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Elastic γ-p scattering at 40 to 70 MeV and polarizability of the proton
Nuclear Physics 18 (1960) 473
491, (~) North-Holland Pubhsh,ng Co, Amsterdam
Not to be reproduced by photopnnt or tmcrofllm without written pertmssmn from the pubhsher
E L A S T I C 7-P S C A T T E R I N G A T 40 T O 70 MeV A N D P O L A R I Z A B I L I T Y OF T H E P R O T O N V I GOLDANSKY, O A K A R P U K H I N , A V K U T S E N K O and V V PAVLOVSKAYA
P N Lebedev Phys,cal Inst,tute, USSR Academy o/ Sc*ences, Moscow Received 23 J a n u a r y 1960 The elastic F - - P scattering at 40 to 70 MeV is studied and the differential cross sections are determined for angles of 45 °, 75 °, 90 °, 120 °, 135 ° a n d 150 ° T h e results t h u s obtained are c o m p a r e d w i t h t h e Raylelgh-Powell scattering t h e o r y t a k i n g a c c o u n t of the a n o m a l o u s magnetic m o m e n t of the p r o t o n as well as the effects of m e s o n cloud p o l a n z a t m n S t u d y of t h e f o r w a r d scattering cross-section calculated t h r o u g h dispersion relations a n d t h e a n g u l a r d i s t r i b u t i o n a t 75 ° to 150 ° obtained from e x p e r i m e n t w a r r a n t s t h e conclusion t h a t electric p o l a r l z a b l h t y of t h e p r o t o n ~E = (94-2) × 10 - u cm s a n d its m a g n e t i c polarizability ~M = (2=V2) × 10 - u cm 8 This value of p r o t o n electric polarizability corresponds to t h e m e a n q u a d r a t i c fluctuation of electric dipole equal to (3 5 - - 5 ) × 10 -14 cm
Abstract:
1. I n t r o d u c t i o n
Elastic scattering of 7~quanta by protons essentially differs from the wellknown Compton effect on electrons. This difference is attributable above all to the anomalous magnetic moment of proton. Scattering of y-quanta by particles with spin ½ and anomalous magnetic moment was considered in the general form by Pauli, and later the theory of this scattering was developed by Powell 1), Gell-Mann and Goldberger 2), Low 3), Klein 4) and Capps 5). In refs. 2-6) additional terms linear with respect to the frequency of y-quanta were taken into account in the amplitude of scattering alongside the Thomson term. Corresponchngly, the cross section of 7--P scattering in the laboratory system is expressed, within an accuracy of the terms of order ~2 (where 7 = hv/Mc2; M is the mass of the proton) by a formula of the Powell type 1) da
(0) = ½r0~{[1-2~ (1-cos 0) + 37' 0- c os 0)"] (1 +cos~O) +r~E(1-cos 0)~+/(0)},
(z)
where r o = e2/Mc 2, and the role of the anomalous magnetic moment is described by the term /(0) = a o + a 1 cos O + a 2 cos20. (2) Here, the coefficients a o, a 1 and a t are the power series functions of the 473
474
v
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GOLDANSKY gt /~l
anomalous part of the magnetic moment of the proton 2a = 1 7896 and equal 9 ~1 =
as :
--
2
3
4~a-- 5 ~ a 2 1
2~+~
2
3
4
2~a3 : 3
--~ -~
1
4
--
34 6,
(4)
:
--3.1
(5)
Obviously, the anomalous magnetic moment leads not only to a general increase in the cross section of scattering but also to a definite change of the form of angular distribution, namely to an increase of scattering into the back hemisphere The effects caused b y the anomaly of magnetic moment b y no means exhaust the peculiarities of the scattering of 7-quanta b y protons Due to the meson cloud surrounding the proton core there arises a possibility of direct interaction between y-quanta and this cloud, which is manifest not only in ~-meson photoproduction but also in scattering Thomson's cross section of 7 - - ~ + scattering is 45 times as great as that of 7 - - P scattering, and the meson effect is bound to tell on the picture of 7 - - P scattering not only near the threshold of photoproduction but even at essentially smaller energies The absorption of y-quanta leads to the polarization of the meson cloud, the induction in the proton of electric and magnetic dipoles and subsequently their secondary radiation Thus there arises Rayleigh scattering which is so well known In optics and the role of which in the Compton effect on the proton was noted b y Capps 5) and dlscussed m detail b y Baldin 7) who studied the influence of the polarizability of the proton on 7 - - P scattering The Rayleigh scattering amphtude is proportional to the square of the frequency of y-quanta, the coefficients of proportmnalaty for electric and magnetic dipole transitions being the constants of electric and magnetic polarlzablhty of the proton characterizing the ability of the meson cloud to be deformed b y the outer electric and magnetic fields, as well as the static distribution of electric charge and magnetic moment We shall not discuss here the possibilities of separation of these different phenomena, but shall merely call attention to the fact that the concept of elastic polarlzabihty used here is not altogether Identical to the one commonly used for neutral particles Though the terms in the scattering amplitude conditioned b y the polarlzablhty of the proton are proportional to the square of frequency, they interfere only with the Thomson term and therefore lead to the terms quadratic with respect to the frequency in the formula of the cross section of scattering Confining ourselves to such quadratic terms in the cross section of 7 - - P scattering we arrive at the following expression for differential angular cross sections of Rayleigh-Powell y - - p scattering in the laboratory system: da d.Q (0) = ½ro2{[1--27(1--cos 0)+3~,~(1--cos 0)2--2AE7 ~](l+cos20) (6) --4AMr 2 cos 0 + r ~ [ ( l - - c o s 0)~+/(0)]},
ELASTIC Y-P SCATTERING
475
where ](0) has been determined above in connection with eq (2) and the dimensionless factors AE and AM are the polarlzablhtles a E and a Mexpressed in units (e2/~c) (?i/Mc) a : 6 8 x 10-4a cm 3. As was shown by Petrunkin e), eq (6) is obtained in the region of small frequencies as an exact corollary of dispersion relations Therefore eq (6), m which two parameters: electric and magnetic polarlzabihtles of the proton, are to be determined, can be used m interpreting the experiments on 7--P scattering in the range of energies appreciably below the photo meson threshold (at 7 << 1). It is clear that at low energies the difference of eq (6) from a Powell type formula restricted to the terms y z - - a difference caused by the polarization of protons - - has a mmor effect, and therefore, despite the relative simphcity of the theoretical interpretation of the results, more exacting demands on the accuracy of the experiments have to be made than in studying the scattering of more energetm ),-quanta This leads us up to the aim of the present paper: ensuring as great accuracy of experiment as possible to obtain reformation on the polarizability of protons from the experiments on proton scattenng of 7-quanta at 40 to 70 MeV
2. Experimental Section The experiments were conducted on the 265 MeV synchrotron of the FIAN at a maximum energy of the brehasstrahlung spectrum equal to 75 MeV, i.e, in a range of energies considerably below the threshold of ~°-meson photoproductlon Since it is possible at such energies to restrict oneself to the detection of the scattered 7-quantum (without the coincidence with the recoil proton) a sufficiently large target was used m our experiments ensuring a rate of counting from 7--P scattering of the order of 0 5 to 1 per mm 2 1 DETECTOR
As high-threshold ( ~ 35 MeV) detectors of 7-quanta conventional telescopes were used consisting of four scintillation counters with a lead convertor after the first one and an alummlum filter before the last (fig 1) Every scintillation counter consisted of a glass vessel, filled with a solution of terphenyl in toluene (3 g per htre) and qbay --33 photomultlpllers The photomultlpliers worked an a specially selected regime (Ephotomult ~ 3--4 kV) ensuring the amphtude of output pulses of 30 to 40 V from the Co6° source for direct connection with the cable R K - - 5 0 Under such conditions we could do without adchtlonal amphflcation of input pulses from the photomultipliers 2 2
ELECTRONICS
The block chagram of radio equipment used m experiments is shown in fig 2 Below are some additional explanahons Two fast coincldence-clrcults of
476
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parallel-type operate on germanium D2B diodes. The first discrirmnator (D1) lowenng the loading of slow circuits had a compensation of the thermal drift of the threshold As the second discriminator (D2) the Park 8) discriminator was used, which made it possible to use only one "triple" in the amphfler
-2 Fig
; ....
