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Azimuthal variation of Compton scattering of polarized gamma rays
Nuclear Physics 62 (1965) 267--272; (~) North-Holland Publishing Co., Amsterdam Not to be reproduced by photoprint or microfilm without written permission from the publisher
AZIMUTHAL VARIATION OF COMPTON SCATTERING OF POLARIZED GAMMA RAYS M. SINGH, S. A N A N D and B. S. SOOD
Physics Department, Punjabi University, Patiala, India Received 15 July 1964 Abstract: The azimuthal variation of the Compton scattering of 280, 662 and 1250 keV gamma rays that are partially polarized by a previous Compton scattering through 64 °, 90 ° and 120 °, respectively, has been investigated. The experimental results are found to show good agreement with the predictions of Klein-Nishina formula. E [
I
A T O M I C PHYSICS Compton scattering; measured 7e-(q0) for partially polarized 7
1. Introduction The Compton scattering cross sections of gamma rays of different energies have been measured by a large number of workers [for details see Nelms 1) and Evans 2)] but not many investigations of the polarization effects in Compton scattering are reported. Hoover et al. 3) have measured the azimuthal variation of the Compton scattering at 90° of gamma rays that are partially polarized by a previous Compton scattering of 1250 keV gamma rays through 83° and 50°, respectively. Though their results show an over-all agreement with theory, there are appreciable deviations at some azimuthal angles (see fig. 3); these large deviations were ascribed to low counting rates and drifts in electronics during long counting times needed in their experiments. Therefore, it seemed desirable to repeat these experiments under some modified experimental conditions so as to obtain good statistics in reasonable counting time and extend them to different energies and angles. We have performed similar experiments at scattering angles of 64°, 90 ° and 120° at three energies of 280, 662 and 1250 keV and report the results in this paper. 2. Polarization Effects in Compton Scattering When a beam of unpolarized photons of energy ko undergoes Compton scattering through an angle 01, its energy decreases to kx and it is partially polarized. The degree of polarization p, which depends upon the energy of the incident photons and the angle of scattering is given as p _ JII _ J.
d°'a(01)4,1 = o. ,
d ~ l ( 0 x ) ÷ l = 90 267
(1)
M. $1NGH et
268
aL
where dll and J i are the intensities of tile gamma rays with electric vectors parallel and perpendicular to the scattering plane, respectively, and the Klein-Nishina crosssection is dCrl(01)
½r2 (k1~2(kl \ko] \ko
+ k° - 2 sin 2 01 COS2 ~bl~ / dn.
kl
(2)
Here r 0 is the classical electron radius, and ¢1 is the angle between the scattering plane and the plane of incident polarization. When the gamma rays of energy kl and degree of polarization p are scattered again through 02, the energy of the second scattering reduces to k2 and the number of gamma rays scattered at any azimuthal angle ¢2 = ~ with respect to the number scattered in the first scattering plane, i.e. (¢2 = 0) is given by
N4,2=o/N÷~= ~
= (1 +Pl R1)/(PxR2 +R3),
(3)
where .Pl
=fA 01, A~I dcrltOl)÷,=o/f/1 01, A~! da1(01)÷2 = 9o,
R1 = f a
02,A~2 02, A4)2
R3 =fA
02, d~b2
dff2(O2)#2=°/fA
d°'2(02)•2 = 9° '
02,A¢~2 02, A4~2
dff2(O2)'2=9°-°/f
d ° ' 2 ( 0 e ) o z = 9° "
I ,d /102, aO2
Here A01, A02, Ad?l and A¢2 are the spreads in the angles 01, 02, ¢1 and ¢2, and da2(02) is the Klein-Nishina differential cross-section averaged over the polarizations of the second scattered photons of energy k2 and is given by an expression similar to eq. (2) above. 3. Experimental Procedure and Results The experimental arrangement used to measure the ratio N÷~= olN#~=# is shown in fig. 1. Gamma rays from the source S are collimated onto a thin copper scatterer Sc. The gamma rays Compton scattered through an angle 01 are allowed to undergo Compton scattering again through 02 = 90 ° (kept fixed) by a plastic scintillator A coupled to a 6292 Dumount photomultiplier. The second scattered gamma rays are detected by a NaI(TI) crystal B coupled to RCA 6342-A photomultiplier covered with a mu-metal shield to eliminate the effect of the earth's magnetic field. Counter A is fixed at the centre of a circular rail along which counter B can rotate to vary angle ¢2. The distance between counter A and B can be varied to adjust the angular spreads A02 and A¢2. Large values of spreads are necessary to obtain reasonably
COMPTON SCATTERING
269
good counting rates. Both counters were shielded against direct radiation from the source. Counter B was also shielded from the radiation scattered from the copper scatterer. The shielding was symmetrical about the main axis of the setup which coincides with the axis o f A to avoid any false asymmetry in the counting rates. The recoil electron is counted in A, while the Compton scattered photon escapes it and is detected by counter B, and both give rise to a coincidence. This method of measuring coincidences has the obvious advantage of selecting the significant events only and thus reducing the background effects. The coincidences with counter B in different positions corresponding to different values of ~b2 were recorded by a conventional arrangement. The pulses from the two counters were fed to two amplifiers through pre-amplifiers. The amplified pulses were sorted according to their sizes by
Fig. 1. Experimental setup for azimuthal variation of Compton scattering of polarized gamma gamma ray source, S c a thin copper scatterer, A plastic scatterer- detector crystal B - NaI(TI) crystal.
