HADRON-NUCLEUS AND NUCLEUS-NUCLEUS SCATTERING AT HIGH ENERGIES

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HADRON-NUCLEUS AND NUCLEUS-NUCLEUS SCATTERING AT HIGH ENERGIES

V. Balashov

To cite this version:

V. Balashov. HADRON-NUCLEUS AND NUCLEUS-NUCLEUS SCATTERING AT HIGH ENER- GIES. Journal de Physique Colloques, 1972, 33 (C5), pp.C5-127-C5-140. �10.1051/jphyscol:1972510�.

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JOURNAL DE PHYSIQeTE C o l l o q u e C5, ~ i t p p l B m e b t au no S-9, Tome 33,.AoQt-Septembre 1972, p a g e C5-127

HADRON-NUCLEUS AND NUCLEUS-NUCLEUS SCATTERING

AT HIGH ENERGIES

V. V. BALASHOV

I n s t i t u t e o f N u c l e a r P h y s i c s , Moscow S t a t e U n i v e r s i t y Moscow, U.S.S.R.

RBsume

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The s t u d y of s c a t t e r i n g

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A t t h e same t i m e t h e problem o f s c a t t e r i n g s e r v e s a s a k i n d of symbol o f n u c l e a r r e s e a r c h . I n d e e d , a t e v e r y s t a g e of t h e development of n u c l e a r p h y s i c s t h e l e v e l of i n v e s t i g a t i o n s r e l a t i n g t o t h e problem o f s c a t t e r i n g r e f l e c t e d t h e g e n e r a l l e v e l of t h i s development and i t s main t r e n d s .

E x p e r i m e n t a l a n d t h e o r e t i c a l i n v e s t i g a - t i o n s of t h e problem of hadron-nucleus a n d n u c l e u s - n u c l e u s c o l l i s i o n s a r e c a r r i e d o u t i n a v e r y b r o a d s c o p e . I n o r d e r t o f i n d t h e main t r e n d s of modern i n v e s t i g a t i o n s on t h i s s u b j e c t and t o show t h e i r c o n n e c t i o n w i t h t h e c u r r e n t problems i n t h e o t h e r b r a n c h e s of n u c l e a r p h y s i c s , i t i s u s e f u l t o start from a s h o r t h i s t o r i c a l i n f r o d u c t i o n .

I n 1966 a t CERN e x p e r i m e n t s were p e r f o r - med t o s t u d y s c a t t e r i n g of 2 0 GeV p r o t o n s frcin a number of n u c l e i - from l i t h i u m t o u r a n i a m [I]

.

The CERN e x p e r i m e n t s and a l s o t h e i n v e s t i g a t i o n s o f p r o t o n - n u c l e u s s c a t t e r i n g a t 1 GeV performed i n 1967 i n Brookhaven [ 2 1 c a l l e d i n t o b e i n g t h e Glau- b e r t h e o r y of m u l t i p l e s c a t t e r i n g [3]. I t i s known t h a t t h e f o r m a l i s m of t h i s t h e o r y was e l a b o r a t e d by G l a u b e r much e a r l i e r a n d was d e s c r i b e d i n d e t a i l i n h i s famous ' t l e c t u r e s " i n 1958 ( i n 1958 S i t e n k o , p r o c e e d i n g from t h e Huygens p r i n c i p l e , p r o p o s e d i n - d e p e n d e n t l y a f o r m a l i s m o f hadron-nucleus s c a t t e r i n g a t h i g h e n e r g i e s which i s a d e q u a t e t o G l a u b e r ' s f o r - malism [ 4 ] ). Czyz and L e s n i a k [5],and B a s s e l and W i l k i n [63 have c o n n e c t e d t h e f o r m a l i s m of t h e Glau-

b e r t h e o r y w i t h t h e new e x p e r i m e n t s . S i n c e t h a t t i m e t h e t h e o r y o f m u l t i p l e s c a t t e r i n g h a s become a p i v o t f o r t h e development of i n v e s t i g a t i o n s of high-energy s c a t t e r i n g p r o c e s s e s .