~om
1 C l r c m t of telescopes u s e d for d e t e c t i n g s c a t t e r e d y - q u a n t a
~'yom
synchrotron
~
N4
~
113-N4
> to
~e ~esmpe No.2
chamber
Fig
2 Circuit of r a d l o e q u l p m e n t
The formed outputs from both coincidence-circuits were picked by the slow anti-coincidence-circuit excluchng the counting of the charged particles. The possibihty of simultaneous counting for all three channels made convenient the control of separate elements of the circmt The outputs from both coincidence-clrcmts and from the anti-coincidenceclrcmt were fed to the gate-circuits controlled by an accelerator The counting was possible during a period only shghtly greater than the duration of an intensity pulse from the synchrotron. This time-selection considerably reduces ( ~ to 1/50) the background caused by cosmic rays. To ensure simultaneous
ELASTIC ~-p SCATTERING
477
work wlth other instaUatzons (cloud chamber, for instance) provision was made for the prohibitzonsignal preventing the counting when the synchrotron pulses had to be changed as necessary for other installations. 2 3 PLAN
OF
EXPERIMENT
THE
TARGET
The plan of the entire mstallatzon zs represented m fig. 3 A bremsstrahlung beam from the synchrotron passed through a system of eolhmators and hit a hquid-hydrogen target. The effective section of the target was a cylindrical vessel elongated by the axls of the beam (diameter 12 cm, length 30 cm) and having a capacity of some 3.5 htres The double styrofoam walls (PS-6 with a denszty of some 40 mg/cm 3) 0
~Oom
I Fzg 3 Plan of e x p e r i m e n t a l installation
formed a gap of 1 cm in the non-irradiated section of the target. The gap was filled with hquid nitrogen. The total capacity of the target ( ~ 8.5 litres of hquxd hydrogen) at an average vaporization rate of ~ 0.6 htres per hour ensured "~ 8 hours of constant work between refillings of the target. With an 30 cm effective length of the target its irradiated walls were "out of sight" for the detecting telescopes (except for the experiment with the angle of 150 °) which considerably reduced the background from an empty target. The scattered y-quanta were detected simultaneously at two different angles by approximately identical telescopes with lead protection Paraffin shields of 5 to 7 cm ttnck were placed at the entrance to the telescope channel, which reduced the amount of soft electrons and y-quanta in the first counter. 2 4 MONITORS
A thin-walled ionization chamber placed in front of the first colhmator served as an "intermedmry" momtor All measurements were reduced to a definite
478
V
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n u m b e r of counts of this c h a m b e r T h e absolute value of the e n e r g y flux which had passed t h r o u g h the collimator at a g~ven n u m b e r of counts of the m o m t o r as d e t e r m i n e d at regular intervals b y the activation of s t a n d a r d i z e d c a r b o n detectors in the reaction C 12(y, ~)C u, the cross section of which is k n o w n from refs 9, 10) To make the absolute calibration of the m o n i t o r more accurate the d a t a on the a c t l v a t m n of carbon were c o m p a r e d at intervals ~uth the readings of a thick-wall graphite c h a m b e r with known absolute s e n s m v l t y (the qo-called L a x - c h a m b e r ) The values of the flux of y - q u a n t a o b t a i n e d b y the two m e t h o d s coincided with an a c c u r a c y ~ 3 % 2 5 EFFECTIVENE%S OF TELEqCOPES T o obtain the differential angular cross sections from the m e a s u r e d o u t p u t s of 7 - - P scattering it IS necessary to know the energy dependence of the effective detection of scattered ),-quanta b y the telescopeb used In the present work we e m p l o y e d the m e t h o d we h a d apecIally w o r k e d out u) for determining this dependence In region from 35 to 150 MeV The m e t h o d is based on the d e t e c t m n of the C o m p t o n scattering of a bremsstrahlung b e a m on electrones at a small angle (3 °) Since the s p e c t r u m oi bremsstrahlung and the differential cross section of C o m p t o n scattering on electrons are known, the comparison of d a t a at various m a x i m u m energies of bremsstrahlung yields the w a n t e d energy
30 -
-
~20
,.'a lo
-
-
/ 100 150 y - m y enercjy (MeV)
~'lg 4 Energ}
dependenceoftheeffectl~enessofdetectlonofy-quantabythecomcldencetelescope
dependence. T h e results of d e t e r m l m n g the energy dependence of the effecnvehess of y - q u a n t a detection for one of the telescopes is represented in fig 4 alongside the relevant stanstlcal errors The energy threshold of the telescope h a d been calculated b y the sum of average energy losses of electrons on their leaving the c o n v e r t o r The calculated figure ( ~ 35 MeV) coincided with the result of the e x p e r i m e n t It is essential t h a t in the calibration experiments (as well as m the principal m e a s u r e m e n t s ) the e n n r e effective surface of the telesope be Irradiated at once (since in these experiments the telescope was r e m o v e d at a distance of 11 m
ELASTIC ~ - p SCATTERING
479
from a carbon target of 1 5 cm think) Besides, the absolute d e t e r m m a t m n of the bremsstrahlung beam was c o n d u c t e d b y the same m e t h o d as m the principal experiments Therefore varlou~ errors in the absolutlzatmn of the results of the principal and c a h b r a t m n experiments were e h m m a t e d and, In fact, direct comparison of the differential angular croas aectmns of Compton scattermg was drawn an our experiments the known cross sections for electron~ and those to be d e t e r m m e d for proton> 2 6 P R O C E D U R E Or' E X P E R I M E N T
The maxamum energy of the bremsstrahlung spectrum m the principal experiments was 75 MeV The duration of anten~lty pulses (1 e , the hatting of the s y n c h r o t r o n target b y electrons) was stretch~,d up to ~ 300/is whmh corresponded to change~ an the m a x u n u m energy of the brem~strahlung spectrum from 62 to 75 MeV ()bservatlon of the form of " s t r e t c h i n g " (approximately rectangular) waa wsual, through a IIO-4 oscillograph s y n c h r o m z e d with the accelerator The detecting telescopes were placed at angles of 45 °, 75 °, 90 °, 120 °, 135: and 150 '~ to the dlrectmn of the bremsstrahlung beam, m e a s u r e m e n t s at two angle~ being c o n d u c t e d simultaneously Since the effectlvenebs of two telescopes differed somewhat, t h e y were changed at certain mtervalb and the results averaged with respect to b o t h telescopes were used for each angle The seraes of experiments with h y d r o g e n a l t e r n a t e d with the measurements of the b a c k g r o u n d In the experiments wath the e m p t y target the b a c k g r o u n d at all angles averaged some 40 % from the rate of counting m the prmclpal experiments To check the stability of the o p e r a t m n of the m s t a l l a t m n as a whole, control m e a s u r e m e n t s of counting rate from the thick carbon target were c o n d u c t e d daffy u n d e r w o r k m g conchtmns as well as at a m a x i m u m energy of bremsstrahlung equal to 265 MeV 2 7 TREATMENT OF RESULTS
The n u m b e r of counts of the telescope placed at an angle of 0 ° correlated to a c e r t a m n u m b e r of counts of the m o m t o r c h a m b e r (say 1 000 counts) m a y be represented as
v=.f f f atl(E, Em)o~(E'(E)) da (E, O)nodVd.OdE
(7)
Here, a
Etotal Elll
f£ ~1(E, Em)EdE is the b e a m of 7 - q u a n t a averaged b y the irradiated area (per cm 2, for 1 000
480
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I GOLDANSKY et al
counts), ,1(E, Era) the form of bremsstrahlung spectrum; 6*( E ' ) is the effectiveness of detection of y-quanta with the energy E ' (which corresponds to the mltial energy E) scattered at an angle 0°; n o is the number of hydrogen nuclei in cm a, dV is an element of the effective volume of the target and dr2 is the corresponchng sohd angle of "Vislbihty" of the telescope (from the element dV) The integral I o = S S n o d V d . q pract]cally does not depend on the energy of the primary y-quanta( the account of the absorption of y-quanta in the target will be chscussed below) This integral was calculated for every angle, depending on the specific geometry of each experiment To check the calculation the ratio lo/19o ° was compared with the data of an auxiliary experiment in which the number of counts from a "point target" of styrofoam PS-4 (a cube 2 × 2 × 2 cm 3) was compared with the number of counts from the cyhnder of the same material imitating the effective volume of the hquld-hydrogen target
•a
1 - 150 o
....
35
40
45
50
55
60
65
70
75
F i g 5 The p r o d u c t of t h e effectiveness of the detection of a scattered 7 - q u a n t u m b y the distribution function in the p r i m a r y b r e m s s t r a h l u n g s p e c t r u m (for different scattering angles)
Taking the cross section dg/cLQ averaged b y angles and energies out of the lntegrand, we m a y isolate an mtegra] depending on energy Then
do
B
ckO - - a I ~ I o '
(s)
0
036
--
--
--
--
1 144-0 05
1 30-4-0 08
1 484-0 08
1 824-0 07
90 °
120 °
135 °
150 °
14
66
89
107
--
1 214-008
75 °
--127
4 66=[_0 28
(10 4~ cm~/sr)
--
--
--
--
--
- - 0 47 --03 - - 0 06 - - 0 04 - - 0 O1
--141 --14 --07 018
-- 0 0 9 -- 0 0 4
--
--
146
04
10
16
77
126
Total allowances
--54
Bremsstrahlung at large angles
Allowances for by-processes (10 -*4 cm2/sr)
P r o d u c t i o n of Rutherford electron pairs a t large scattering w i t h ! angles w i t h subsequent subsequent radiation radiation
45 °
Angle
Differential a n g u l a r 7p-scattering cross sections (directly from experiment)
TABLE 1 E x p e r i m e n t a l differential cross secttons
+65
+65
+45
+35
+35
+55
Allowances for the a b s o r p t i o n of p r i m a r y a n d registered 7 - q u a n t a In the t a r g e t Aa/a(%)
I
z
1 104-0 05
1 934-0 07
1 564-0 08
1 344-0 08
*4 ~4
x
~4
t~
1 124-0 08
3 4 0 ± 0 28
(10 -s~ cm~/sr)
Differential a n g u l a r 7P cross sections (final q u a n t l t m s )
482
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el al
where
IE = [~m~,, ~I(E ' Emax)o~(E,(E))dE JEth
The bremsstrahlung spectrum of the synchrotron for a thick target is expressed b y Eyges' formula 12) and the dependence o~(E) was represented above in fig 4, it IS evident that the energy of the scattered q u a n t u m E ' = EMc~/ {Mc2+E (1--cos 0)) changes with the scattering angle 0° and consequently the entire integral I E changes as well Fig 5 contains the products of the effectiveness of detection of the scattered v-ray b y the distribution function in the spect ru m of primary bremsstrahlung for various angles of scattering depending on the energy of the Incident v-quanta. It can be seen that the curves are roughly symmetrical and have a m axi m um at ~ 56 MeV and half width averaging about 25 MeV The absolute value of I~ for 90 ° was calculated graphically Corrections for a change In the effectiveness of detection at other angles was also calculated graphically: by the relation of the areas under the relevant curves These corrections equalled from + 5 % for 75 ° and put to --15 4 % for 150 °. The differential cross sections of y - - p scattering for 45 °, 75 °, 90 °, 135 ° and 150 ° thus obtained from the experiment are shown in the second column of table 1 2 8 CORRECTIONS FOR ABSORPTION IN TARGET For absolute determination of the average beam of y-quanta hitting the target, carbon detectors were located in the centre of the target Under working conchtions a certain amount of bremsstrahlung is absorbed in the walls and the hydrogen of the target ( ~ 1.5 °) and some scattered radlatlon is also absorbed depending on the angle, from 2 2% for 90 ° up to 4 70/0 for 150 °. Corrections for the absorption in the paraffin shield and the walls of the telescope were eliminated due to the fact t hat the calibration measurements ~ (E) were also conducted with the absorbers. Corrections for the absorption of the incident, scattered and background v-quanta in the target are represented m the seventh column of table 1 (after the allowances for the contribution of background processess). 2 9 BACKGROUND Since we do not separate the Compton V--P scattering by the detection of coincidences between the scattered y-ray and the recoil proton, it is highly i m po r tan t to consider all posmble sources of background which m a y contribute appreciably to the detection of v-rays by the telescope wath a threshold ~ 35 MeV. At a high threshold the possibility of detection of v-electron Compton scattering at large angles is entirely excluded for the telescope as a whole (m 35 MeV) as well as for each separate counter (a few MeV) The Delbruck scattering and the radlatlon creation of pairs are processes