rays. S
differential pulse-height analysers and fed to a coincidence unit. The counts were registered by three sealers, one for recording coincidences and the other two for recording pulses from the two individual counters. To set the channels of the two counters so as to count only the required events, the NaI(T1) counter was set to accept energies corresponding to the second scattered photon and a coincidence spectrum was taken by varying the bias of the plastic counter. The position of the peak in the coincidence spectrum was found to correspond to the energy of the recoil electron in the second scattering. The channels of the platic counter were set to cover full width at half height o f the maximum of the coincidence spectrum. With this setting of the plastic counter, another coincidence spectrum was taken by varying the bias of the NaI(TI) counter, to check the channel settings of the latter. The position of the maximum in the second coincidence spectrum agreed with the channels of NaI(T1) counter. Some of the spectra are shown in fig. 2.
270
M. SINGH et al.
The counts in the three sealers were recorded for five minutes at five different positions of the counter B, gb2 corresponding to 0, 30, 50, 70 and 90 degrees, respectively. The sequence o f observations was so arranged as to minimize the effects of electronic drift. The consistency of the data provided an indirect check on the electronic stability. The coincidence counts were corrected for the background and chance coincidences. The measurements were made with gamma rays of energy 280, I0 9
8
t~
6
tt-
3
\ I
I
I
I
I
I
I
I
10
20
30
0
10
20
0
10
PULSE
,1, 6 ~-
I
I
I
I
ZO
30
40
50
50
60
I\1 60
HEIGHT
(1
b
O
2 1 o o
]o
2o
3o
40
50
PULSE
60
1o
2.0
30
40
HEIGHT
Fig. 2. Some o f the spectra taken with the above arrangement. (a) and (b) are the direct spectra o f 662 keV g a m m a rays t a k e n with t h e NaI(T1) c o u n t e r a n d plastic counter, respectively. (e) Spectrum o f 662 keV 120 ° C o m p t o n scattered radiation t a k e n with N a I ( T l ) counter. (c) a n d (d) are t h e coincidence spectra o f scattered r a d i a t i o n in (e) t a k e n by varying t h e channels o n N a I ( T l ) a n d plastic counters, respectively, t h e c h a n n e l s on the o t h e r being kept fixed at appropriate energy.
271
COMPTON SCATTERING
4.0 3.8 3.6
3.4
3.2
3.C
Z.6
2.'1
•
7
2.2
2x
/
/
2
t /?
t.(
1.t
5
1.~
?