T h e G l a u b e r t h e o r y is b a s e d on t h e c l o s e a n a l o g y between t h e high-energy n u c l e a r s c a t t e r i n g and t h e g e o m e t r i c a l o p t i c s . I t s b a s i c p r i n c i p l e s

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1972510

C 5-1 28 V.V. BALASHOV

are : ( a ) a p a r t i c l e t r a v e r s e s a n u c l e u s i n a n a l - most s t r a i g h t t r a j e c t o r y , t h e r e f o r e a c h a n g e i n t h e impact p a r a m e t e r b i n t h e c o u r s e of i t s motion c a n b e n e g l e c t e d ; ( b ) t h e l o n g i t u d i n a l ( a l o n g t h e d i r e c t i o n of p a r t i c l e m o t i o n ) c a n p o n e n t of momentum t r a n s f e r qz i s n e g l i g i b l y s m a l l ; ( c ) d u r i n g t h e t i m e of t h e s c a t t e r i n g t h e n u c l e o n s of t h e n u c l e u s d o n o t c h a n g e t h e i r p o s i t i o n ( t h e n u c l e o n s a r e

"frozen") ; ( d ) t h e t o t a l p h a s e s h i f t a c q u i r e d by a p a r t i c l e moving t h r o u g h t h e n u c l e u s i s t h e sum of p h a s e s h i f t s a c q u i r e d by i t i n c o l l i s i o n s w i t h i n d i - v i d u a l n u c l e o n s :

A

T h e s e a p p r o x i m a t i o n s l e a d t o t h e d i r e c t r e l a t i o n between t h e h a d r o n - n u c l e u s s c a t t e r i n g am- p l i t u d e F i f ( q ) -+ a n d t h e e l e m e n t a r y a m p l i t u d e s f(';;) o f t h e h a d r o n - n u c l e u s i n t e r a c t i o n . :

I n t h e l i m i t A >> 1 t h e s e f o r m u l a e t r a n s - form i n t o t h e o p t i c a l model f o r m u l a e

The G l a u b e r model u n i f i e s t h e mechanisms of c o h e r e n t and i n c o h e r e n t s c a t t e r i n g . The r a n g e of i t s a p p l i c a t i o n s i s v e r y wide ( s e e P i g s . 1 ) . T h i s mo- d e l was u s e d f o r d e s c r i b i n g p r o t o n - n u c l e u s scatte- r i n g i n c l u d i n g t h e Coulomb-nuclear i n t e r f e r e n c e i n e l a s t i c s c a t t e r i n g a t v e r y s m a l l a n g l e s [8 1. With t h e a i d of i t t h e d a t a on t h e t o t a l c r o s s s e c t i o n s f o r t h e hadron-nucleus i n t e r a c t i o n from 1 €?eV t o t h e Serpukhov e n e r g i e s a r e b e i n g a n a l y s e d [ 9 ] . In c o n n e c t i o n w i t h t h e problem of t h e asymptotic beha-

v i o u r of h a d r o n c r o s s s e c t i o n s it was u s e d f o r ana- l y s i n g t h e d a t a on t h e t o t a l c r o s s s e c t i o n s f o r i n e l a s t i c p r o c e s s e s i n t h e i n t e r a c t i o n of cosmic r a y s w i t h n u c l e i i n t h e i n t e r v a l 2 0 - 1200 GeV and q u i t e r e c e n t l y even a t h i g h e r e n e r g i e s [lo]. The G l a u b e r model h a s p r o v e d r e m a r k a b l y s u i t a b l e f o r t h e d e s c r i p t i o n of p i o n - n u c l e u s s c a t t e r i n g even i n t h e r e g i o n of t h e s t r o n g p i o n - n u c l e o n i n t e r a c t i o n n e a r t h e ( 3 , 3 ) r e s o n a n c e [ l l 1. I t i s a l s o employed f o r c o n s i d e r i n g a v a r i e t y of p o l a r i z a t i o n phenomena i n s c a t t e r i n g [12].