ELASTIC
•-p
483
SCATTERING
yielding 7 - q u a n t a of high e n e r g y at the angles of interest to us. The cross section of the first process 13) on h y d r o g e n is small (atot -m 10 -34 cm*), and besides, the Delbruck scattering is v e r y strongly directed forward (m 0 -¢) so t h a t we can neglect it already at 45 ° . T h e r e are no accurate theoretical calculations for the radiative p r o d u c t i o n of pairs According to the estimates of F e y n m a n and Gomez cited in ref. 14) for the l a b o r a t o r y angle 50 ° at E~ = 40 MeV, the cross sectlon of this process is approxi m a t e l y equal to t h a t of the Compton 7 - - P scattering %p, while at E~ = 50 MeV is no less t h a n I aTp As a result of a strong energetic and angular (approxim a t e l y ~ 0-4) dependence of the cross sections of this process, its total contrib u t i o n for E~ = 56 MeV and 75 ° Is no more t h a n a b o u t 3 % of 7 - - p - s c a t t e r i n g If account is also t a k e n of the fact t h a t only a small portlon of y-rays e m i t t e d 25
1AE--AM=O
/
r
2AE-O ~ = 1 6 3AE=16 AM-O [
E
8 o x
t
0
:0 iA X E]
Our dato 45"466.¢08~L-[17] 5 0 " 4 8 *-04 [18] [10] 45" 4 8 *~09
i
L ! o
30
6o
90
12o
15o
e- 18o
Fig 6 E x p e r i m e n t a l d a t a of the p r e s e n t p a p e r and refs ]7-]9) on y - - p scattering at the energy of y - q u a n t a a b o u t 60 MeV Between curves 2 and 3 hes the region of values of 7 - - p scattering crosssections compatible w i t h the value of the s u m A E + : / M = 16 (with positive A s and AR)
m the radiative p r o d u c t i o n of pairs possess energ]es exceeding 35 MeV (the threshold of our telescope) it wall be not d]fflcnlt to conclude t h a t the role of this process at all angles under investigation, except 45 °, is neghgably small. The corresponding correct]ons for angles from 75 ° to 150 ° were not introduced, while the d a t a for 45 ° (obviously including not only 7 - - P scattering) were not
484
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gl~ a l
used for further calculahons of the polarizability of the proton because of an indefinite value of the correction to be subtracted from the cross section shown in table 1. Other sources of background are multiple plocesses toccurrlng in the substance up to the target, in the target itself and, finally, between the target and the first counter of the telescope and leading to the penetration into the telescope of v-rays with energies exceeding 35 MeV To estimate the contributmn of these processes the creation of high energy electrons at small angles through Compton scattering and production of pairs in the target and in the substance before the target were calculated. Then a study was made of (a) bremsstrahlung of these electrons at large angles (accordmg to ref. 15)) in the direction of the counters and (b) Rutherford scattenng of these electrons (according to the Mott formula) in the direction of the counters with subsequent bremsstrahlung in forward direction in the substance before the telescope Besides the production of pairs at large angles in the hydrogen of the target Is) with the subsequent brer ~strahlung was considered The results are shown in the third to the sixth columns of table 1. The last column of this table represents the final values of differential angular cross sections of 7--P scattering after allowances made for the background processes and the absorption in the target Fig. 6 represents these final values alongside the data of other experimental work 1~-19) for similar energies of y-rays (m 60 MeV). 2 10 S Y S T E M A T I C E R R O R S
The errors shown in table 1 in determining the cross section of 7--P scattering are merely due to the statistical errors of principal measurements The main possible source of systematic errors: inaccuracy m determlmng the bremsstrahlung flux is ehmmated owing to direct comparison of the Compton scattering cross sections on protons and electrons Nevertheless there remains an error on account of two inaccuracies in determining the product of the effective volume of the target multiplied by the solid angle of the telescope's vlslbiht y in the calibration and principal (integral Io) experiments This error is set down at 1 4 % In comparing the results of the calibration and principal experiments, additional statistical errors arise from determining the beam of v-rays by the number of counts of the momtor in both kinds of experiments and summing the dispersions of m a n y points at the curve of the effectiveness of the telescopes in the detection of y-rays Systematic errors due to possible Inaccuracy m the form of the bremsstrahlung spectrum used are directed oppositely in both calibration and principal experiments and are nearly completely ehmlnated. The total value of possible systematic error in determlmng the cross section of y - - p scattering at angles from 75 ° to 150 ° is estimated as ~ 6 % To return to the statistical errors shown in table 1, we notice that these lie within 3 6 to + 7 2 % for five experimental points; the square root of the sum
ELASTIC 7 - P SCATTERING
485
of dispersions for all five points corresponds to 11 7 %. Thus, in using experimental points for comparison wath calculated theoretical curves, the average statistical error for one point is about 2 4 % and the total error (statistic plus systematic error) about 8 % 3. D i s c u s s i o n of R e s u l t s
The results offered in table 1 and in fig. 6 are to be compared with eq (6) for determining the electric and magnetic polarizablhtles of the proton Even relectlng the obviously overestimated q u a n t i t y of the cross section of 7--P scatterlng at 65 ° we have five experimental quantltles for determining the two parameters of eq. (6) A E and AM It wall be borne in mind, however, that by no means all measurements of angular dlstlabutlon are equally sensitive to the values AE and AM. Indeed, as is clear from eq (6) the cross section of forward scattering (at 0 °) is determined merely by the sum of A E and A M, and not by each of them taken separately: da
(0°) =
½ro2{2[1--2(AE+AM)~]2+5.1372}.
(9)
On the other hand, backward scattering (at 180 ° ) does not depend on each of the quantities AE and AM, but only on their difference: da 4~Q (180°) = ½%2(211--4r+ 12y2--2(AE--AM)r2] + 78 39r2}.
(10)
Our experiments described the ~--p scattering mainly in the back hemisphere at laboratory angles from 75 ° to 150 ° Proceeding from these experimental data only A E m a y be obtained with sufficient certainty, since the cross sections of ~--p scattering at angles close to 90 ° are httle sensitive to A M Relying only on the value da/dD (90 °) : (1 104-0 05)× 10-a2 cm2/sr we obtain A E ----- 164-5 8 Dispersion relations m a y be used as an adchtIonal source of information enabling us to take into account the forward V--p scattelang which was not measured in the experiment and thereby to make the value A E more accurate as well as to estimate the magnetic polarizability A M As is shown in ref 2o) the cross sections of forward 7--P scattering (da/d.(2(0°)) at energies below the photomeson threshold are entirely determined by the experimental total cross section of z-meson photoproductlon when acted upon by non-polarized ~,-quanta Only at higher energies is it necessary for the calculation of da/cLQ(0°) to know separately the meson photo-production cross sections for ~,-quanta polarized parallel and anti-parallel to the spin of the proton
486
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Using the relations given b y Clm a n d Stroffohni 20) it is easy to show t h a t
da
(°°) =
I ~y~ e2
4~ 2 ~
J0
y'2
~,2
dy
y2 Mcf°° ~(y,)_~ (y,) dy,]2 +~i~
c 2 ~ M~2
4:~2 h J0
y,(y,2_y~)
(11)
[%~(y) _ o 2(~,)], where %(y) and aa(y ) are the total cross sections of meson p h o t o - p r o d u c t i o n on protons for ),-quanta with the l a b o r a t o r y energy ~, polarized parallel (%) and anti-parallel (aa) to the spin of protons; the sum a p ( y ) + a a ( 7 ) -~ at(y) is the total cross section of p h o t o - p r o d u c t i o n for a non-polarized b e a m of y-quanta. Below the threshold of meson p h o t o - p r o d u c t i o n the last t e r m is equal to 0, and hence, with an a c c u r a c y to the t e r m s of order ~,z,
(0°)=r0* 1 - 2;~ ~
e~ 30
r'~-y ~
r2"
Comparing (12) and (9) (bearing in m i n d t h a t b y the v e r y meaning of polanzab l h t y It is d e t e r m i n e d for zero energy q u a n t a ) and changing over from A s and A M to a s and ~M, we obtain
o~,~+~M - 2--2 Mc3o ~ -
dr
(13)
Obviously, since a a and :¢M are positive, eq (13) characterizes the u p p e r limit of the values of each of the two polarlzablhtles of the proton. Using the latest d a t a on n-meson p h o t o - p r o d u c t i o n , given for ~± in ref. 21) and for ~o in refs 22,23) (see fig. 7), we o b t a i n a E + ~ M ~ 11 × 10 -aa cm a, i.e., A E + A M ~- 16 Since eq. (13) is o b t a i n e d from the most general properties o* the scattering m a t r i x there are no grounds to question it in a n y degree at all T h e r e f o r e if eq (6) IS accurate, I e , the t h e o r y of Raylelgh-Powell scattering is applicable with sufficient a c c u r a c y a n d there is no need to take account of higher terms in the f r e q u e n c y of the ~,-quanta, xt m a y easily be established within what hmits the cross sections of ~ - - p scattering should he at a n y angles I n a s m u c h as A E a n d A Mare positive a n d the sum A E + A M ---- 16, these limits he within the curves according to eq (6) at A E ~ - 0 , A M = 16 and A ~ = 16, AM----0 As is clear from fig. 6, in which the region of the values da/d.Q(O) compatible with A E + A M ~ 16 lies between curves 2 and 3, all our e x p e r i m e n t a l d a t a for 75°--150 ° are to be found within this region, whereas the values of the cross
ELASTIC
~-p
487
SCATTERING
sections of 7 - - p scattering into the b a c k hemisphere o b t a i n e d in refs 17--19) seem somewhat u n d e r e s t i m a t e d . Regarding the value A~+AM : 16 as given and calculating the value As offering the best a g r e e m e n t with our results b y the m e t h o d of the least squares we obtain A E : 13-+-3 and A M : 3:~3, the sum of the weighted squares of errors being D : 1.8 X 10 -ee cm4/sr 2. Thus, we come to the conclusion t h a t o~E : (9::t:2)× 10 -43 cm ~ and o~M = ( 2 ~ 2 ) × 10 -4a cm 3.
o
o
I 40O
30(2
20C
100 :2 0
01
012
02,
014
or5
06
017
I Oe
09
10
F i g 7 D a t a on t o t a l p h o t o - p r o d u c t i o n cross s e c t i o n s of ~+ a n d n o m e s o n s on p r o t o n s us e d for d e t e r m i n i n g t h e s u m of electric a n d m a g n e t i c p o l a r i z a b l h t i e s of t h e p r o t o n
Thus, the magnetic p o l a n z a b l l i t y of the p r o t o n is far smaller t h a n the electric one. The d e t e r m i n a t i o n of the former is more sensitive to the possible c o n t r i b u t i o n to the cross section of 7 - - p s c a t t e n n g of the terms proportional to the high powers of the f r e q u e n c y of v - q u a n t a (over y2) and therefore a detailed analysis of the role of these terms is of special interest for determining AM more accurately. As for the electric polarizability it 1s clear t h a t not only the sum As+AM is in agreement with the d a t a of our experiments, b u t the o p t i m u m value A ~ = 1 3 ~ 3 , also coincides within errors with the d a t a o b t a i n e d above from the cross section of scattering at 90 ° (A~ = 1 6 ~ 5 . 8 ) . Direct comparison of the results of the experiment with the curve based on eq. (2) w i t h o u t allowances for the polarizability the p r o t o n yields a far larger sum of the weighted squares of errors t h a n for eq. (6): D = 10.3 × 10 -6e cm4/sr 2. The best agreement wath eq. (2) is a t t a i n e d b y increasing our e x p e r i m e n t a l cross sections b y 8 %, which, however, hes on the margin of possible systematic errors.