t.( q0
60
60
0
10
~o
60
8o
0
10
40
60
80
0
10
40
60
S0
0
Z0
q0
60
BO
Fig. 3. C o m p a r i s o n o f the experimental and theoretical results. Curves denote the theoretically calculated values f r o m eq. (3) and the points are the experimental values; the errors s h o w n are those due to statistics, the other errors have been discussed in the text. The curves and points 1-9 are for the present measurements and are to be compared with 10 and 11 due to H o o v e r e t al. 3). 1-3 correspond to 01 = 64 °, 02 = 90 ° for /co, respectively, at 280, 662 and 1250 keV and AO= = A~= = 40 ° for all. 4-6 correspond to 0t = 90 °, 0~ = 90 °, k 0 , respectively, at 280, 662 and 1250 keV and AOz = A~b= at 45 °, 55 ° and 55 °, respectively. 7-9 01 = 120 °, 0= = 90 °, ko . . . . 280, 662 and 1250 keV, respectively, and AO~ = A~2 at 35 °, 40 ° and 40 °, respectively. 10 and 11 are due to H o o v e r e t aL for 1250 keV at 01 = 83 °, 0= = 90 ° and 01 = 50 °, 02 = 90 °, respectively. The values o f spreads in these results are not available.
272
M. S~GH et al.
662 and 1250 keV partially polarized by a previous Compton scattering through 0a. Experiments were performed at three different values of 01 corresponding to 64 °, 90 ° and 120 ° . The measured values of N¢~=o/N¢2= ~ are compared with the theoretical values calculated from eq. (3) in fig. 3. The results of Hoover et al. 3) have also been plotted for comparison. The errors indicated are the statistical errors in the counts. The effect of multiple scattering of gamma rays in the copper scatterer was investigated by using scatterers of two different thicknesses. The results agreed within statistics in both the cases indicating that the effects of multiple scattering, if any, are small in our experiment. The spreads AO 1 and A~bI in 01 and ~bI are about 2 ° because a collimated beam of gamma rays is used. This will have negligible effect on p (0.2 %). The spreads A02 and A~b2 are different for various angles and energies and vary from 35 ° to 55 °. These can be ascertained to within +_5 ° from the geometry of the setup and involve an uncertainty of the order o f 10 ~ in the calculated values of N÷:=o/N÷,=~. The consistent agreement of the experimental results with theory at all angles and energies indicates that values of the angular spreads used in the present investigations are correct. The present measurements show a better agreement with the predictions of KleinNishina formula than those of earlier workers 3).
References
1) A. T. Nelms, N.B.S. Circular 542 (1953) 2) R. D. Evans, in Encyclopedia of physics, ed. by S. Flfigge Vol. 34 (Springer, Berlin, 1958) p. 218
3) J. I. Hoover W. R. Faust and C. F. Dohne, Phys. Rev. 85 (1952) 58
AZIMUTHAL VARIATION OF COMPTON SCATTERING OF POLARIZED GAMMA RAYS M. SINGH, S. A N A N D and B. S. SOOD
Physics Department, Punjabi University, Patiala, India Received 15 July 1964 Abstract: The azimuthal variation of the Compton scattering of 280, 662 and 1250 keV gamma rays that are partially polarized by a previous Compton scattering through 64 °, 90 ° and 120 °, respectively, has been investigated. The experimental results are found to show good agreement with the predictions of Klein-Nishina formula. E [
I
A T O M I C PHYSICS Compton scattering; measured 7e-(q0) for partially polarized 7
1. Introduction The Compton scattering cross sections of gamma rays of different energies have been measured by a large number of workers [for details see Nelms 1) and Evans 2)] but not many investigations of the polarization effects in Compton scattering are reported. Hoover et al. 3) have measured the azimuthal variation of the Compton scattering at 90° of gamma rays that are partially polarized by a previous Compton scattering of 1250 keV gamma rays through 83° and 50°, respectively. Though their results show an over-all agreement with theory, there are appreciable deviations at some azimuthal angles (see fig. 3); these large deviations were ascribed to low counting rates and drifts in electronics during long counting times needed in their experiments. Therefore, it seemed desirable to repeat these experiments under some modified experimental conditions so as to obtain good statistics in reasonable counting time and extend them to different energies and angles. We have performed similar experiments at scattering angles of 64°, 90 ° and 120° at three energies of 280, 662 and 1250 keV and report the results in this paper. 2. Polarization Effects in Compton Scattering When a beam of unpolarized photons of energy ko undergoes Compton scattering through an angle 01, its energy decreases to kx and it is partially polarized. The degree of polarization p, which depends upon the energy of the incident photons and the angle of scattering is given as p _ JII _ J.