Advances i n t h e s t u d y of hadron-nucleus s c a t t e r i n g h a v e had a g r e a t e f f e c t o n t h e develop- ment of t h e t h e o r y o f c o h e r e n t a n d i n c o h e r e n t pro- cesses of p a r t i c l e p r o d u c t i o n ( r e s o n a n c e s ) on n u c l e i and on t h e d e s i g n of new e x p e r i m e n t s i n t h i s f i e l d . A f t e r t h e model f o r t h e h a d r o n - n u c l e u s i n ' i c r a c t i o n , a model f o r t h e i n t e r a c t i o n between complex n u c l e i was a l s o c o n s t r u c t e d [13]. I t i s b a s e d on t h c a s s u m p t i o n of t h e a d d i t i v i t y of n u c l e u s . n u c l e u s s c a t t e r i n g p h a s e s a t h i g h e n e r g i e s o v e r a l l p a i r s of c o l l i d i n g n u c l e o n s

From t h i s , i n t u r n , one c a n s e e ways t o t h e modern models of d i f f r a c t i o n hadron-hadron s c a t t e r i n g ; t h e v e r y a p p e a r a n c e o f many of them i s a s s o c i a t e d w i t h t h e development of h i g h e n e r g y n u c l e a r phy- s i c s . High-energy n u c l e a r p h y s i c s a l s o h a s a marked e f f e c t on t h e development o f t h e t h e o r y of e l e c t r o - n i c and a t o m i c c o l l i s i o n s where r e c e n t l y a h o s t of i n v e s t i g a t i o n s based on t h e e i k o n a l and G l a u b e r ap- p r o x i m a t i o n s h a v e appeared.

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The G l a u b e r model h a s made f e a s i b l e a uni- f i e d d e s c r i p t i o n of v a r i o u s p r o c e s s e s o f m u l t i p l e s c a t t e r i n g i n n u c l e i , Y e t , based on p o s t u l a t e s t h e s i g n i f i c a n c e of which i s o f t e n r e v e a l e d w i t h t h e a i d of o p t i c a l a n a l o g i e s , t h i s model s t i l l r e m a i n s un- c l e a r i n many r e s p e c t s . The e x p e r i m e n t a l c h e c k o f t h e model i s i n s u f f i c i e n t , n o matter fiow d e t a i l e d i t might be. T h e r e f o r e , g r e a t e f f o r t s a r e b e i n g made t o d e t e r m i n e t h e p o s i t i o n of t h e model i n t h e g e n e r a l

HADRON AND NUCLEUS SCATTERING

. . .

F i g . l

Some t y p i c a l c a l c u l a t i o n s i n t h e G l a u b e r model and t h e i r comparison w i t h e x p e r i m e n t :

a ) t h e d i f f e r e n t i a l c r o s s - s e c t i o n f o r c o h e r e n t a n d b) t h e t o t a l a b s o r p t i o n c r o s s - s e c t i o n s o f high- i n c o h e r e n t s c a t t e r i n g a t high-energy p r o t o n s by e n e r g y n e g a t i v e c h a r g e d h a d r o n s on n u c l ' e i a t P b c a l c u l a t e d by G l a u b e r and M a t t h i a e [7] 40 GeVfc ( f r o m Ref. 191) t h e t h r e e c u r v e s c o r r e s -

pond t o a n t i - p r o t o n s , p i o n s a n d k a o n s

c ) t h e a n g u l a r d i s t r i b u t i o n of 270 M e V p i o n s e l a s - d ) t h e o b s e r v a t i o n of t h e d e u t e r o n a l i g n m e n t i n t i c a l l y s c a t t e r e d by 0'' ; t h e c u r v e s c o r r e s p o n d d-p e l a s t i c s c a t t e r i n g a t 3.6 GeV/c (from Ref.

t o d i f f e r e n t v e r s i o n s of t h e G l a u b e r model c a l c u - f12b1) ; t h e two c o e f f i c i e n t s A and B c o r r e s p o n d l a t i o n s (from Ref. [lib]). t 3 t h e f i t Nd(q) = ^{N (1 +} A c o s 2 q + B c o s q ) ; t h e so-

l i d c u r v e s a r e . c a l c u l g t i o n s i n t h e fr.anework of t h e G l a u b e r model.

C5-130 V.V. BALASHOV

t h e o r y of m u l t i p l e s c a t t e r i n g by a m a n y - p a r t i c l e s y s t e m ( t h e Goldberger-Watson t h e o r y , t h e Faddeev e q u a t i o n s , t h e Feynmann g r a p h t e c h n i q u e ) .