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T h e question of the electric polarizability of nucleons has r e c e n t l y been wadely discussed as a result of the d e v e l o p m e n t of theoretical concepts 24, 25) on the role of the polarizability of n e u t r o n s in their electric s c a t t e n n g at small angles in the Coulomb field of h e a v y nuclei The value of electric polarizability of the n e u t r o n c o m p u t e d b y A l e x a n d r o v 28) from an analysis of his e x p e r i m e n t on n e u t r o n scattering ~ = (84-3 5) × 10 -41 cm 3 certainly contradicts all d a t a on ?-rays scattering a n d n-meson p h o t o - p r o d u c t i o n , which was a l r e a d y n o t e d in theoretical papers 7, 27-31) and is now again confirmed b y our experiments The latest analysis of new experiments on n e u t r o n s c a t t e n n g 29) led to a reduction in the u p p e r value of ~E namely, 0 < (xB)n < 2 2 × 10 -41 cm 3 but yaelded no more definite results. I n a s m u c h as a s ~ 10 -42 cm 3, n e u t r o n experiments will in general not enable us q u a n t i t a t i v e l y to estabhsh the c o n t r i b u t i o n of electric p o l a r i z a b i h t y T h e r e f o r e the a v e n u e to a s t u d y of the electric a n d magnetic polanzablhties of the nucleon, the properties conditioned b y changes in the s t r u c t u r e of the meson cloud in the nuclei, lies in the investigation of n-meson p h o t o - p r o d u c t i o n and nucleon C o m p t o n effect R o u g h estimates of electric p o l a r i z a b l h t y of a n e u t r o n on the basis of meson theories are of order of (e2[2/li2c2)(l~/lzc)3= 1 . 6 × 1 0 -42 c m 327'29) where /2/1~c = 0.08 A result close to this estimate: (x~)n ~-- (1.6 to 1 8) × 10 -42 cm 3 was o b t a i n e d 27) b y estimating the polarizability of the meson cloud in the nucleon with the help of the Chew-theory for the Gauss and exponential formfunctions at the cutting p a r a m e t e r 5.6 ~c/?i. Analysing the d a t a on n-meson p h o t o - p r o d u c t i o n and ~,--p scattering, B a l d m 7) o b t a i n e d the q u a n t i t y (0cE)p = 4 × 10 -43 cm 3 as the lower limit of nucleon electric p o l a n z a b l h t y (under the assumption of only one-meson exchange) The u p p e r limit (a~)p is o b t a i n e d in ref. 7) on the basis of the p r o x i m i t y of the cross section of y - - p scattering at 90 ° to T h o m s o n ' s (½ro2) and is set down at 1.4 × 10 -43 cm 3. F r o m the d a t a on n-meson p h o t o - p r o d u c t i o n a close estimate is o b t a m e d for the n e u t r o n in ref. 30): ( ~ ) n ~ 2 × 10 -42 cmz I t should be borne in mind t h a t since the cross section a - of the process 7 + n - - > r ~ - + p n e a r the threshold exceeds the cross section a + of the process r + p --> ~ + + n a n d the c o n t r i b u t i o n of the near-threshold region to the chsper sion integral (13) is considerable, the electric polarizability of the n e u t r o n should exceed the corresponding q u a n t i t y for the p r o t o n b y 20 to 30 % (refs 7b,3o)). As is clear from the calculations in which eq (13) was used, the u p p e r limit for the electric p o l a r l z a b l h t y of the p r o t o n m a y be lowered to (~E)p = 1.1 × 10 -42 cm 3. In the final conclusion of our p a p e r concerning the q u a n t i t y (aE)p we additionally use the calculated u p p e r value of the sum (~s+x~t)p = 1.1 × 10 -42 cmS; even the direct result of the e x p e r i m e n t s on the whole confirms the abovem e n t i o n e d theoretical estimates of (as)p. In conclusion we shall consider the problem of the m e a n q u a d r a t i c fluctuation
ELASTIC ~/-p SCATTERING
489
of the displacement (allied with ~E) of the centre of electric charge distribution in the polarized proton with respect to the centre of its gravity According to refs. 7b, 3o) thls quantity V/O is connected with the electric polarlzablhty of the proton through the common relation
%/~ •
OCEe2 hC'
where A E is the difference of energies between the ground and virtual polarized states of the proton Since the polarlzatxon is conditioned by the excitation of a meson cloud or the origin of resonance isobaric state it is worth while to accept A E in the range from M c 2 to 2 M c 2. At aE : 9 x 10-4a cm 3 we obtain from eq (14) for the mean quadratic fluctuation of the length of the proton electric dipole V'~ = (3.5 to 5) × 10-14 cm It is certainly of interest to develop a more detailed theory of the magnetic polarizabihty of the proton to connect ~E and ~Mwith the contribution of various mechamsms of ~-meson photo-productlon, to obtain the relevant theoretical h i l t s for aM and compare them with experiment as well as to compare the fluctuations of the length of electric and magnetic dipoles
4. C o n c l u s i o n s 1) Elastic scattering of 7-rays with energies from 40 to 70 MeV (the average being 56 MeV) by protons has been studied The new method of determmlng the effectiveness of 7-rays detection has made it possible to draw direct comparison of the cross sections of Compton scattering on protons and electrons and obtain the cross sections of ~,--p scattermg for 75 °, 90 °, 120 °, 135 ° and 150 ° in the laboratory system within an average accuracy of 4-8 % (with allowances for statistical as well as systematic errors) 2) The data thus obtained are compared with the theory of Rayleigh-Powell scattering of y-rays by particles possessing anomalous magnetic moments and electric and magnetic polarlzablhties The scattering cross section at 90 ° corresponds to the electric polarizablhty aE---- (114-4)× 10-4a cm a 3) Alongside experimental data, the cross section of forward 7--P scattering (at 0 °) was drawn upon for comparing with the theory. This cross section IS determined by the sum of electric (~E) and magnetic (aM) polarizabmhtles of the proton ~E+~M -- 2 ~ M c J o
73
4) On the basis of experimental data on 7--P scattering from 75 ° to 150 ° and the calculated cross section for 0 °, the electric polarlzablhty of the proton is
49(1
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GOLDANSKY
d e t e r m i n e d and the magnetic one e s t i m a t e d ~
=
(9±2) x lo-~ cmL
~
=
( 2 ~ : 2 ) x 1 0 - ~ cm~
5) The electric polarizability thus found corresponds to the mean q u a d r a t i c t l u c t u a t m n ot the length of the p r o t o n electric d~pole ~/N = (3 5 to 5) :/. 10 - ~ cm The authors are greatly i n d e b t e d to R G Vasllkov, S P Balatyev, Ye V Mmarlk and A Samuflhn for their assistance in conducting the experiments and G I v a n o v for his active p a m c l p a t l o n in the t r e a t m e n t of the results o b t a i n e d \Ve are glad to t h a n k the entire m a i n t e n a n c e staff of the 265 MeV s y n c h r o t r o n of the F I A N for ensuring m a n y hours' e x p e r i m e n t a t i o n for us and express our sincere acknowledgements to A M. Balchn and V N Grlbov for their participation m discussing the results Note added ~n proof. The general expression for the a m p l i t u d e of y - p scattering (in CMS) is of the form T = Rl(ee')+R2(ss')-l-~Ra(~[e'e])+~R4(a[s's])
+ ~Rs{(~k)(s' e ) - (ok')(se')}+, R~{ (~k')(~' e ) - (ok)(e' ~)} g w e n b y Rltu~ 32) and Lapldus aa) If we take, as in refb 2-s), R I = 1, R 2 = R 5 = 0 , R 3=1y, R 4 = ly,~2, R 6 = ½72 (all R, values are in e"/ffc 2 units) we obtain formula (1) for crosssections To obtain eq (6) we h a v e to take R 1 = 1 - - A ~ v 2, R 2 = At, yz As was shown b y Arlstov a4)
=
3
~
\~l
where r e = 0 8. 10 -t~ cm is the electric radius of the p r o t o n and
A*~ = ~*~ ~c ~*E being the electric polarizability of the p r o t o n in c o n v e n t i o n a l sense (1 e , dipole m o m e n t p = ~*~E). References 1) J I, Pop, ell, Ph:,s Rev 75 (1949) 32 2) M Gell-Mann and M Goldberger, Phys Rev 96 (1954)1433 3) I: E Lo~, Ph)~ Rev 96 (1954) I423 4) A Klein, Phys Rev 99 (1955) 998 5) R Capps, Phys Rev 106 (1957) 1031 6) V A Petrunkm (private commumcatlon)
ELASTIC
~]-p
SCATTERING
491
7) A M Baldm, a) Report at tile Conference on Elementary Particles at Padua-Venice (1957), b) Nuclear Physics 18 (1960) 8) E C Park, J Scl Instr 33 (1956)257 9) V~~ Baffler, \V George and D Reagan, Phys Rev 58 (1955) 73 10) P S Baranov, Thesis, P N Lebedev Phvsmal Institute (1955) 11) V I Goldanskv, O A Karpukhm and V V Pa~lovska,~a, Instruments and Techmque of Experiment 3 (1960) 23 12) L Esgeb, P h \ s Rex 81 (1951) ~82 13) A I \khmzer and V B Berebtetskv, Quantum Electrodynanncs, ~econd edttton (Flzmatlzdat, lq59) 14) L G Hxman, MIT Ph D The~l~ (1959) 151 P V ( Hough, Ph~s Rev 74 (1948) 80 1~) R ( Miller, Ph.~s Re~ 95 (1954) 796 17) C Oxlex and V L Telegdl, Phvs Re~ 100 (1955)435 18) C Oxlev, Phys Rev 110 (1958) 733 19) G Pugh, R Gomez, D Frlsch and G Janes, Phys Rev 105 (1957) q82 20) M Cml and R Stroffohnl, Nuclear Physics 5 (1958) 684 21) G Bernardlm, Report at the I X t h Conference on High Energy Physics, Klev (1959) :~2) R G Vassflkov, t3 ]3 Govorkov and V [ Goldansky, J E T P 3 7 (1959)11, Nuclear Phy~ms 12 (195q) 337 23) K Berkelman and J \Vaggoner, Phys Rev 117 (1960) 1364 241 Yu A Mexandrov and I Bondarenko, J E T P 31 (1956) 726 25) V S Barashenkov, I P Stakhanov and Yu A Alexandrov, J E T P 32 (1957) 1546 2b) Yu A Alexandrov, J E T P 32 (1957) 561, 33 (195"/) 294 27) V S Barashenkov and ]3 M Barbashov, Nuclear Physms 9 (1958) 426 '28) 13 I Blokhlntsev, V S Barashenkov and ]3 M Barbashov, Usp Flz Nauk 68 (1959) 417 29) R M Thaler, Phys Rev 114 (1959) 827 30) G Brmt and M L Rustgl, P h ~ Rev 114 (1959)830 311 L L Fold~, Phy~ Rev Letter~, 3 (1959)105 32) V I R~tus, J E T P 33 (19571 1264 33) L I Lapldu~, J E T P 34 (1958) 922 34) Yu Arl~to~ (private commumcat~on)
