HIGASIMURA, Takenobu

KINOSITA, Katuhiro

SIDEI, Tunahiko

English

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RIGHT:URL:CITATION:AUTHOR(S):ISSUE DATE:TITLE:The Self-Scattering of the ComptonRecoil Electrons Produced by CoGamma-RaysSIDEI, Tunahiko; HIGASIMURA, Takenobu;KINOSITA, KatuhiroSIDEI, Tunahiko ...[et al]. The Self-Scattering of the Compton Recoil Electrons Produced by Co Gamma-Rays. Memoirs ofthe Faculty of Engineering, Kyoto University 1957, 18(4): 367-3771957-01-10http://hdl.handle.net/2433/280365The Self-Scattering of the Compton Recoil Electrons Produced by Co60 Gamma-Rays By Tunahiko SmEr, Takenobu HrGASIMURA and Katuhiro KrNOSITA Department of Applied Physics (Received August 31, 1956) 367 When r-rays penetrate through a matter, electrons are ejected by the three processes: the photoelectric effect, the Compton effect, and the pair creation. Suffering multiple scattering and degrading its energy, the secondary electrons ejected by the photon pass some distance in the matter. If the scatterer is a thin layer, some of the electrons penetrate it. It is difficult to calculate the energy spectrum and the angular distribution of penetrated electrons, because this process is very complicated. But, since the problems of the efficiency of G-M counter for the r-ray, the back-scattering and the self-scattering of the /3-ray belong to this process, it is important to study the phenomena by various ways. Concerning the efficiency of the G-M counter for r-rays, many works were done since about 1930,') but they were only for r-rays of a few certain energies because r-rays of natural radioactive elements, such as Ra and ThC', were used for most of the early measurements. In these days, the G-M counter became to be less important as the detector of r-rays in the field of nuclear physics; however, on the other hand, the utilization of radioactive isotopes has extended into various fields of science and technology and it has become important to clarify the dependence of its efficiency on the energy of r-rays. Some measurements have been conducted in a wide energy region in the last ten years.2) 3 ) 4 ) Also, some fundamental data were obtained for the back-scattering and self-scatteing of /3-rays. 5) As a way to study these phenomena-the process by which the multiple-scattering of the electron became mixed with the degradation of its energy-we measured the self-scattering of the secondary electrons by the r-rays of Co60 and obtained the results which are explained hereinafter. I. The Angular Distribution Experimental Procedure The geometry of our measurement is shown schematically in Fig. 1. A collimated 368 Tunahiko SIDE!, Takenobu HIGASIMURA and Katuhiro KINOSITA l I sca.tteve,. \i Fig. 1. Schematic drawing of the experimental arrangement. Fig. 2. Dual counter. r-ray beam of Co60 is applied perpendi-cularly on the sample (scatterer) and the emergent electrons are detected at each scattering angle 8 by the G-M counter A and B. Electrons ejected from the container of the source or the layer of the air along the path of the ray can be removed from the incident beam by the magnetic field of a electromagnet. The counter A is a usual end-window counter with a mica window of 2.2 cm in dia-meter and of 1.82 mg/cm2 in thickness. The distance from the scatterer to the front surface of its counting volume is 3.7 cm. A is used to measure the inten-sity of the emergent electrons at the scattering angle 8 = 0°, 12.5°, 25°. At the position where 8 is larger than 25°, the background counting rate is very large on account of the leakage of the r-ray and the standard deviation of the mea-surement becomes larger. Therefore, we produced a dual counter B to avoid this disadvantage. It consists of two G-M counters joined together which has a thin aluminium foil (1.68 mg/cm2 in thickness) between them as shown in Fig. 2. The thickness of the mica window of the forward counter is 4.1 mg/cm2 and its diameter, 1.5 cm and the distance from the mica window to the scatterer, 3.7 cm. As the main background count are due to the electrons ejected from the wall by the leaked r-ray, and these electrons have scarecely a chance to penetrate both counters, the background counting rate will be reduced remarkably when coincidence counts are taken. By this technique our measurements were easily carried out at the scattering angle of 8=25°, 45°, 65°, 115°, 135° in the relatively high r-ray field. The curves in Fig. 6 are connected at 8 = 25° by the data obtained by the two methods. Results Obtained Relations of the number of the emergent electrons with the thickness of the scatterer are shown in Figs. 3, 4 and 5. Assuming the usual self-scattering formula of the /j-rays to be approximately The Self-Scattering of thf Compton Recoil Electrons Produced by Co60 Gamma-Rays 369 JO 20 10 ~ ~ 'I-So / ""'"" ~ /1 ,r• I/ v ---- 135° ~!