I n t h e c o u r s e of t h e s o l u t i o n of t h i s problem two d i f f i c u l t q u e s t i o n s a r e

b e i n g o u t l i n e d . T h e i r e s s e n c e c a n b e b e s t s e e n i f one t a k e s hadron-deuteron s c a t t e r i n g a s a n example.

I t h a s l o n g been shown t h a t t h e u s u a l Feynmann ap- p r o a c h t o t h i s problem, when a p a r t from s i n g l e S c a t - t e r i n g g r a p h s a d o u b l e e l a s t i c s c a t t e r i n g g r a p h i s a l s o t a k e n i n t o a c c o u n t , l e a d s t o t h e G l a u b e r model.

I n t h i s c a s e , however, i t i s n e c e s s a r y t o c a r r y o u t a number of i m p o r t a n t s i m p l i f i c a t i o n s i n c a l c u l a t i n g t h i s g r a p h , namely : t o r e d u c e t h e Green f u n c t i o n t o t h e e i k o n a l form, t o n e g l e c t t h e o f f - m a s s - s h e l l e f f e c t s i n t h e a m p l i t u d e s of hadron-nucleon s c a t t e - r i n g , e t c . . . I n t h i s c a l c u l a t i o n a n i m p o r t a n t can- c e l l a t i o n e f f e c t a r i s e s [14 ]. I n p a r t i c u l a r , some o f f - m a s s - s h e l l e f f e c t s a r e c a n c e l l e d by t a k i n g a c c o u n t of t h e n u c l e o n r e s c a t t e r i n g e f f e c t s . T h i s

c a n c e l l a t i o n mechanism moves down t h e low e n e r g y

c e s s a r y t o g e t a r e a l i s t i c t h e o r y of t h e r e s c a t t e - r i n g e f f e c t s . The problem becomes e x t r e m e l y impor- t a n t i n c o n n e c t i o n w i t h t h e f u t u r e p d - s c a t t e r i n g e x p e r i m e n t s i n B a t a v i a .

T a k i n g i n t o a c c o u n t t h e i n e l a s t i c shadow e f f e c t s t h e t o t a l c r o s s s e c t i o n f o r t h e hadron- d e u t e r o n i n t e r a c t i o n c a n b e e s t i m a t e d u s i n g t h e f o l - lowing i n t e g r a l

where

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t i n g t h e e l a s t i c s c a t t e r i n g d i f f e r e n t i a l c r o s s s e c - t i o n f o r i n t h e i n t e g r a l ( 7 ) one o b t a i n s t h e u s u a l G l a u b e r c o r r e c t i o n . A number of a u t h o r s have done t h e q u a n t i t a t i v e e s t i m a t e of t h e c o r r e c t i o n AcT f o r p i o n - d e u t e r o n and p r o t o n - d e u t e r o n s c a t t e - r i n g a t h i g h e n e r g i e s u s i n g t h e e x p e r i m e n t a l d a t a o n

i n e l a s t i c p r o c e s s e s . l i m i t of t h e G l a u b e r model a p p l i c a b i l i t y . However,

F o r example, i n t h e r e c e n t work of Kayda- t h i s q u e s t i o n h a s been worked o u t more o r less i n

l o v and Kondratyuk [17 ] a n e s t i m a t e i s made of t h e d e t a i l o n l y f o r t h e c a s e of t h e d e u t e r o n and i t i s

v a r i o u s mechanisms of i n e l a s t i c shadowing, which i s n o t q u i t e c l e a r how t h e c a n c e l l a t i o n mechanism ope-

based on t h e e x p e r i m e ? t a l d a t a on t h e i n c l u s i v e r a t e s i n t h e c a s e of h e a v i e r n u c l e i .

r e a c t i o n c r o s s s e c t i o n s and on t h e Regge-pole pheno- The problem of t h e high-energy l i m i t of

t h e G l a u b e r method i s p r a c t i c a l l y t h e problem of t h e s o c a l l e d i n e l a s t i c shadowing [15] :