491, (~) North-Holland Pubhsh,ng Co, Amsterdam
Not to be reproduced by photopnnt or tmcrofllm without written pertmssmn from the pubhsher
E L A S T I C 7-P S C A T T E R I N G A T 40 T O 70 MeV A N D P O L A R I Z A B I L I T Y OF T H E P R O T O N V I GOLDANSKY, O A K A R P U K H I N , A V K U T S E N K O and V V PAVLOVSKAYA
P N Lebedev Phys,cal Inst,tute, USSR Academy o/ Sc*ences, Moscow Received 23 J a n u a r y 1960 The elastic F - - P scattering at 40 to 70 MeV is studied and the differential cross sections are determined for angles of 45 °, 75 °, 90 °, 120 °, 135 ° a n d 150 ° T h e results t h u s obtained are c o m p a r e d w i t h t h e Raylelgh-Powell scattering t h e o r y t a k i n g a c c o u n t of the a n o m a l o u s magnetic m o m e n t of the p r o t o n as well as the effects of m e s o n cloud p o l a n z a t m n S t u d y of t h e f o r w a r d scattering cross-section calculated t h r o u g h dispersion relations a n d t h e a n g u l a r d i s t r i b u t i o n a t 75 ° to 150 ° obtained from e x p e r i m e n t w a r r a n t s t h e conclusion t h a t electric p o l a r l z a b l h t y of t h e p r o t o n ~E = (94-2) × 10 - u cm s a n d its m a g n e t i c polarizability ~M = (2=V2) × 10 - u cm 8 This value of p r o t o n electric polarizability corresponds to t h e m e a n q u a d r a t i c fluctuation of electric dipole equal to (3 5 - - 5 ) × 10 -14 cm
Abstract:
1. I n t r o d u c t i o n
Elastic scattering of 7~quanta by protons essentially differs from the wellknown Compton effect on electrons. This difference is attributable above all to the anomalous magnetic moment of proton. Scattering of y-quanta by particles with spin ½ and anomalous magnetic moment was considered in the general form by Pauli, and later the theory of this scattering was developed by Powell 1), Gell-Mann and Goldberger 2), Low 3), Klein 4) and Capps 5). In refs. 2-6) additional terms linear with respect to the frequency of y-quanta were taken into account in the amplitude of scattering alongside the Thomson term. Corresponchngly, the cross section of 7--P scattering in the laboratory system is expressed, within an accuracy of the terms of order ~2 (where 7 = hv/Mc2; M is the mass of the proton) by a formula of the Powell type 1) da
(0) = ½r0~{[1-2~ (1-cos 0) + 37' 0- c os 0)"] (1 +cos~O) +r~E(1-cos 0)~+/(0)},
(z)
where r o = e2/Mc 2, and the role of the anomalous magnetic moment is described by the term /(0) = a o + a 1 cos O + a 2 cos20. (2) Here, the coefficients a o, a 1 and a t are the power series functions of the 473
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anomalous part of the magnetic moment of the proton 2a = 1 7896 and equal 9 ~1 =
as :
--
2
3
4~a-- 5 ~ a 2 1
2~+~
2
3
4
2~a3 : 3
--~ -~
1
4
--
34 6,
(4)
:
--3.1
(5)
Obviously, the anomalous magnetic moment leads not only to a general increase in the cross section of scattering but also to a definite change of the form of angular distribution, namely to an increase of scattering into the back hemisphere The effects caused b y the anomaly of magnetic moment b y no means exhaust the peculiarities of the scattering of 7-quanta b y protons Due to the meson cloud surrounding the proton core there arises a possibility of direct interaction between y-quanta and this cloud, which is manifest not only in ~-meson photoproduction but also in scattering Thomson's cross section of 7 - - ~ + scattering is 45 times as great as that of 7 - - P scattering, and the meson effect is bound to tell on the picture of 7 - - P scattering not only near the threshold of photoproduction but even at essentially smaller energies The absorption of y-quanta leads to the polarization of the meson cloud, the induction in the proton of electric and magnetic dipoles and subsequently their secondary radiation Thus there arises Rayleigh scattering which is so well known In optics and the role of which in the Compton effect on the proton was noted b y Capps 5) and dlscussed m detail b y Baldin 7) who studied the influence of the polarizability of the proton on 7 - - P scattering The Rayleigh scattering amphtude is proportional to the square of the frequency of y-quanta, the coefficients of proportmnalaty for electric and magnetic dipole transitions being the constants of electric and magnetic polarlzablhty of the proton characterizing the ability of the meson cloud to be deformed b y the outer electric and magnetic fields, as well as the static distribution of electric charge and magnetic moment We shall not discuss here the possibilities of separation of these different phenomena, but shall merely call attention to the fact that the concept of elastic polarlzabihty used here is not altogether Identical to the one commonly used for neutral particles Though the terms in the scattering amplitude conditioned b y the polarlzablhty of the proton are proportional to the square of frequency, they interfere only with the Thomson term and therefore lead to the terms quadratic with respect to the frequency in the formula of the cross section of scattering Confining ourselves to such quadratic terms in the cross section of 7 - - P scattering we arrive at the following expression for differential angular cross sections of Rayleigh-Powell y - - p scattering in the laboratory system: da d.Q (0) = ½ro2{[1--27(1--cos 0)+3~,~(1--cos 0)2--2AE7 ~](l+cos20) (6) --4AMr 2 cos 0 + r ~ [ ( l - - c o s 0)~+/(0)]},
ELASTIC Y-P SCATTERING
475
where ](0) has been determined above in connection with eq (2) and the dimensionless factors AE and AM are the polarlzablhtles a E and a Mexpressed in units (e2/~c) (?i/Mc) a : 6 8 x 10-4a cm 3. As was shown by Petrunkin e), eq (6) is obtained in the region of small frequencies as an exact corollary of dispersion relations Therefore eq (6), m which two parameters: electric and magnetic polarlzabihtles of the proton, are to be determined, can be used m interpreting the experiments on 7--P scattering in the range of energies appreciably below the photo meson threshold (at 7 << 1). It is clear that at low energies the difference of eq (6) from a Powell type formula restricted to the terms y z - - a difference caused by the polarization of protons - - has a mmor effect, and therefore, despite the relative simphcity of the theoretical interpretation of the results, more exacting demands on the accuracy of the experiments have to be made than in studying the scattering of more energetm ),-quanta This leads us up to the aim of the present paper: ensuring as great accuracy of experiment as possible to obtain reformation on the polarizability of protons from the experiments on proton scattenng of 7-quanta at 40 to 70 MeV
2. Experimental Section The experiments were conducted on the 265 MeV synchrotron of the FIAN at a maximum energy of the brehasstrahlung spectrum equal to 75 MeV, i.e, in a range of energies considerably below the threshold of ~°-meson photoproductlon Since it is possible at such energies to restrict oneself to the detection of the scattered 7-quantum (without the coincidence with the recoil proton) a sufficiently large target was used m our experiments ensuring a rate of counting from 7--P scattering of the order of 0 5 to 1 per mm 2 1 DETECTOR
As high-threshold ( ~ 35 MeV) detectors of 7-quanta conventional telescopes were used consisting of four scintillation counters with a lead convertor after the first one and an alummlum filter before the last (fig 1) Every scintillation counter consisted of a glass vessel, filled with a solution of terphenyl in toluene (3 g per htre) and qbay --33 photomultlpllers The photomultlpliers worked an a specially selected regime (Ephotomult ~ 3--4 kV) ensuring the amphtude of output pulses of 30 to 40 V from the Co6° source for direct connection with the cable R K - - 5 0 Under such conditions we could do without adchtlonal amphflcation of input pulses from the photomultipliers 2 2
ELECTRONICS
The block chagram of radio equipment used m experiments is shown in fig 2 Below are some additional explanahons Two fast coincldence-clrcults of
476
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parallel-type operate on germanium D2B diodes. The first discrirmnator (D1) lowenng the loading of slow circuits had a compensation of the thermal drift of the threshold As the second discriminator (D2) the Park 8) discriminator was used, which made it possible to use only one "triple" in the amphfler
-2 Fig
; ....