~ - 0 "'11$ I /00 200 300 600 700 800 900 "19/cm• Fig. 3. Relations between the intensity of emergent electrons and the thickness of silver scatterers at each scattering angle shown. The ordinate is in the arbitrary scale. 60 t-----.----~-------~ Fig. 4. Relations between the intensity of emergent electrons and the thickness of lead scatterers at each scattering angle shown. The ordinate is in the arbitrary scale. 370 60 so IJ.0 JO 20 /0 0 -JO 0 Tunahiko SIDEI, Takenobu HIGASIMURA and Katuhiro KINOSITA ~ - Ph V ... . -., I/ / v.--- i----- --Pb __ ..o-1/ . /,' ..---- ------ -------- 0 ltJ ~--- ---t :o --p---~? ·/, ,p I ,rf/ I I I ! If/ I I I i ,L ' I/ f.t 0 '/ t \ ;7 ,.._, \:) /00 200 300 !JOO soo 700 900 900 mff./cm• Fig. 5. Relations between the intensity of emergent electrons and the thickness of silver and lead scatterers at the scattering angle 0°. The ordinate is in the arbitrary scale. then we obtained the following µ's: scattering angle 8 I µ for lead (cm2/mg) I µ for silver (cm2/mg) oo 0.0092 0.0124 25° 0.0067 45° 0.0085 0.0086 65° 0.0047 0.0048 115° 0.0055 0.0058 135° 0.0076 In the case of the forward scattering the saturation thickness (the thickness where the intensity of the emergent electrons reaches 90% of the saturation value) decreases as the scattering angle increases. The decrease is slower than in the case of the self-scattering of 0-rays where it is proportional to cos fJ. It is quite natural that there is a large difference between the saturation thickness of the forward scattering The Self-Scattering of the Compton Recoil Electrons Ptoduced by Cr,60 Gamma-Rays 371 (8<90°) and that of the backward scattering (8>90°). It is interesting to note that the shape of the curve of fJ = 135° for lead is remarkably different from others. ln Fig. 5, the dotted curves represent the intensity when the magnetic field is removed. In this case the electrons ejected from the container of the source and the layer of the air are mixed in the incident r-ray beam. These electrons are absorbed in the sample, while the r-ray ejects secondary electrons from it. When the sample is thin, the absorption of the incident electrons is dominant and the counting rate of the detector decreases with the thickness of the sample and the intensity curve has the negative value. When the sample is thick enough, all incident electrons are absorbed and the counting rate is gov-erned only by the secondary electrons; and the intensitiy in-creases with the thickness of the sample and the shape of the curve becomes the same as in the case where the incident ray is not mixed with the electrons. Fig. 6 shows the results of the measurement of the angular distribution of emergent elec-trons from the scatter~rs. The curve A represents the results for the lead scatterer of 220 mg/cm2 in thickness and the curve B represents that of 19.1 mg/cm2• At fJ = 12.5°, the r-ray beam struck directly the wall of the counter and we 12.-----,------~---,------,----,----,------, 0-6 ,-.-----~--+----+-----,----,----, \c O.IJ. t----+-t---t---~t---t-----i~---ii-----i 20 40 80 /00 120 Fig. 6. Angular distributions of emergent electrons. Curve A : Experimental value for the lead scatterer of 220 mg/cm2 in thickness. Curve B : Experimental value for the lead scatterer of 19.1 mg/cm2 in thickness. Curve A': Calculated value for the lead scatterer of 220 mg/ cm2 in thickness. Curve B': Calculated value for the lead scatterer of 19.1 mg/cm2 in thickness. Curve C : Angular distribution of the Compton recoil electron. had to take a long measuring time. Therefore, considering the variation of the characteristics of the instrument during the measurement, the error at this angle might be larger than the statistical error shown in the figure. Comparing these curves with the curve C which represents the angular distribu-tion of the Compton recoil electron, the flat part of the curve A and B is remarkable. This is conceivable as the result of multiple scattering of the recoil electrons in the scatterer. In order to verify this effect, we calculated roughly the angular distribution 372 where Tunahiko SIDEI, Takenobu HIGASIMURA and Katuhiro KINOSITA Fig. 7. of the emergent electrons as follows. We took the recoil electron to the direction 81 in dx and put its distribution as a(81) sin 81d81d1p 1 , as shown in Fig. 7. These electrons go out of the scatterer after passing the distance t. The direction of emerging electrons, however, is different from 81 as they perform multiple scattering on their way out. If this variation of direction is denoted by 82 and take the distribution at 82 as /( 82 , t) dfJ2 , the angular distribution of the emergent electrons becomes (1) Various expressions of the distribution of multiple scattered electron have been presented by many authors, but we used the theory of S. Goudsmit and J. L. Saunderson6) because it is rigourous and its analytical formulae are easy to handle. Putting t = x/cos fJi, (2) Ze2 ✓l-{32 " = _m_c_2 -~0=2- , log~ = log (1.l~ao Z -- ¼) l ( 3) where a0 is the classical electronic radius, i is the