T h i s problem is of p a r t i c u l a r p r a c t i c a l i m p o r t a n c e i n t h e a n a l y s i s of h a d r o n - d e u t e r o n s c a t t e r i n g . Q u i t e r e c e n t l y t h e Dubna group [ 1 6 ] h a v e summed u p t h e r e s u l t s o f t h e i r work of many y e a r s i n Serpukhow on t h e e x p e r i m e n t a l s t u d y of p-d e l a s t i c s c a t t e r i n g . They h a v e p r e s e n t e d t h e i m p o r t a n t d a t a on t h e e n e r - gy dependence of t h e s l o p e o f t h e d i f f r a c t i o n peak and of t h e r a t i o of t h e r e a l t o t h e i m a g i n a r y p a r t o f t h e e l a s t i c s c a t t e r i n g a m p l i t u d e . I n o r d e r t o t r e a t t h e s e d a t a t o g e t h e r w i t h t h e c o r r e s p o n d i n g da- t a on t h e p r o t o n - p r o t o n e l a s t i c s c a t t e r i n g i t ' s ne-

menology. I n t h a t work some v e r s i o n s of t h e reggeon exchange a r e c o n s i d e r e d :

N a t u r a l l y , t h e Pomeron exchange ( d i f f r a c t i o n d i s s o - c i a t i o n mechanism) p l a y s t h e dominant r o l e . Accor- d i n g t o t h e a u t h o r s ' e s t i m a t e , t h e r a t i o of t h e c o r - r e s p o n d i n g shadow c o r r e c t i o n t o t h e c o r r e c t i o n d u e t o e l a s t i c s c a t t e r i n g i s l a r g e :

The t o t a l c o r r e c t i o n c a l c u l a t e d by t h i s method i s i n good agreement w i t h e x p e r i m e n t :

HADRON AND NUnEUS SCATTERING

...

T h e s e e x p e r i m e n t a l d a t a a r e t a k e n from t h e r e c e n t Serpukhov work El81 i n which t h e t o t a l c r o s s s e c - t i o n s f o r t h e x +, p and ~ - d i n t e r a c t i o n i n t h e i n c i d e n t momentum r e g i o n 15-60 GeV/c have been measured.

A c c o r d i n g t o t h e G l a u b e r model t h e e l a s - t i c shadow c o r r e c t i o n i s r e l a t e d t o t h e d e u t e r o n wa- v e f u n c t i o n by t h e s i m p l e r e l a t i o n

T h e q u a n t i t y (--) 1 c a n be c o n s i d e r e d t o b e a phe- nomenological p a r a m e t e r which i n c l u d e s t h e i n e l a s - r2 t i c shadowing e f f e c t s a n d , t h e r e f o r e , c a n depend on e n e r g y and on t h e k i n d o f t h e i n c i d e n t hadron. Ana- l y s i s of t h e Serpukhov d a t a shows [IS ] t h a t t h i s pa- r a m e t e r d o e s depend on t h e i n c i d e n t p i o n momentum :

Moreover, t h e v a l u e s of

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T h e most r i g o r o u s c r i t e r i a f o r t e s t i n g v a r i o u s models and t h e o r i e s r e l a t i n g t o t h e r e s c a t - t e r i n g mechanism c o u l d b e o b t a i n e d by s e p a r a t i n g t h e m u l t i p l e s c a t t e r i n g e f f e c t s e x p e r i m e n t a l l y . I n t h i s r e s p e c t t h e e x p e r i m e n t s on p r o t o n - d e u t e r o n s c a t t e r i n g c a r r i e d o u t by t h e group of A l l a b y , Amaldi and o t h e r s [19] a t CERN a t a n e n e r g y of a b u t 2 0 GeV a r e of g r e a t i m p o r t a n c e , They h a v e shown t h a t a t f a i r l y l a r g e s c a t t e r i n g a n g l e s t h e s e p a r a t i o n o f t h e s i n g l e and d o u b l e s c a t t e r i n g e f f e c t s i n t h e spec- tra o f s c a t t e r e d p r o t o n s o c c u r s ( s e e Fig.2). Analy- s i s o f t h e s e d a t a w i t h i n t h e framework of t h e G l a u b e r model made i t p o s s i b l e t o u n d e r s t a n d a l l t h e main

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a L ^I _{21 22 23} 24

ynmpn(nCM MOMENTUM. p (GeVk)

f e a t u r e s o f t h i s phenomenum 1201 even w i t h t h e u s e o f s i m p l e o s c i l l a t o r wave f u n c t i o n s f o r t h e i n i t i a l and finnl q t ~ lof t ~t h e r l ~ r ~ t ~ r n n ~ ( s e e F i u . 3 1 .