~om
1 C l r c m t of telescopes u s e d for d e t e c t i n g s c a t t e r e d y - q u a n t a
~'yom
synchrotron
~
N4
~
113-N4
> to
~e ~esmpe No.2
chamber
Fig
2 Circuit of r a d l o e q u l p m e n t
The formed outputs from both coincidence-circuits were picked by the slow anti-coincidence-circuit excluchng the counting of the charged particles. The possibihty of simultaneous counting for all three channels made convenient the control of separate elements of the circmt The outputs from both coincidence-clrcmts and from the anti-coincidenceclrcmt were fed to the gate-circuits controlled by an accelerator The counting was possible during a period only shghtly greater than the duration of an intensity pulse from the synchrotron. This time-selection considerably reduces ( ~ to 1/50) the background caused by cosmic rays. To ensure simultaneous
ELASTIC ~-p SCATTERING
477
work wlth other instaUatzons (cloud chamber, for instance) provision was made for the prohibitzonsignal preventing the counting when the synchrotron pulses had to be changed as necessary for other installations. 2 3 PLAN
OF
EXPERIMENT
THE
TARGET
The plan of the entire mstallatzon zs represented m fig. 3 A bremsstrahlung beam from the synchrotron passed through a system of eolhmators and hit a hquid-hydrogen target. The effective section of the target was a cylindrical vessel elongated by the axls of the beam (diameter 12 cm, length 30 cm) and having a capacity of some 3.5 htres The double styrofoam walls (PS-6 with a denszty of some 40 mg/cm 3) 0
~Oom
I Fzg 3 Plan of e x p e r i m e n t a l installation
formed a gap of 1 cm in the non-irradiated section of the target. The gap was filled with hquid nitrogen. The total capacity of the target ( ~ 8.5 litres of hquxd hydrogen) at an average vaporization rate of ~ 0.6 htres per hour ensured "~ 8 hours of constant work between refillings of the target. With an 30 cm effective length of the target its irradiated walls were "out of sight" for the detecting telescopes (except for the experiment with the angle of 150 °) which considerably reduced the background from an empty target. The scattered y-quanta were detected simultaneously at two different angles by approximately identical telescopes with lead protection Paraffin shields of 5 to 7 cm ttnck were placed at the entrance to the telescope channel, which reduced the amount of soft electrons and y-quanta in the first counter. 2 4 MONITORS
A thin-walled ionization chamber placed in front of the first colhmator served as an "intermedmry" momtor All measurements were reduced to a definite
478
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n u m b e r of counts of this c h a m b e r T h e absolute value of the e n e r g y flux which had passed t h r o u g h the collimator at a g~ven n u m b e r of counts of the m o m t o r as d e t e r m i n e d at regular intervals b y the activation of s t a n d a r d i z e d c a r b o n detectors in the reaction C 12(y, ~)C u, the cross section of which is k n o w n from refs 9, 10) To make the absolute calibration of the m o n i t o r more accurate the d a t a on the a c t l v a t m n of carbon were c o m p a r e d at intervals ~uth the readings of a thick-wall graphite c h a m b e r with known absolute s e n s m v l t y (the qo-called L a x - c h a m b e r ) The values of the flux of y - q u a n t a o b t a i n e d b y the two m e t h o d s coincided with an a c c u r a c y ~ 3 % 2 5 EFFECTIVENE%S OF TELEqCOPES T o obtain the differential angular cross sections from the m e a s u r e d o u t p u t s of 7 - - P scattering it IS necessary to know the energy dependence of the effective detection of scattered ),-quanta b y the telescopeb used In the present work we e m p l o y e d the m e t h o d we h a d apecIally w o r k e d out u) for determining this dependence In region from 35 to 150 MeV The m e t h o d is based on the d e t e c t m n of the C o m p t o n scattering of a bremsstrahlung b e a m on electrones at a small angle (3 °) Since the s p e c t r u m oi bremsstrahlung and the differential cross section of C o m p t o n scattering on electrons are known, the comparison of d a t a at various m a x i m u m energies of bremsstrahlung yields the w a n t e d energy
30 -
-
~20
,.'a lo
-
-
/ 100 150 y - m y enercjy (MeV)
~'lg 4 Energ}
dependenceoftheeffectl~enessofdetectlonofy-quantabythecomcldencetelescope
dependence. T h e results of d e t e r m l m n g the energy dependence of the effecnvehess of y - q u a n t a detection for one of the telescopes is represented in fig 4 alongside the relevant stanstlcal errors The energy threshold of the telescope h a d been calculated b y the sum of average energy losses of electrons on their leaving the c o n v e r t o r The calculated figure ( ~ 35 MeV) coincided with the result of the e x p e r i m e n t It is essential t h a t in the calibration experiments (as well as m the principal m e a s u r e m e n t s ) the e n n r e effective surface of the telesope be Irradiated at once (since in these experiments the telescope was r e m o v e d at a distance of 11 m
ELASTIC ~ - p SCATTERING
479
from a carbon target of 1 5 cm think) Besides, the absolute d e t e r m m a t m n of the bremsstrahlung beam was c o n d u c t e d b y the same m e t h o d as m the principal experiments Therefore varlou~ errors in the absolutlzatmn of the results of the principal and c a h b r a t m n experiments were e h m m a t e d and, In fact, direct comparison of the differential angular croas aectmns of Compton scattermg was drawn an our experiments the known cross sections for electron~ and those to be d e t e r m m e d for proton> 2 6 P R O C E D U R E Or' E X P E R I M E N T
The maxamum energy of the bremsstrahlung spectrum m the principal experiments was 75 MeV The duration of anten~lty pulses (1 e , the hatting of the s y n c h r o t r o n target b y electrons) was stretch~,d up to ~ 300/is whmh corresponded to change~ an the m a x u n u m energy of the brem~strahlung spectrum from 62 to 75 MeV ()bservatlon of the form of " s t r e t c h i n g " (approximately rectangular) waa wsual, through a IIO-4 oscillograph s y n c h r o m z e d with the accelerator The detecting telescopes were placed at angles of 45 °, 75 °, 90 °, 120 °, 135: and 150 '~ to the dlrectmn of the bremsstrahlung beam, m e a s u r e m e n t s at two angle~ being c o n d u c t e d simultaneously Since the effectlvenebs of two telescopes differed somewhat, t h e y were changed at certain mtervalb and the results averaged with respect to b o t h telescopes were used for each angle The seraes of experiments with h y d r o g e n a l t e r n a t e d with the measurements of the b a c k g r o u n d In the experiments wath the e m p t y target the b a c k g r o u n d at all angles averaged some 40 % from the rate of counting m the prmclpal experiments To check the stability of the o p e r a t m n of the m s t a l l a t m n as a whole, control m e a s u r e m e n t s of counting rate from the thick carbon target were c o n d u c t e d daffy u n d e r w o r k m g conchtmns as well as at a m a x i m u m energy of bremsstrahlung equal to 265 MeV 2 7 TREATMENT OF RESULTS
The n u m b e r of counts of the telescope placed at an angle of 0 ° correlated to a c e r t a m n u m b e r of counts of the m o m t o r c h a m b e r (say 1 000 counts) m a y be represented as
v=.f f f atl(E, Em)o~(E'(E)) da (E, O)nodVd.OdE
(7)
Here, a
Etotal Elll
f£ ~1(E, Em)EdE is the b e a m of 7 - q u a n t a averaged b y the irradiated area (per cm 2, for 1 000
480
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I GOLDANSKY et al
counts), ,1(E, Era) the form of bremsstrahlung spectrum; 6*( E ' ) is the effectiveness of detection of y-quanta with the energy E ' (which corresponds to the mltial energy E) scattered at an angle 0°; n o is the number of hydrogen nuclei in cm a, dV is an element of the effective volume of the target and dr2 is the corresponchng sohd angle of "Vislbihty" of the telescope (from the element dV) The integral I o = S S n o d V d . q pract]cally does not depend on the energy of the primary y-quanta( the account of the absorption of y-quanta in the target will be chscussed below) This integral was calculated for every angle, depending on the specific geometry of each experiment To check the calculation the ratio lo/19o ° was compared with the data of an auxiliary experiment in which the number of counts from a "point target" of styrofoam PS-4 (a cube 2 × 2 × 2 cm 3) was compared with the number of counts from the cyhnder of the same material imitating the effective volume of the hquld-hydrogen target
•a
1 - 150 o
....
35
40
45
50
55
60
65
70
75
F i g 5 The p r o d u c t of t h e effectiveness of the detection of a scattered 7 - q u a n t u m b y the distribution function in the p r i m a r y b r e m s s t r a h l u n g s p e c t r u m (for different scattering angles)
Taking the cross section dg/cLQ averaged b y angles and energies out of the lntegrand, we m a y isolate an mtegra] depending on energy Then
do
B
ckO - - a I ~ I o '
(s)
0
036
--
--
--
--
1 144-0 05
1 30-4-0 08
1 484-0 08
1 824-0 07
90 °
120 °
135 °
150 °
14
66
89
107
--
1 214-008
75 °
--127
4 66=[_0 28
(10 4~ cm~/sr)
--
--
--
--
--
- - 0 47 --03 - - 0 06 - - 0 04 - - 0 O1
--141 --14 --07 018
-- 0 0 9 -- 0 0 4
--
--
146
04
10
16
77
126
Total allowances
--54
Bremsstrahlung at large angles
Allowances for by-processes (10 -*4 cm2/sr)
P r o d u c t i o n of Rutherford electron pairs a t large scattering w i t h ! angles w i t h subsequent subsequent radiation radiation
45 °
Angle
Differential a n g u l a r 7p-scattering cross sections (directly from experiment)
TABLE 1 E x p e r i m e n t a l differential cross secttons
+65
+65
+45
+35
+35
+55
Allowances for the a b s o r p t i o n of p r i m a r y a n d registered 7 - q u a n t a In the t a r g e t Aa/a(%)
I
z
1 104-0 05
1 934-0 07
1 564-0 08
1 344-0 08
*4 ~4
x
~4
t~
1 124-0 08
3 4 0 ± 0 28
(10 -s~ cm~/sr)
Differential a n g u l a r 7P cross sections (final q u a n t l t m s )
482
v
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where
IE = [~m~,, ~I(E ' Emax)o~(E,(E))dE JEth
The bremsstrahlung spectrum of the synchrotron for a thick target is expressed b y Eyges' formula 12) and the dependence o~(E) was represented above in fig 4, it IS evident that the energy of the scattered q u a n t u m E ' = EMc~/ {Mc2+E (1--cos 0)) changes with the scattering angle 0° and consequently the entire integral I E changes as well Fig 5 contains the products of the effectiveness of detection of the scattered v-ray b y the distribution function in the spect ru m of primary bremsstrahlung for various angles of scattering depending on the energy of the Incident v-quanta. It can be seen that the curves are roughly symmetrical and have a m axi m um at ~ 56 MeV and half width averaging about 25 MeV The absolute value of I~ for 90 ° was calculated graphically Corrections for a change In the effectiveness of detection at other angles was also calculated graphically: by the relation of the areas under the relevant curves These corrections equalled from + 5 % for 75 ° and put to --15 4 % for 150 °. The differential cross sections of y - - p scattering for 45 °, 75 °, 90 °, 135 ° and 150 ° thus obtained from the experiment are shown in the second column of table 1 2 8 CORRECTIONS FOR ABSORPTION IN TARGET For absolute determination of the average beam of y-quanta hitting the target, carbon detectors were located in the centre of the target Under working conchtions a certain amount of bremsstrahlung is absorbed in the walls and the hydrogen of the target ( ~ 1.5 °) and some scattered radlatlon is also absorbed depending on the angle, from 2 2% for 90 ° up to 4 70/0 for 150 °. Corrections for the absorption in the paraffin shield and the walls of the telescope were eliminated due to the fact t hat the calibration measurements ~ (E) were also conducted with the absorbers. Corrections for the absorption of the incident, scattered and background v-quanta in the target are represented m the seventh column of table 1 (after the allowances for the contribution of background processess). 2 9 BACKGROUND Since we do not separate the Compton V--P scattering by the detection of coincidences between the scattered y-ray and the recoil proton, it is highly i m po r tan t to consider all posmble sources of background which m a y contribute appreciably to the detection of v-rays by the telescope wath a threshold ~ 35 MeV. At a high threshold the possibility of detection of v-electron Compton scattering at large angles is entirely excluded for the telescope as a whole (m 35 MeV) as well as for each separate counter (a few MeV) The Delbruck scattering and the radlatlon creation of pairs are processes
