Volume 28B, number 1 P H Y S I C S L E T T E R S 28 October 1968

A C O M M E N T ON T H E P O L A R I S A T I O N IN P R O T O N - P R O T O N S C A T T E R I N G A T L O W E N E R G Y

J. S. C. McKEE Physics Department, University of Birmingham, UK

and

T. OSBORN Department of Mathematical Physics, University of Birmingham, UK

Received 1 August 1968

An estimate is made of the polarisation in proton-proton scattering due to the interaction between the magnetic moment of the incident particle and the Coulomb field of the target. The effect is seen to be significant at low energies.

In a r e c e n t expe r imen t Slobodrian et al. [1] have studied the po la r i sa t ion in pro ton-pro ton sca t t e r ing as a function of angle, for s e v e r a l d i f ferent ene rg ie s . At 10 MeV and 15 MeV i n c i - dent pa r t i c l e energy, the m e a s u r e d po la r i sa t ion at 45 ° (in the cen t r e of mass) is compat ib le with that p red ic t ed f rom the phenomenologica l phase shift ana lys i s of MacGregor et al. [2]. This point i s made by these authors in a subsequent paper [3].

At angles fo rward of 45 ° however , a g r e e m e n t i s not so marked , and t h e r e i s a tendency for the expe r imen ta l points to a cqu i r e s m a l l pos i t ive va lues r a the r than to become m o r e nega t ive with d e c r e a s i n g angle. The data under d i scuss ion a r e shown in fig. 1. The expe r imen ta l points a r e those of ref . 1. The continuous cu rves co r r e spond to the var ia t ion in po la r i sa t ion c r o s s sect ion qo P) with angle, obtained f r o m the phenomenol - ogical ampl i tudes of Stapp and Ypsi lant is [4] u s - ing the phases of MacGregor et al . [2] at each energy . In th is ana lys i s S, P and D waves only a r e taken into account , and coupling between P and F waves is included through the p a r a m e t e r E 2. In the f igure the expe r imen ta l points tend to d ive rge f r o m the t heo re t i c a l cu rve at points f o r - ward of 45 ° .

The purpose of this l e t t e r i s to sugges t that an explanation of the obse rved d i sc repancy may l ie in addit ional po la r i sa t ion due to the in te rac t ion between the magnet ic moment of the incident p r o - ton and the Coulomb f ie ld of the t a rge t , in p-p sca t t e r ing . That such po la r i sa t ion can occur was f i r s t sugges ted by Schwinger [5] who cons ide red

the p rob lem of the s ca t t e r i ng of fas t neut rons by heavy nuclei . This phenomenon has s ince been demons t r a t ed on s e v e r a l occas ions [6,7]. In o r - der to e s t ima te the magnitude of this effect in the p rob lem of p-p sca t t e r ing at fo rward angles , we have used the Schwinger p re sc r ip t ion , which u t i l i s e s the f i r s t Born approximat ion , and r e - p laces Coulomb waves by plane waves whenever they occur .

The Coulomb in te rac t ion potential (V) is w r i t - ten in the fo rm,

e2t/ a . r

V = ~P 2M2-~ " - x 3

/~1~ being the magnet ic momentum of the proton, arid Mp i ts mass . This in te rac t ion c l ea r ly has the c h a r a c t e r of a long range ! . a fo rce . Using the Born approximat ion , the over lap in teg ra l (~blVl~a)> i s evaluated for a sca t t e r ing p rob lem in which q~b and 4/a denote the wave functions of the incident proton before and a f te r sca t t e r ing . Cor responding momentum v e c t o r s k b and k a en- able us to define the unit vec to r n as

k b × k a = k 2 sin 0 . In I -- 1 .

The sca t t e r ing ampl i tude due spec i f ica l ly to the e l ec t romagne t i c in te rac t ion is then given by:

~+)(o)--- Mp (%iriS(a÷)> 2nt/2

1 = ~zo'.n cot½0 ~ a

Volume 28B, number 1 P H Y S I C S L E T T E R S 28 October 1968

x l d 6

"02

0"(] 10 30 t M

- .02

011

loP ICROSS-SECTION]

IO.OMeV.