Pig.J

Momentum s p e c t r a a t 19.2 GeV/c p r o t o n s s c a t t e r e d on d e u t e r i u m . The c u r v e s a r e c a l c u l a t e d i n Ref. [20]

i n t h e framework o f t h e G l a u b e r model,

V.V. BALASHOV

The s e p a r a t i o n , under c e r t a i n c o n d i t i o n s , of t h e d o u b l e s c a t t e r i n g e f f e c t s i s a phenomenon o f t h e g e n e r a l c h a r a c t e r . F i g . 4 shows t h e e n e r g y s p e c t r a . o f a r g o n i o n s s c a t t e r e d from t h e s u r f a c e o f a c o p p e r s i n g l e c r y s t a l 121 1. The s c a l e of t h i s p i c - t u r e i s q u i t e d i f f e r e n t from what i t i s i n t h e high- e n e r g y n u c l e a r p h y s i c s : t h e i o n energy i s 30 keV, t h e s c a t t e r i n g a n g l e s a r e one o r d e r l a r g e r t h a n i n t h e CERN e x p e r i m e n t s and s o on. But t h e main q u a l i - t a t i v e f e a t u r e s of t h i s p i c t u r e a r e j u s t t h e same a s i n t h e c a s e of p d s c a t t e r i n g . A t s m a l l s c a t t e - r i n g a n g l e s t h e c o ~ : t r i b i t i o n from d o u b l e s c a t t e r i n g i s s m a l l , w i t h i n c r e a s i n c : a n g l e i t r i s e s and t h e d o u b l e s c a t t e r i n g peak becomes s e p a r a t e d .

Now t u r n back t o n u c l e a r p h y s i c s . I s t h e r e a s i m i l a r e f f e c t of t h e " s h o r t - r a n g e o r d e r " i n s c a t - t e r i n g of h a d r o n s by more complex n u c l e i t h a n t h e d e u t e r o n ?

L e t u s s t a r t from a v e r y s i m p l e p u r e l y s t h e m a t i c model : a n u c l e u s i s r e p l a c e d by a system of two n u c l e o n s moving i n d e p e n d e n t l y of one a n o t h e r i n t h e f i e l d of a common c e n t r a l potential. The a m p l i t u d e of p r o t o n s c a t t e r i n g w i t h t h e e x c i t a t i o n of t h e n u c l e u s c a n b e c a l c u l a t e d a c c o r d i n g t o Glau- b e r . As can b e s e e n from F i g . 5 , t h e d o u b l e s c a t t e - r i n g s u b s t a n t i a l l y a f f e c t s t h e s h a p e of t h e e n e r g y s p e c t r u m of s c a t t e r e d p r o t o n s and i t i n c r e a s e when

one t a k e s i n t o acc:ount t h e y i e l d of p r o t o n s with sm+.ll e n e r g y l o s s

.

.

Fig.J

The i n t e n s i t y of t h e i n e l a s t i c p r o t o n - n u c l e u s s c a t - t e r i n g v e r s u s t h e e x c i t a t i o n e n e r g y of t h e t a r g e t n u c l e u s ( s c h e m a t i c c a l c u l a t i o n s ) . The d o t t - d a s h e d l i n e i s t h e s c s t t e r i r l g w i t h e j c c t i o n t h c s t r o n g l y c o r r e l a t e d n u c l e o n p a i r .

The c a l c u l a t i o n s i n t h e s c h e m a t i c n o d e l a r e a l s o s u g g e s t i v e of t h e h i g h p r o b a b i l i t y of t h e f a c t t h a t a s a r e s u l t of d o u b l e p r o t o n s c a t t e r i n g a s t r o n g l y c ~ r r e l a t e d p a i r of n u c l e o n s i s e j e c t e d from t h e n u c l e u s [23 I. Thus, we s e e i n t e r e s t i n g indicati.0n.s of t h e p o s s i b l e o v e r l a p p i n g of t h e e x i s - + i n g s i n g l e n u c l e o n q u a s i e l a s t i c knock-out t h e o r y and t h e t h e o r y of a complex p a r t i c l e p r o d u c t i o n i n hadron-nucleus c o l l i s i o n s .