ELASTIC
•-p
483
SCATTERING
yielding 7 - q u a n t a of high e n e r g y at the angles of interest to us. The cross section of the first process 13) on h y d r o g e n is small (atot -m 10 -34 cm*), and besides, the Delbruck scattering is v e r y strongly directed forward (m 0 -¢) so t h a t we can neglect it already at 45 ° . T h e r e are no accurate theoretical calculations for the radiative p r o d u c t i o n of pairs According to the estimates of F e y n m a n and Gomez cited in ref. 14) for the l a b o r a t o r y angle 50 ° at E~ = 40 MeV, the cross sectlon of this process is approxi m a t e l y equal to t h a t of the Compton 7 - - P scattering %p, while at E~ = 50 MeV is no less t h a n I aTp As a result of a strong energetic and angular (approxim a t e l y ~ 0-4) dependence of the cross sections of this process, its total contrib u t i o n for E~ = 56 MeV and 75 ° Is no more t h a n a b o u t 3 % of 7 - - p - s c a t t e r i n g If account is also t a k e n of the fact t h a t only a small portlon of y-rays e m i t t e d 25
1AE--AM=O
/
r
2AE-O ~ = 1 6 3AE=16 AM-O [
E
8 o x
t
0
:0 iA X E]
Our dato 45"466.¢08~L-[17] 5 0 " 4 8 *-04 [18] [10] 45" 4 8 *~09
i
L ! o
30
6o
90
12o
15o
e- 18o
Fig 6 E x p e r i m e n t a l d a t a of the p r e s e n t p a p e r and refs ]7-]9) on y - - p scattering at the energy of y - q u a n t a a b o u t 60 MeV Between curves 2 and 3 hes the region of values of 7 - - p scattering crosssections compatible w i t h the value of the s u m A E + : / M = 16 (with positive A s and AR)
m the radiative p r o d u c t i o n of pairs possess energ]es exceeding 35 MeV (the threshold of our telescope) it wall be not d]fflcnlt to conclude t h a t the role of this process at all angles under investigation, except 45 °, is neghgably small. The corresponding correct]ons for angles from 75 ° to 150 ° were not introduced, while the d a t a for 45 ° (obviously including not only 7 - - P scattering) were not
484
V
I
GOLDANSKY
gl~ a l
used for further calculahons of the polarizability of the proton because of an indefinite value of the correction to be subtracted from the cross section shown in table 1. Other sources of background are multiple plocesses toccurrlng in the substance up to the target, in the target itself and, finally, between the target and the first counter of the telescope and leading to the penetration into the telescope of v-rays with energies exceeding 35 MeV To estimate the contributmn of these processes the creation of high energy electrons at small angles through Compton scattering and production of pairs in the target and in the substance before the target were calculated. Then a study was made of (a) bremsstrahlung of these electrons at large angles (accordmg to ref. 15)) in the direction of the counters and (b) Rutherford scattenng of these electrons (according to the Mott formula) in the direction of the counters with subsequent bremsstrahlung in forward direction in the substance before the telescope Besides the production of pairs at large angles in the hydrogen of the target Is) with the subsequent brer ~strahlung was considered The results are shown in the third to the sixth columns of table 1. The last column of this table represents the final values of differential angular cross sections of 7--P scattering after allowances made for the background processes and the absorption in the target Fig. 6 represents these final values alongside the data of other experimental work 1~-19) for similar energies of y-rays (m 60 MeV). 2 10 S Y S T E M A T I C E R R O R S
The errors shown in table 1 in determining the cross section of 7--P scattering are merely due to the statistical errors of principal measurements The main possible source of systematic errors: inaccuracy m determlmng the bremsstrahlung flux is ehmmated owing to direct comparison of the Compton scattering cross sections on protons and electrons Nevertheless there remains an error on account of two inaccuracies in determining the product of the effective volume of the target multiplied by the solid angle of the telescope's vlslbiht y in the calibration and principal (integral Io) experiments This error is set down at 1 4 % In comparing the results of the calibration and principal experiments, additional statistical errors arise from determining the beam of v-rays by the number of counts of the momtor in both kinds of experiments and summing the dispersions of m a n y points at the curve of the effectiveness of the telescopes in the detection of y-rays Systematic errors due to possible Inaccuracy m the form of the bremsstrahlung spectrum used are directed oppositely in both calibration and principal experiments and are nearly completely ehmlnated. The total value of possible systematic error in determlmng the cross section of y - - p scattering at angles from 75 ° to 150 ° is estimated as ~ 6 % To return to the statistical errors shown in table 1, we notice that these lie within 3 6 to + 7 2 % for five experimental points; the square root of the sum
ELASTIC 7 - P SCATTERING
485
of dispersions for all five points corresponds to 11 7 %. Thus, in using experimental points for comparison wath calculated theoretical curves, the average statistical error for one point is about 2 4 % and the total error (statistic plus systematic error) about 8 % 3. D i s c u s s i o n of R e s u l t s
The results offered in table 1 and in fig. 6 are to be compared with eq (6) for determining the electric and magnetic polarizablhtles of the proton Even relectlng the obviously overestimated q u a n t i t y of the cross section of 7--P scatterlng at 65 ° we have five experimental quantltles for determining the two parameters of eq. (6) A E and AM It wall be borne in mind, however, that by no means all measurements of angular dlstlabutlon are equally sensitive to the values AE and AM. Indeed, as is clear from eq (6) the cross section of forward scattering (at 0 °) is determined merely by the sum of A E and A M, and not by each of them taken separately: da
(0°) =
½ro2{2[1--2(AE+AM)~]2+5.1372}.
(9)
On the other hand, backward scattering (at 180 ° ) does not depend on each of the quantities AE and AM, but only on their difference: da 4~Q (180°) = ½%2(211--4r+ 12y2--2(AE--AM)r2] + 78 39r2}.
(10)
Our experiments described the ~--p scattering mainly in the back hemisphere at laboratory angles from 75 ° to 150 ° Proceeding from these experimental data only A E m a y be obtained with sufficient certainty, since the cross sections of ~--p scattering at angles close to 90 ° are httle sensitive to A M Relying only on the value da/dD (90 °) : (1 104-0 05)× 10-a2 cm2/sr we obtain A E ----- 164-5 8 Dispersion relations m a y be used as an adchtIonal source of information enabling us to take into account the forward V--p scattelang which was not measured in the experiment and thereby to make the value A E more accurate as well as to estimate the magnetic polarizability A M As is shown in ref 2o) the cross sections of forward 7--P scattering (da/d.(2(0°)) at energies below the photomeson threshold are entirely determined by the experimental total cross section of z-meson photoproductlon when acted upon by non-polarized ~,-quanta Only at higher energies is it necessary for the calculation of da/cLQ(0°) to know separately the meson photo-production cross sections for ~,-quanta polarized parallel and anti-parallel to the spin of the proton
486
v i GOLDANSKY et al
Using the relations given b y Clm a n d Stroffohni 20) it is easy to show t h a t
da
(°°) =
I ~y~ e2
4~ 2 ~
J0
y'2
~,2
dy
y2 Mcf°° ~(y,)_~ (y,) dy,]2 +~i~
c 2 ~ M~2
4:~2 h J0
y,(y,2_y~)
(11)
[%~(y) _ o 2(~,)], where %(y) and aa(y ) are the total cross sections of meson p h o t o - p r o d u c t i o n on protons for ),-quanta with the l a b o r a t o r y energy ~, polarized parallel (%) and anti-parallel (aa) to the spin of protons; the sum a p ( y ) + a a ( 7 ) -~ at(y) is the total cross section of p h o t o - p r o d u c t i o n for a non-polarized b e a m of y-quanta. Below the threshold of meson p h o t o - p r o d u c t i o n the last t e r m is equal to 0, and hence, with an a c c u r a c y to the t e r m s of order ~,z,
(0°)=r0* 1 - 2;~ ~
e~ 30
r'~-y ~
r2"
Comparing (12) and (9) (bearing in m i n d t h a t b y the v e r y meaning of polanzab l h t y It is d e t e r m i n e d for zero energy q u a n t a ) and changing over from A s and A M to a s and ~M, we obtain
o~,~+~M - 2--2 Mc3o ~ -
dr
(13)
Obviously, since a a and :¢M are positive, eq (13) characterizes the u p p e r limit of the values of each of the two polarlzablhtles of the proton. Using the latest d a t a on n-meson p h o t o - p r o d u c t i o n , given for ~± in ref. 21) and for ~o in refs 22,23) (see fig. 7), we o b t a i n a E + ~ M ~ 11 × 10 -aa cm a, i.e., A E + A M ~- 16 Since eq. (13) is o b t a i n e d from the most general properties o* the scattering m a t r i x there are no grounds to question it in a n y degree at all T h e r e f o r e if eq (6) IS accurate, I e , the t h e o r y of Raylelgh-Powell scattering is applicable with sufficient a c c u r a c y a n d there is no need to take account of higher terms in the f r e q u e n c y of the ~,-quanta, xt m a y easily be established within what hmits the cross sections of ~ - - p scattering should he at a n y angles I n a s m u c h as A E a n d A Mare positive a n d the sum A E + A M ---- 16, these limits he within the curves according to eq (6) at A E ~ - 0 , A M = 16 and A ~ = 16, AM----0 As is clear from fig. 6, in which the region of the values da/d.Q(O) compatible with A E + A M ~ 16 lies between curves 2 and 3, all our e x p e r i m e n t a l d a t a for 75°--150 ° are to be found within this region, whereas the values of the cross
ELASTIC
~-p
487
SCATTERING
sections of 7 - - p scattering into the b a c k hemisphere o b t a i n e d in refs 17--19) seem somewhat u n d e r e s t i m a t e d . Regarding the value A~+AM : 16 as given and calculating the value As offering the best a g r e e m e n t with our results b y the m e t h o d of the least squares we obtain A E : 13-+-3 and A M : 3:~3, the sum of the weighted squares of errors being D : 1.8 X 10 -ee cm4/sr 2. Thus, we come to the conclusion t h a t o~E : (9::t:2)× 10 -43 cm ~ and o~M = ( 2 ~ 2 ) × 10 -4a cm 3.
o
o
I 40O
30(2
20C
100 :2 0
01
012
02,
014
or5
06
017
I Oe
09
10
F i g 7 D a t a on t o t a l p h o t o - p r o d u c t i o n cross s e c t i o n s of ~+ a n d n o m e s o n s on p r o t o n s us e d for d e t e r m i n i n g t h e s u m of electric a n d m a g n e t i c p o l a r i z a b l h t i e s of t h e p r o t o n
Thus, the magnetic p o l a n z a b l l i t y of the p r o t o n is far smaller t h a n the electric one. The d e t e r m i n a t i o n of the former is more sensitive to the possible c o n t r i b u t i o n to the cross section of 7 - - p s c a t t e n n g of the terms proportional to the high powers of the f r e q u e n c y of v - q u a n t a (over y2) and therefore a detailed analysis of the role of these terms is of special interest for determining AM more accurately. As for the electric polarizability it 1s clear t h a t not only the sum As+AM is in agreement with the d a t a of our experiments, b u t the o p t i m u m value A ~ = 1 3 ~ 3 , also coincides within errors with the d a t a o b t a i n e d above from the cross section of scattering at 90 ° (A~ = 1 6 ~ 5 . 8 ) . Direct comparison of the results of the experiment with the curve based on eq. (2) w i t h o u t allowances for the polarizability the p r o t o n yields a far larger sum of the weighted squares of errors t h a n for eq. (6): D = 10.3 × 10 -6e cm4/sr 2. The best agreement wath eq. (2) is a t t a i n e d b y increasing our e x p e r i m e n t a l cross sections b y 8 %, which, however, hes on the margin of possible systematic errors.
