for a fixed source-detector distance, and a good geometrical arrangement for the detector shielding. A review of earlier investigators showed that high Z 0168-9002/86/$03.50 © Elsevier Science Publishers B.V. (North-Holland Physics Publishing Division)

absorber (copper) has been used [2] leading to wide gap between experimental and theoretical results of lB. A relatively small source-detector distance (10 cm from a 1.75" x 2" detector) also contributed 5% EB in IB spectra [3]. With a good geometry, aluminium beta stopper contributed high EB in IB spectra [4]. A1-Konsol et al. [5] not only used aluminium beta stopper but they have placed the absorber directly below the beta source and at only 2.5 cm from the detector face. Both lead to a high contribution of EB in IB spectra, and hence their results involve large errors.

2. Experimental arrangements Figs. l a and l b represent the spectrometer chambers used for 3" × 3" and 2" × 2" NaI(T1) detectors respectively. The solid angle subtended by the detector at the source (in steradians) is I2m, and that at the absorber is I2EB, while $2t~ is the solid angle subtended by the absorber at the source. Fig lc represents the main distances used in the geometrical factor. The large distance between the detector crystal and the shielding was aimed to reduce EB from the shield material. The previous geometries were used with three IB sources; 9°Sr/9°Y, 2°4T1 and 147pmof different specifications (table 1) placed at 38, 28 and 18 cm from each crystal respectively with its own chamber. The crystals used were coupled with a photomultiplier. A high sensitive and stable electronic apparatus was used with a 1024 multichannel analyzer in the measurement of IB spectra.

496

S.S. Al-Dargazelli, M.M. Elias / Minimizing external bremsstrahlung 11

a

9,

I

2

,

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10 ~2B

o . "~f I~/

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Fig. 1. Experimental arrangements. (a) 3"x3" spectrometer chamber: 1: beta-source holder; 2: beta-absorber; 3: perspex annual disc; 4: lead collimater; 5: NaI(T1) crystal; 6: photomultiplier; 7: aluminium and iron plates; 8: shielding base (of lead); 9: cylinderical container (stainless steel); 10: lead plates; 11: perspex disc. (b) 2 " x 2" spectrometer chamber: 1. beta-source holder; 2. collimater tube; 3. beta-absorber; 4. NaI(T1) crystal with photomultiplier; 5. cylinderical container (stainless steel); 6. lead plates. (c) A sketch showing the solid angles for beta, IB and EB emission.

3. Minimizing method 3.1. Absorber of low atomic number and low radioactivity One of the main factors affecting the probability of the EB production q~EB is the absorber atomic n u m b e r Z. According to Bethe and Heithler [6], ~ EB varies with Z to Z z d e p e n d i n g on the absorber thickness, hence a low Z value is necessary. Perspex (effective Z = 5.852) was used not only as beta stopper but also as an envelope under the source. It was pointed out [7] that some c o m m o n materials used in constructing detector systems show a level of radioactivity, especially aluminium which is not free of

radioactivity, hence the choice of a low Z material for beta absorber should be accompanied with low radioactivity, and aluminium should be avoided due to this factor.

3.2. Reducing the solid angle of EB relative to that of IB Reducing the solid angle of EB relative to that of IB was achieved by choosing a proper distance of the absorber between the source, c, and the detector, b, as can be seen in fig. l c. The experimental probabilities of IB and EB emission of energy E v per single beta particle (for total absorption of beta particles for the EB case) are respec-

Table 1 Sources specifications Source

Activity (MBq)

Geometrical features

Amersham a) code number

90Sr/90 y 204T1 ]47Pm

370 185 37

point source, a = 0.1 cm extended source, a = 2.1 cm point source, a = 0.1 cm

SIF 0.33 TEC 0.23 PHC 0.32

~) Amersham International (England).