R e c e n t l y Abul-hlagd and G u a r d i o l a [24 ]

h a v e e s t i m a t 6 d t h e d o u b l e s c a t t e r i n g e f f e c t s i n q u a s i e l a s t i c p r o t o n - n u c l e u s s c a t t e r i n g u s i n g a r e a - l i s t i c m a n y - p a r t i c l e n u c l e a r model. U n f o r t u n a t e l y , d u e t o i n v o l v e d c o n s i s t e n t c a i c u l a t i o r l s t h e y had t o u s e t h e c l o s u r e a p p r o x i m a t i o n . So, t h e q u e s t i o n a b o u t t h e s p e c t r u p of n u c l e a r e x c i t a t i o n i n d o u b l e s c a t t e r i n g remained u n r e s o l v e d .

11.3 - On t h e o p t i c a l model and d i s t o r t e d - w a v e a p p r o x i m a t i o n s

The DWIA a p p r o a c h i s one of t h e w i d c l y u s e d methods of n u c l e a r r e a c t i o n t h e o r y . I t s employ- ment i s c l o s e l y c o n n e c t e d w i t h t h e n o t i o n of a n o p t i c a l p o t e n t i a l . A t h i g h e n e r g i e s t h e o p t i c a l po- t e n t i a l of t h e h a d r o n - n u c l e u s i n t e r a c t i o n i s d e t e r - mined, i n a f i r s t a p p r o x i m a t i o n , from t h e hadron- n u c l e u s i n t e r a c t i o n a m p l i t u d e by means of a s i m p l e

HADRON AND NUCLEXJS SCATTERING

. . .

T h e DWBA method c a n b e d e r i v e d a s a p a r t i - c u l a r c a s e f r o m m u l t i p l e s c a t t e r i n g t h e o r y i f A >> 1 . I t s employment f o r d e s c r i b i n g t h e d i f f r a c t i o n pro- d u c t i o n of r e s o n a n c e s on n u c l e i [ 2 5 ] o r i n e l a s t i c h a d r o n - n u c l e u s s c a t t e r i n g [ 2 6 ] i s b a s e d on t h e ad- d i t i o n a l a s s u m p t i o n of t h e s i n g l e c h a r a c t e r of t h e a p p r o p r i a t e i n e l a s t i c p r o c e s s i n t h e n u c l e u s (accom- p a n i e d by m u l t i p l e e l a s t i c r e s c a t t e r i n g ) . I n t h e DWIA a p p r o a c h t h e a m p l i t u d e of t h e i n e l a s t i c p r o c e s s on t h e n u c l e u s t a k e s t h e form

where

2 & ( b ) =

-

k . -m ( i n ) + +

a n d P . (b-s ) i s t h e p r o f i l e f u n c t i o n c o r r e s -

J j

p o n d i n g t o t h e i n e l a s t i c p r o c e s s i n t h e c o l l i s i o n of t h e h a d r o n w i t h t h e j - n u c l e o n of t h e n u c l e u s .

Can t h e e x p r e s s i o n ( 1 0 ) a l s o b e u s e d t o c a l c u l a t e t h e e l a s t i c hadron-nucleus a m p l i t u d e ? I t t u r n s o u t t h a t t h e r e s u l t s t h u s o b t a i n e d c o n s i d e r a - b l y d i s a g r e e w i t h what t h e m u l t i p l e s c a t t e r i n g d i f - f r a c t i o n model p r e d i c t s ( F i g . 6 ) .