488
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T h e question of the electric polarizability of nucleons has r e c e n t l y been wadely discussed as a result of the d e v e l o p m e n t of theoretical concepts 24, 25) on the role of the polarizability of n e u t r o n s in their electric s c a t t e n n g at small angles in the Coulomb field of h e a v y nuclei The value of electric polarizability of the n e u t r o n c o m p u t e d b y A l e x a n d r o v 28) from an analysis of his e x p e r i m e n t on n e u t r o n scattering ~ = (84-3 5) × 10 -41 cm 3 certainly contradicts all d a t a on ?-rays scattering a n d n-meson p h o t o - p r o d u c t i o n , which was a l r e a d y n o t e d in theoretical papers 7, 27-31) and is now again confirmed b y our experiments The latest analysis of new experiments on n e u t r o n s c a t t e n n g 29) led to a reduction in the u p p e r value of ~E namely, 0 < (xB)n < 2 2 × 10 -41 cm 3 but yaelded no more definite results. I n a s m u c h as a s ~ 10 -42 cm 3, n e u t r o n experiments will in general not enable us q u a n t i t a t i v e l y to estabhsh the c o n t r i b u t i o n of electric p o l a r i z a b i h t y T h e r e f o r e the a v e n u e to a s t u d y of the electric a n d magnetic polanzablhties of the nucleon, the properties conditioned b y changes in the s t r u c t u r e of the meson cloud in the nuclei, lies in the investigation of n-meson p h o t o - p r o d u c t i o n and nucleon C o m p t o n effect R o u g h estimates of electric p o l a r i z a b l h t y of a n e u t r o n on the basis of meson theories are of order of (e2[2/li2c2)(l~/lzc)3= 1 . 6 × 1 0 -42 c m 327'29) where /2/1~c = 0.08 A result close to this estimate: (x~)n ~-- (1.6 to 1 8) × 10 -42 cm 3 was o b t a i n e d 27) b y estimating the polarizability of the meson cloud in the nucleon with the help of the Chew-theory for the Gauss and exponential formfunctions at the cutting p a r a m e t e r 5.6 ~c/?i. Analysing the d a t a on n-meson p h o t o - p r o d u c t i o n and ~,--p scattering, B a l d m 7) o b t a i n e d the q u a n t i t y (0cE)p = 4 × 10 -43 cm 3 as the lower limit of nucleon electric p o l a n z a b l h t y (under the assumption of only one-meson exchange) The u p p e r limit (a~)p is o b t a i n e d in ref. 7) on the basis of the p r o x i m i t y of the cross section of y - - p scattering at 90 ° to T h o m s o n ' s (½ro2) and is set down at 1.4 × 10 -43 cm 3. F r o m the d a t a on n-meson p h o t o - p r o d u c t i o n a close estimate is o b t a m e d for the n e u t r o n in ref. 30): ( ~ ) n ~ 2 × 10 -42 cmz I t should be borne in mind t h a t since the cross section a - of the process 7 + n - - > r ~ - + p n e a r the threshold exceeds the cross section a + of the process r + p --> ~ + + n a n d the c o n t r i b u t i o n of the near-threshold region to the chsper sion integral (13) is considerable, the electric polarizability of the n e u t r o n should exceed the corresponding q u a n t i t y for the p r o t o n b y 20 to 30 % (refs 7b,3o)). As is clear from the calculations in which eq (13) was used, the u p p e r limit for the electric p o l a r l z a b l h t y of the p r o t o n m a y be lowered to (~E)p = 1.1 × 10 -42 cm 3. In the final conclusion of our p a p e r concerning the q u a n t i t y (aE)p we additionally use the calculated u p p e r value of the sum (~s+x~t)p = 1.1 × 10 -42 cmS; even the direct result of the e x p e r i m e n t s on the whole confirms the abovem e n t i o n e d theoretical estimates of (as)p. In conclusion we shall consider the problem of the m e a n q u a d r a t i c fluctuation
ELASTIC ~/-p SCATTERING
489
of the displacement (allied with ~E) of the centre of electric charge distribution in the polarized proton with respect to the centre of its gravity According to refs. 7b, 3o) thls quantity V/O is connected with the electric polarlzablhty of the proton through the common relation
%/~ •
OCEe2 hC'
where A E is the difference of energies between the ground and virtual polarized states of the proton Since the polarlzatxon is conditioned by the excitation of a meson cloud or the origin of resonance isobaric state it is worth while to accept A E in the range from M c 2 to 2 M c 2. At aE : 9 x 10-4a cm 3 we obtain from eq (14) for the mean quadratic fluctuation of the length of the proton electric dipole V'~ = (3.5 to 5) × 10-14 cm It is certainly of interest to develop a more detailed theory of the magnetic polarizabihty of the proton to connect ~E and ~Mwith the contribution of various mechamsms of ~-meson photo-productlon, to obtain the relevant theoretical h i l t s for aM and compare them with experiment as well as to compare the fluctuations of the length of electric and magnetic dipoles
4. C o n c l u s i o n s 1) Elastic scattering of 7-rays with energies from 40 to 70 MeV (the average being 56 MeV) by protons has been studied The new method of determmlng the effectiveness of 7-rays detection has made it possible to draw direct comparison of the cross sections of Compton scattering on protons and electrons and obtain the cross sections of ~,--p scattermg for 75 °, 90 °, 120 °, 135 ° and 150 ° in the laboratory system within an average accuracy of 4-8 % (with allowances for statistical as well as systematic errors) 2) The data thus obtained are compared with the theory of Rayleigh-Powell scattering of y-rays by particles possessing anomalous magnetic moments and electric and magnetic polarlzablhties The scattering cross section at 90 ° corresponds to the electric polarizablhty aE---- (114-4)× 10-4a cm a 3) Alongside experimental data, the cross section of forward 7--P scattering (at 0 °) was drawn upon for comparing with the theory. This cross section IS determined by the sum of electric (~E) and magnetic (aM) polarizabmhtles of the proton ~E+~M -- 2 ~ M c J o
73
4) On the basis of experimental data on 7--P scattering from 75 ° to 150 ° and the calculated cross section for 0 °, the electric polarlzablhty of the proton is
49(1
V
I
el tzl
GOLDANSKY
d e t e r m i n e d and the magnetic one e s t i m a t e d ~
=
(9±2) x lo-~ cmL
~
=
( 2 ~ : 2 ) x 1 0 - ~ cm~
5) The electric polarizability thus found corresponds to the mean q u a d r a t i c t l u c t u a t m n ot the length of the p r o t o n electric d~pole ~/N = (3 5 to 5) :/. 10 - ~ cm The authors are greatly i n d e b t e d to R G Vasllkov, S P Balatyev, Ye V Mmarlk and A Samuflhn for their assistance in conducting the experiments and G I v a n o v for his active p a m c l p a t l o n in the t r e a t m e n t of the results o b t a i n e d \Ve are glad to t h a n k the entire m a i n t e n a n c e staff of the 265 MeV s y n c h r o t r o n of the F I A N for ensuring m a n y hours' e x p e r i m e n t a t i o n for us and express our sincere acknowledgements to A M. Balchn and V N Grlbov for their participation m discussing the results Note added ~n proof. The general expression for the a m p l i t u d e of y - p scattering (in CMS) is of the form T = Rl(ee')+R2(ss')-l-~Ra(~[e'e])+~R4(a[s's])
+ ~Rs{(~k)(s' e ) - (ok')(se')}+, R~{ (~k')(~' e ) - (ok)(e' ~)} g w e n b y Rltu~ 32) and Lapldus aa) If we take, as in refb 2-s), R I = 1, R 2 = R 5 = 0 , R 3=1y, R 4 = ly,~2, R 6 = ½72 (all R, values are in e"/ffc 2 units) we obtain formula (1) for crosssections To obtain eq (6) we h a v e to take R 1 = 1 - - A ~ v 2, R 2 = At, yz As was shown b y Arlstov a4)
=
3
~
\~l
where r e = 0 8. 10 -t~ cm is the electric radius of the p r o t o n and
A*~ = ~*~ ~c ~*E being the electric polarizability of the p r o t o n in c o n v e n t i o n a l sense (1 e , dipole m o m e n t p = ~*~E). References 1) J I, Pop, ell, Ph:,s Rev 75 (1949) 32 2) M Gell-Mann and M Goldberger, Phys Rev 96 (1954)1433 3) I: E Lo~, Ph)~ Rev 96 (1954) I423 4) A Klein, Phys Rev 99 (1955) 998 5) R Capps, Phys Rev 106 (1957) 1031 6) V A Petrunkm (private commumcatlon)
ELASTIC
~]-p
SCATTERING
491
7) A M Baldm, a) Report at tile Conference on Elementary Particles at Padua-Venice (1957), b) Nuclear Physics 18 (1960) 8) E C Park, J Scl Instr 33 (1956)257 9) V~~ Baffler, \V George and D Reagan, Phys Rev 58 (1955) 73 10) P S Baranov, Thesis, P N Lebedev Phvsmal Institute (1955) 11) V I Goldanskv, O A Karpukhm and V V Pa~lovska,~a, Instruments and Techmque of Experiment 3 (1960) 23 12) L Esgeb, P h \ s Rex 81 (1951) ~82 13) A I \khmzer and V B Berebtetskv, Quantum Electrodynanncs, ~econd edttton (Flzmatlzdat, lq59) 14) L G Hxman, MIT Ph D The~l~ (1959) 151 P V ( Hough, Ph~s Rev 74 (1948) 80 1~) R ( Miller, Ph.~s Re~ 95 (1954) 796 17) C Oxlex and V L Telegdl, Phvs Re~ 100 (1955)435 18) C Oxlev, Phys Rev 110 (1958) 733 19) G Pugh, R Gomez, D Frlsch and G Janes, Phys Rev 105 (1957) q82 20) M Cml and R Stroffohnl, Nuclear Physics 5 (1958) 684 21) G Bernardlm, Report at the I X t h Conference on High Energy Physics, Klev (1959) :~2) R G Vassflkov, t3 ]3 Govorkov and V [ Goldansky, J E T P 3 7 (1959)11, Nuclear Phy~ms 12 (195q) 337 23) K Berkelman and J \Vaggoner, Phys Rev 117 (1960) 1364 241 Yu A Mexandrov and I Bondarenko, J E T P 31 (1956) 726 25) V S Barashenkov, I P Stakhanov and Yu A Alexandrov, J E T P 32 (1957) 1546 2b) Yu A Alexandrov, J E T P 32 (1957) 561, 33 (195"/) 294 27) V S Barashenkov and ]3 M Barbashov, Nuclear Physms 9 (1958) 426 '28) 13 I Blokhlntsev, V S Barashenkov and ]3 M Barbashov, Usp Flz Nauk 68 (1959) 417 29) R M Thaler, Phys Rev 114 (1959) 827 30) G Brmt and M L Rustgl, P h ~ Rev 114 (1959)830 311 L L Fold~, Phy~ Rev Letter~, 3 (1959)105 32) V I R~tus, J E T P 33 (19571 1264 33) L I Lapldu~, J E T P 34 (1958) 922 34) Yu Arl~to~ (private commumcat~on)