d°'a(01)4,1 = o. ,
d ~ l ( 0 x ) ÷ l = 90 267
(1)
M. $1NGH et
268
aL
where dll and J i are the intensities of tile gamma rays with electric vectors parallel and perpendicular to the scattering plane, respectively, and the Klein-Nishina crosssection is dCrl(01)
½r2 (k1~2(kl \ko] \ko
+ k° - 2 sin 2 01 COS2 ~bl~ / dn.
kl
(2)
Here r 0 is the classical electron radius, and ¢1 is the angle between the scattering plane and the plane of incident polarization. When the gamma rays of energy kl and degree of polarization p are scattered again through 02, the energy of the second scattering reduces to k2 and the number of gamma rays scattered at any azimuthal angle ¢2 = ~ with respect to the number scattered in the first scattering plane, i.e. (¢2 = 0) is given by
N4,2=o/N÷~= ~
= (1 +Pl R1)/(PxR2 +R3),
(3)
where .Pl
=fA 01, A~I dcrltOl)÷,=o/f/1 01, A~! da1(01)÷2 = 9o,
R1 = f a
02,A~2 02, A4)2
R3 =fA
02, d~b2
dff2(O2)#2=°/fA
d°'2(02)•2 = 9° '
02,A¢~2 02, A4~2
dff2(O2)'2=9°-°/f
d ° ' 2 ( 0 e ) o z = 9° "
I ,d /102, aO2
Here A01, A02, Ad?l and A¢2 are the spreads in the angles 01, 02, ¢1 and ¢2, and da2(02) is the Klein-Nishina differential cross-section averaged over the polarizations of the second scattered photons of energy k2 and is given by an expression similar to eq. (2) above. 3. Experimental Procedure and Results The experimental arrangement used to measure the ratio N÷~= olN#~=# is shown in fig. 1. Gamma rays from the source S are collimated onto a thin copper scatterer Sc. The gamma rays Compton scattered through an angle 01 are allowed to undergo Compton scattering again through 02 = 90 ° (kept fixed) by a plastic scintillator A coupled to a 6292 Dumount photomultiplier. The second scattered gamma rays are detected by a NaI(TI) crystal B coupled to RCA 6342-A photomultiplier covered with a mu-metal shield to eliminate the effect of the earth's magnetic field. Counter A is fixed at the centre of a circular rail along which counter B can rotate to vary angle ¢2. The distance between counter A and B can be varied to adjust the angular spreads A02 and A¢2. Large values of spreads are necessary to obtain reasonably
COMPTON SCATTERING
269
good counting rates. Both counters were shielded against direct radiation from the source. Counter B was also shielded from the radiation scattered from the copper scatterer. The shielding was symmetrical about the main axis of the setup which coincides with the axis o f A to avoid any false asymmetry in the counting rates. The recoil electron is counted in A, while the Compton scattered photon escapes it and is detected by counter B, and both give rise to a coincidence. This method of measuring coincidences has the obvious advantage of selecting the significant events only and thus reducing the background effects. The coincidences with counter B in different positions corresponding to different values of ~b2 were recorded by a conventional arrangement. The pulses from the two counters were fed to two amplifiers through pre-amplifiers. The amplified pulses were sorted according to their sizes by
Fig. 1. Experimental setup for azimuthal variation of Compton scattering of polarized gamma gamma ray source, S c a thin copper scatterer, A plastic scatterer- detector crystal B - NaI(TI) crystal.
rays. S
differential pulse-height analysers and fed to a coincidence unit. The counts were registered by three sealers, one for recording coincidences and the other two for recording pulses from the two individual counters. To set the channels of the two counters so as to count only the required events, the NaI(T1) counter was set to accept energies corresponding to the second scattered photon and a coincidence spectrum was taken by varying the bias of the plastic counter. The position of the peak in the coincidence spectrum was found to correspond to the energy of the recoil electron in the second scattering. The channels of the platic counter were set to cover full width at half height o f the maximum of the coincidence spectrum. With this setting of the plastic counter, another coincidence spectrum was taken by varying the bias of the NaI(TI) counter, to check the channel settings of the latter. The position of the maximum in the second coincidence spectrum agreed with the channels of NaI(T1) counter. Some of the spectra are shown in fig. 2.