wave length of the electron and N and Z has their usual meanings. By use of the relation I( 8) is expressed as follows: l ( 4) Integrating it with x, a's become The Self-Scattering of the Compton Recoil Electrons Produced by Co60 Gamma-Rays 373 1 a =-x• <1 o 2n e an= (2n + 1) ~:12 Pn(cos 81) 0(81) [1 -exp{-2m,2N co: 81 n(n+ 1) [10g ~ -( 5) -(-~+ t + ··· + ~)]}]sin81 cos81d81dq,1/2rri.:2Nn(n+l)[log~--(} + ! + · · · + ~ ) ] for n =t 0 where For simplicity we assumed the interaction of the r-ray with the•scatterer is only with the Compton effect. This assumption does not affect essentially the result of this calculation as the cross-section of the photoelectric effect, in the case of lead, is less than 20% of the Compton effect. By integrating (5) numerically7) and summing ( 4) up to n = 7 we obtained the curve A' and B' of Fig. 6. This calculation is based on various approximations. They do not hold when scattering angle is large, especially for the thick scatterer. For this reason the curve A' and B' have their meanings only when the scatterer is thin or the scattering angle is small. Comparing the curve A' and B' with the experimental results A and B, the consistency is rather good and the flattening of the top of the curves are well shown. II. 2rr-Forward and 2rr-Backward Scattering Experimental Procedure For the purpose of measuring the intensity of the electrons which emerge forward and backward within a solid angle 2n, we produced a drum-shaped G-M counter which is shown in Fig. 8- The counter is 49.5 mm long and has a wall of aluminium of 0.2 mm thick and the cathode of 26.5 mm inner diameter. The thick-ness of the mica window of both sides is 7 mg/cm2• The background counting rate is small because the collimated r-ray beam pass through the counter without striking the wall. Since the scatterer is put close to a window of the counter as shown in the figure, we are able to count the electrons scattered within a solid angle of about 1.3n steradian, '-;;;~;:::::::===r.=;-'' Sca.tt,-e,---Fig. 8. Schematic drawing of the apparatus to measure 21t-forward and backward scattering. This direction of the incident beam is at the case of the measure-ment of the backward scattering. 374 Tunahiko SIDEI, Takenobu HrGASIMURA and Katuhiro KrNOSITA We measured the relation of the intensity of 2rr-scattered electrons with the thick-ness of the scatterer and obtained the results as shown in Fig. 9 and Fig. 10. The saturation thickness are 270 mg/cm2 for the forward scattering and 190 mg/cm2 for the backward scattering, and they are quite uniform regardless of the kind of scat-terer. These curves were not influenced at all when the magnetic field was removed. M..--------,...----,,----,,__---,----, 00 100 200 JOO roo ,oo o .., "'1/<m• Fig. 9. Relations between the intensity of 2n:-forward scattering electrons and the thick-ness of the scatterers of various elements. The ordinate is in the arbitrary scale. 1100 S-00 ,oo ..,;.,.• Fig. 10. Relations between the intensity of 2n:-backward scattering electrons and the thick-ness of the scatterers of various elements. The ordinate is in the sarne scale as Fig. 9. Relations of the saturation values of the intensity of the scattered elec-trons with the atomic number Z of the scattering materials are shown in Fig. 11. In the case of the backward scattering, saturation values are pro-portional to Z and this is similar to the Z-dependency of the #-ray of about 0.1 Mev. 5J G. J. Hine had carried out similar measurement employing his integration ionization chamber and he obtained the ratio of the intensity of the backward scattering to that of the forward scattering twice or thrice greater than that of ours. However, this is thought to be quite reasonable Fig. 11. The Z-dependency of the intensity of the scattering elec-trons. Curve A : 2n:-forward scattering Curve B: 2n:-backward scattering Curve C : 4n:-scattering Thf Self-Scattering of the Compton Recoil Ehctrons Produced by Co60 Gamma-Rays 375 considering that the average energy of the backward scattering electrons is about 0.1 Mev. as has been discussed above and the specific ionization of these electron is larger than that of forward scattering electrons. The curve C in Fig. 11 shows the total intensity of the emergent electrons (forward scattering plus backward scat-tering), and it is conceivable that it expresses the r-ray efficiency of the counter which have the walls of given materials. The Z-dependency of the efficiency of G-M counter for r-rays was measured by some workers. Our results are quite consistent with those of Norling,2) but the data of Bradt et al.3) are somewhat different from ours. Bradt et al. measured the energy dependence of the efficiency of aluminium, brass and lead cylindrical counters and their data showed that the efficiency of lead counter at the energy of 1.2 Mev. is larger than that of aluminium counter. On the contrary, our results showed that the alumi-nium counter tias a larger