SS. Al-Dargazelli, M.M. Elias / Minimizing external bremsstrahlung

497

10

tively [8]:

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(1)

NEB(Ev) ~E,(Ev,

Zab~ ) =

S

u,I Z

E

(No~2E,/4~r)(~213/4~r),

(2)

hu

where NIB and NEB are the counting rate of IB and EB respectively. N o represents the number of beta particles emitted per unit time. ~2's are the corresponding solid angles defined earlier, then dPE8 ( E - r , Zabs)

NE8 ( E v ) 4 ~ 2 m

(~IB(E.y)

= Nm(Ev) #EB£#

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1

....~ O.S _m

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0.1 SOLID C U R V E S : 3 " X 3 " G E O M E T R Y Z

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ABSORBER.TO_DETECTOR DISTANCE

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ABSORBER_TO_DETECTOR DISTANCE

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Fig. 2. V a r i a t i o n o f t h e s o l i d a n g l e s a s a f u n c t i o n o f absorber-detector distances. (a) For the 9°Sr/9°Y experiment, point source, d ~ 38 cm. (b) For the 147pm experiment, point source, d =18 cm. (c) For 2°4T1 experiment, extended source (a = 2.1 cm), d ~ 28 cm.

0.2

0.1

I 5

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ABSORBER_TO. DETECTOR DISTANCE ( c m }

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498

S.S. A l-Dargazelli, M.M. Elias / Minimizing external bremsstrahlung F

or

I

2o

~bEB(Ey, Zabs) 1 [ f/EB ] qSm( E y ) 4~" ~ ~,-IB-IB) f/p"

NEB(Ey) Nm ( E v )

b (3)

Relation (3) shows the dependence of N E B / N m on f/EB, f/m and f/p, such that this ratio becomes minim u m when (f/EB/f/IB) f/p is minimum. At a fixed source-detector distance, d, f/EB can be lowered if the absorber-detector distance, b, is increased, but this will increase f/p at the same time. The contradictory effects of two angles will lead to a minim u m value at a certain distance, c. Fig. 2a shows the variation of f/~B, f/p, f/IB and (f/EB/f/m)f/p as a function of the absorber-detector distance b for a 9°Sr/9°Y source which lies 38 cm from

I

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\\ 3°x3" H ',I~ / l _ 2 , ~ 2 \ I ~ O 10 20 30 40 ABSORBER .TO- DETECTOR DISTANCE(cm)

Fig. 3. Variation of the (NEB//NIB) ratio of each absorber-detector distance. (Curves were normalized at minimum NEB/N m values.) a, b, c have the same meaning as in fig. 2.

J I

0

S 10 IS 20 25 ABSORBER -TO. DETECTOR DISTANCE(GIn)

S.S. AI-Dargazelli, M.M. Elias / Minimizingexternal bremsstrahlung the two detectors used in this work. The solid angles were calculated using the following formula [9]: ~2 = 2~r(1

D

3~: ( aR ]2[

D

)5,

(4)

Table 2 Contribution of EB photons in IB spectrum from 2°4T1 for two different geometries. Comparison with other work is also shown.

Ey

(NEB/NIB)×IO0%

(MeV)