• Slobodrian

SO OC.of Mass.

26 xlO

.0~

0.0

-- .02

tl loP[CROSS SECTION]

15.0 MeV.

Fig. 1. The exper imenta l points (lop) a re polar isa t ion data f rom ref . 1 plotted as a product with the interpolated c r o s s - s e c t i o n for e las t ic sca t t e r ing at each energy. The continuous curves are obtained f rom the phase shifts of

ref . 2 as descr ibed in the text.

w h e r e ~ i s t h e f i ne s t r u c t u r e c o n s t a n t . T h e t o t a l s c a t t e r i n g a m p l i t u d e can now b e w r i t t e n ,

f(O) = fo(O) +Af(+)(O)

w h e r e fo(O) i s t h e a m p l i t u d e of t h e w a v e s c a t t e r e d by p u r e l y n u c l e a r f o r c e s .

In t h i s e a s e t he p o l a r i s a t i o n a t a l a b o r a t o r y a n g l e of s c a t t e r i n g 0 i s g i v e n by:

2 I m fo(O)v cot ½0 P(O) =

i fo(0) I 2 +w2 cot 2 ½0

w h e r e V = ½g~" (~i/MpC)(e2/hc). W e e s t i m a t e t h e r a t i o Imfo(O) / I fo(O)l f r o m a k n o w l e d g e of t h e S w a v e p h a s e s h i f t a t low e n e r g i e s . R e s u l t s o b - t a i n e d a r e s h o w n in t a b l e 1.

C l e a r l y , t he e s t i m a t e d p o l a r i s a t i o n c r o s s s e c - t i o n s show the r a p i d r i s e a t f o r w a r d a n g l e s s u g - g e s t e d by t h e d a t a f r o m r e f . 1, a n d e v e n a t 45 ° t h e e f f e c t i s f a r f r o m n e g l i g i b l e . I t h a s a l s o b e e n p o s s i b l e to p r e d i c t a v a l u e f o r t h e p o l a r i s a t i o n a t 45 ° f o r t h e s c a t t e r i n g of p r o t o n s of 3 MeV i n c i - d e n t e n e r g y (~ 0.4%), w h i c h i s no t in d i s a g r e e - m e n t w i t h t h e so f a r u n e x p l a i n e d r e s u l t s of A l e x - e l f a n d H a e b e r l i [8] a t W i s c o n s i n .

Table 1

Angle of s ca t t e r IoP (cm × 1026)

0 (C.ofM) 10MeV 15MeV

25 0.068 0.053

30 0.065 0.044

35 0.048 0.038

40 0.042 0.033

45 0.037 0.028

In c o n c l u s i o n i t wou ld a p p e a r t h a t any f u r t h e r d e t a i l e d a n a l y s i s of t h e n u c l e o n - n u c l e o n s c a t t e r - i ng p r o b l e m a t low e n e r g i e s m u s t t a k e a c c o u n t of t h e s p i n - o r b i t i n t e r a c t i o n a r i s i n g f r o m m o t i o n of t h e n u c l e o n m a g n e t i c m o m e n t in t h e C o u l o m b f i e l d of t h e t a r g e t .

References 1. R . J . Slobodrian, J. S. C. McKee, H. Bichsel and W.F.

Tivol, Phys. Rev. Le t te r s 19 (1967) 704. 2. M.H. MacGregor , R.M. Wright and R. A. Arndt,

UCRL. 70075 (1967).

Volume28B, number 1 P H Y S I C S L E T T E R S 28 October 1968

3. M.H. MacGregor, R.M. Wright and R. A. Arndt, Phys. Rev. Le t te rs 19 (1967) 1209.

4. H .P . Stapp, T . J . Ypsilantis and N.Metropol is , Phys. Rev. 105 (1957) 302.

5. J . Schwinger, Phys. Rev. 73 (1948} 407.

6. J .E .Monahan and A.J .E lwyn, Phys. Rev. 136 (1964} 1678.

7. A . J . Elwyn, R. O, Lane, A. Langsdorf J r . and J. E. Monahan, Phys. Rev. 133 {1964} 80.

8. I. Alexeff and W. Haeberli , Nucl. Phys. 15 {1960} 609.