efficiency for the r-rays of Co60 than the lead counter. This discrepancy might have been caused by the fact that they used the counter of cylindrical type whereas our m¢asurements are equivalent to use the rectangular counter. However, they did not measure in the neighborhood of 1.2 Mev. but they had simply interpolated the curves between 0.5 Mev. and 2.6 Mev. Theoretical calculation of the efficiency of the G-M counter for r-ray was done by von Droste9) quite long ago and his methods are still used today. By his expres-sion the efficiency is where -r, a and ,;, is the cross-section of the photoelectric effect, the Compton effect and the pair production, and R's are the ranges of the electrons ejected by each process, k is the probability of the secondary electron jumping into the counter and it depends on the initial distribution of the electrons. He assumed a cubically sym-metric distribution of emergent electrons and obtained k = 1/ 4. This assumption is correct for the low energy region. But as the energy of the r-ray becomes higher, the approximation becomes unsatisfactory. In the neighborhood of 1.2 Mev., the initial distribution of the electrons deviates from the cubic symmetry and the effect of their multiple scattering becomes very large. We will show that, when the multiple scattering is taken into consideration, the value of k becomes small when the atomic number Z of a substance on the wall is large. Let us take a G-M counter with rectangular cross-section and let the r-ray pene-trate perpendicularly on the wall. We neglect the electrons entering from the backside wall of the counter. This neglection of the backward scatrering is permissible according to the results of our experiment. We assume also that the secondary electrons are ejected only to the same direction as r-ray. This assumption is closer to the reality than the assumption of cubically symmetric distribution for the energy 376 Tunahiko SmE:1, Takenobu HrGASIMURA and :Katuhiro KINosIT J, of 1.2 Mev. After the secondary electrons passed the distance x in the scatterer, the probability that their direction is within the cone, of half angle flo is ~80 2 _ 02;a2 - 2 fJ e dfJ o a (6) where 2 _. 8-n:NZ(Z+l) e• l [ 4 z•l3N (__i___)2J a - p2tf x og n x mv ( 7) If we approximate ~ = ~ and neglect the variation of the logarithmic part, X e2 ~R ~cos-lR 1 -bZx k= dx -b- e fJdfJ 0 O zx (8) where b is a constant and R is the range of the secondary electrons. ~ntegrating (8), we obtain (9) where E; is the exponential integral. For the secondary electrons of the r-ray of 2 1.2 Mev., bR =10. By use of this value 2 R k = 0.25, 0.27, 0.25 and 0.20 for aluminium, copper, silver and lead respectively. Thus, we obtained the result that the efficiency became smaller for the heavy elements than that obtained by von Droste. III. Conclusion From these results, it became obvious that the scattering of the electrons has the most important meaning in discussing the behavior of the secondary electrons of the r-ray of 1.2 Mev. in various substances. In this energy region, the approximation of the complete diffusion of the electron and of the neglection of its scattering are not adequate. It became obvious also that the efficiency of the G-M counter for the r-rays of Co60 can be smaller for the heavy element than the value calculated by von Droste by a factor which depends on Z of the wall material. But we cannot determine which is more efficient, the lead counter or the aluminium counter, in the case of cylindrical type, as we are not yet tested experimentally. However, the truth of the traditional belief that the counter, whose wall consists of a heavy element, has a larger efficiency, is doubtful when the energy of the r-ray is about 1.2 Mev. · The Self-Scattering of the Ccnnpton Recoil El€ctrons Produced by Co60 Gamma-Rays 377 Authors wish to express their sincere thanks to Mr. I. Kumabe for his helpful advice pertaining to the experimental apparatus and his valuable discussions on the results. References 1) Kikuchi, Aoki and Fushimi : Proc. Phys.-Math. Soc. Japan, 18, 727 (1936). 2) F. Norling: Phys. Rev., 58, 277(L) (1940). 3) H. L. Bradt, P. C. Gugelot, 0. Huber, H. Medicus, P. Preiswerk and P. Scherrer: Helv. Phys. Acta., 19, 77 (1946). 4) E. T. JLirney and F. Mainenshein: R. S. I., 20, 932 (1949). 5) H. H. Seliger: Phys. Rev., 78, 491 (1950), 88, 408 (1952). I. Kumabe and S. Shimizu: Bulletin of Institute for Chemical Research, Kyoto Univ., 32, 183 (1955). 6) S. Goudsmidt and J. L. Saunderson: Phys. Rev., 57, 24 (1940). 7) A. T. Nelm : Natl. Bur. Stands. Circular No. 542. B) G. J. Hine: Nucleonics, 10, No. 1, 11 (1952). 9) von Droste: Zeits. for Phys., 100, 529 (1936). 

The Self-Scattering of the Compton Recoil Electrons Produced by Co⁶⁰ Gamma-Rays

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The Self-Scattering of the Compton Recoil Electrons Produced by Co⁶⁰ Gamma-Rays

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