Present work

4 \ D 2 ] l~D2/~'~2+R2 where R represents r for calculating (12EB, 12is ), and l for calculating 12#, D equals d, c and b for calculating 12m, I2~ and ~2EB respectively, and a is the source radius for calculating 12m and ~2~. Similar calculations were carried out for 147pm and 2°4T1 sourcers. Fig. 2b shows the variation of (12EB/12m)~2a as a function of b for the two detectors using a l * 7 p m radioactive source placed 18 cm above each detector. Also 12EB is shown for each case. Fig. 2c shows the variation for the 2°4T1 source with d = 28 cm. For all cases, I2 m was constant except for the case shown in fig. 2a; the deviation observed when 0 ~< b d/2 is due to the elimination of a part of IB photons from reaching the 3 " × 3" detector face by the lead holder of the beta absorber. F r o m the above figures, it is clear that the minimum (I2EB/~2IB)I2~ value is achievable at a certain b value (bin). In the case of a 3" × 3" detector, bm was always equal to d/2, but in the case of a 2" × 2" detector this was only true when d = 18, but when d = 38 cm, b m = 29 cm and when d = 28 cm, bm = 19 cm. This is due to the combination of R and D in eq. (4). These results show that placing the absorber in the midway between the source and the detector (b = d/2) is not always the best choice and an exact calculation of the solid angles for each geometrical arrangement gives b m. Large d value are recommended (if the source activity is high) to achieve large bm values and hence to reduce I2EB. Small r also reduces 12EB but will decrease the IB detection efficiency at the same time. F r o m relation (3), NEB/N m was determined for the two geometrical arrangements. Figs. 3a, 3b and 3c show the variation of the (NEa/Nm) ratio with b for the three sources and each with two detectors. The curves were normalized at minimum ( N E J N m ) values which correspond to minimum (fgEa/12m)12a values. It is obvious that high values of (NEB/Nm) occur when b either is much less or much higher than bm, reaching as high as 37.8 times that at the minimum value (fig. 3a).

4. Discussion The thallium source was chosen to show the comparison of the theoretical predications with the experiment and with other works. ~ m values were determined experimentally as a function of Ev, while ~Ea from perspex was calculated according to Bethe and

499

0.10 0.14 0.18 0.22 0.26 0.275 0.30

2" × 2" crystal, d = 28 cm

3" × 3", d = 28 cm

1.46 1.07 0.86 0.78 0.73 0.69 0.67

3.94 2.78 2.15 1.93 1.78 1.68 1.61

Powar et al. [11] 1.75" × 2" crystal d = 20 cm 57 36 -

Heitler (Elwert) theory [10] as a function of E v. The results are tabulated in table 2. It is evident from table 2, that the contribution of EB photons in IB spectrum from 2°4T1 varied from 0.67 to 1.46% in the 2" × 2" geometry, and 1.61 to 3.94% in the 3" x 3" geometry, both in the energy range 0.1-0.3 MeV which shows the correct choice of geometry on EB contribution to IB spectra. In a similar work by Powar et al. [11], the contribution varied from 57% at 0.1 MeV to 36% at 0.275 MeV. This high contribution in comparison to the low one obtained here is due to bad geometry used by them, where the perspex was placed directly below the beta source, i.e. c = 0 leading to low I2EB but very high 12~. The reduction of the EB effect, by simply choosing the proper beta absorber and correct geometrical arrangement, is of great importance in the measurement of IB spectra, and it should be observed strictly to decrease the gap between the experimental results and theoretical predictions. This gap is mainly due to inaccurate experimental procedures (such as using high Z material [2,4,5] or bad geometry [3,5,11]) rather than inaccurate theoretical predictions. References [1] K. Narasimha Murty and R. Prasad Babu, J. Sci. Ind. Res. 39 No. 3 (1980) 145. [2] B. Saraf, Phys. Rev. 94 (1954) 642. [3] M.S. Powar and M. Singh, J. Phys. A5 (1972) 460; J. Phys. G2 (1976) 43. [4] B. Singh and S.S. A1-Dargazelli, Phys. Rev. C3 (1971) 346; C4 (1971) 2144. [5] S. El-Konsol, A.M. Basha, S.A. Gaafer, A.A. EI-Sayed and A.S. Yousef, Atomkerneng. Kerntech. 42 (1983) 120. [6] H. Bethe and W. Heitler, Proc. Roy. Soc. A146 (1934) 83. [7] D.C. Camp, Nucl. Instr. and Meth. 117 (1974) 189. [8] D. Berenyi and D. Varga, Acta Phys. Hung. 29 (1970) 1. [9] W.R. Hendee, Radioactive Isotopes in Biological Research (Wiley, New York, 1973). [10] G. Elwert, Ann. Phys. 34 (1939) 178. [11] M.S. Powar, S. Ahmed and M. Singh, Phys. Rev. A21 (1980) 1884.