270
M. SINGH et al.
The counts in the three sealers were recorded for five minutes at five different positions of the counter B, gb2 corresponding to 0, 30, 50, 70 and 90 degrees, respectively. The sequence o f observations was so arranged as to minimize the effects of electronic drift. The consistency of the data provided an indirect check on the electronic stability. The coincidence counts were corrected for the background and chance coincidences. The measurements were made with gamma rays of energy 280, I0 9
8
t~
6
tt-
3
\ I
I
I
I
I
I
I
I
10
20
30
0
10
20
0
10
PULSE
,1, 6 ~-
I
I
I
I
ZO
30
40
50
50
60
I\1 60
HEIGHT
(1
b
O
2 1 o o
]o
2o
3o
40
50
PULSE
60
1o
2.0
30
40
HEIGHT
Fig. 2. Some o f the spectra taken with the above arrangement. (a) and (b) are the direct spectra o f 662 keV g a m m a rays t a k e n with t h e NaI(T1) c o u n t e r a n d plastic counter, respectively. (e) Spectrum o f 662 keV 120 ° C o m p t o n scattered radiation t a k e n with N a I ( T l ) counter. (c) a n d (d) are t h e coincidence spectra o f scattered r a d i a t i o n in (e) t a k e n by varying t h e channels o n N a I ( T l ) a n d plastic counters, respectively, t h e c h a n n e l s on the o t h e r being kept fixed at appropriate energy.
271
COMPTON SCATTERING
4.0 3.8 3.6
3.4
3.2
3.C
Z.6
2.'1
•
7
2.2
2x
/
/
2
t /?
t.(
1.t
5
1.~
?
t.( q0
60
60
0
10
~o
60
8o
0
10
40
60
80
0
10
40
60
S0
0
Z0
q0
60
BO
Fig. 3. C o m p a r i s o n o f the experimental and theoretical results. Curves denote the theoretically calculated values f r o m eq. (3) and the points are the experimental values; the errors s h o w n are those due to statistics, the other errors have been discussed in the text. The curves and points 1-9 are for the present measurements and are to be compared with 10 and 11 due to H o o v e r e t al. 3). 1-3 correspond to 01 = 64 °, 02 = 90 ° for /co, respectively, at 280, 662 and 1250 keV and AO= = A~= = 40 ° for all. 4-6 correspond to 0t = 90 °, 0~ = 90 °, k 0 , respectively, at 280, 662 and 1250 keV and AOz = A~b= at 45 °, 55 ° and 55 °, respectively. 7-9 01 = 120 °, 0= = 90 °, ko . . . . 280, 662 and 1250 keV, respectively, and AO~ = A~2 at 35 °, 40 ° and 40 °, respectively. 10 and 11 are due to H o o v e r e t aL for 1250 keV at 01 = 83 °, 0= = 90 ° and 01 = 50 °, 02 = 90 °, respectively. The values o f spreads in these results are not available.
272
M. S~GH et al.
662 and 1250 keV partially polarized by a previous Compton scattering through 0a. Experiments were performed at three different values of 01 corresponding to 64 °, 90 ° and 120 ° . The measured values of N¢~=o/N¢2= ~ are compared with the theoretical values calculated from eq. (3) in fig. 3. The results of Hoover et al. 3) have also been plotted for comparison. The errors indicated are the statistical errors in the counts. The effect of multiple scattering of gamma rays in the copper scatterer was investigated by using scatterers of two different thicknesses. The results agreed within statistics in both the cases indicating that the effects of multiple scattering, if any, are small in our experiment. The spreads AO 1 and A~bI in 01 and ~bI are about 2 ° because a collimated beam of gamma rays is used. This will have negligible effect on p (0.2 %). The spreads A02 and A~b2 are different for various angles and energies and vary from 35 ° to 55 °. These can be ascertained to within +_5 ° from the geometry of the setup and involve an uncertainty of the order o f 10 ~ in the calculated values of N÷:=o/N÷,=~. The consistent agreement of the experimental results with theory at all angles and energies indicates that values of the angular spreads used in the present investigations are correct. The present measurements show a better agreement with the predictions of KleinNishina formula than those of earlier workers 3).
References
1) A. T. Nelms, N.B.S. Circular 542 (1953) 2) R. D. Evans, in Encyclopedia of physics, ed. by S. Flfigge Vol. 34 (Springer, Berlin, 1958) p. 218
3) J. I. Hoover W. R. Faust and C. F. Dohne, Phys. Rev. 85 (1952) 58