S i t e n k o [27 ] h a s s u g g e s t e d t h a t t h e e l a s t i c s c a t t e - r i n g a m p l i t u d e o b t a i n e d w i t h i n t h e framework of m u l t i p l e s c a t t e r i n g d i f f r a c t i o n t h e o r y i s r e d u c e d n o t t o Eq.(lO) b u t t o a n o t h e r e x p r e s s i o n of t h e f o l l o w i n g t y p e

F d ( q )

* 2 /

where T

.(g-z

J j

n u c l e o n s c a t t e r i n g a m p l i t u d e . C a l c u l a t i o n s by t h i s f o r m u l a a r e i n good agreement w i t h t h e r e s u l t s ob- t a i n e d i n t h e G l a u b e r model ( s e e F i g . 6 ) . Note t h a t i n e l e m e n t a r y - p a r t i c l e p h y s i c s t h e s i m i l a r ques- t i o n a b o u t t h e r e d u c t i o n of t h e g e n e r a l e x p r e s s i o n of m u l t i p l e s c a t t e r i n g a m p l i t u d e t o t h e d i s t o r t e d - wave a p p r o x i m a t i o n was c o n s i d e r e d i n t e r m s of t h e q u a s i p o t e n t i a l a p p r o a c h i n t h e problem of t h e hadron- hadron i n t e r a c t i o n ( s e e , f o r example, r e f . [ 2 8 ] ) .

The r c l e of t h e DkZA method i n t h e t h e o r y of e l a s t i c h a d r o n - n u c l e u s s c a t t e r i n g i s n o t q u i t e c l e a r . I n any c a s e a n o p t i c a l p o t e n t i a l , when cons- t r u c t e d , c a n b e u s e d f o r o b t a i n i n g t h e e l a s t i c s c a t - t e r i n g a m p l i t u d e i n many ways. A n o t h e r a s p e c t of t h e problem i s how a d e q u a t e t h e o p t i c a l p o t e n t i a l i t s e l f

is. Nowadays a l o n g w i t h wide a p p l i c a t i o n s of t h e G l a u b e r model a n i n t e n s i v e work i s b e i n g c a r r i e d o u t t o e l a b o r a t e t h e t h e o r y of hadron-nucleus o p t i - c a l p o t e n t i a l which would i n c l u d e t h e r e s c a t t e r i n g e f f e c t s . W e l l known a r e t h e works of t h e Feshbach group [ 2 9 ] where s u c h a p o t e n t i a l i s c o n s t r u c t e d t a - k i n g i n t o a c c o u n t s i n g l e and d o s b l e hadron-nucleon c o l l * . s i o n s i n t h e n u c l e u s . The method b e i n g d e v e l o - ped by F e s h t a c h and h i s c o w o r k e r s e n a b l e s o n e t o a c c o u n t f o r t h e s p i n and i s o s p i n e f f e c t s i n hadron- n u c l e u s s c a t t e r i n g and t o i n v e s t i g a t e t h e e f f e c t s of t h e s h o r t - r a n g e c o r r e l a t i o n s i n t h e n u c l e u s ( s e e F i g . 7 t a k e n from Ref. [29b]). T h i s method p r o p o s e s a c o n s i s t e n t p r o c e d u r e f o r i n c l u d i n g t h e l o n g i t u d i n a l component of momentiun t r a n s f e r i n t h e o r y : t h i s seems t o b e v e r y i m p o r t a n t f o r e x t e n d i n g t h e domain of a p p l i c a b i l i t y of m u l t i p l e s c a t t e r i n g t h e o r y t o - wards l a r g e s c a t t e r i n g a n g l e s and g r e a t i n e l a s t i c l o s s e s .

Fig.G

E l a s t i c p-12C s c a t t e r i n g a t 1 GeV ; t h e c a l c u l a t e d c u r v e s

-

V.V. BALASHOV

l o o

,

' H e l p . ~ ) ~ H e D , . ~ e 1 69 Gev/c u,::' = 152 2 Brnb Stanaora N-N

- NO dynornacol m r r e l o t ~ m s U,.,; 146mb .... r c = 0 4 frn o,., = 148mb - .- Rela soft-core m,., ; 146 mD

11.4

-

The c o i n c i d e n c e e x p e r i m e n t s become more a n d more i m p o r t a n t i n n u c l e a r i n v e s t i g a t i o n s , p r o - v i d i n g t h e most e x t e n s i v e i n f o r m a t i o n a b o u t n u c l e a r s t r u c t u r e and t h e mechanisms of n u c l e a r p r o c e s s e s . They a r e u s e d a t p r e s e n t t o test v a r i o u s models and t h e o r i e s . U n f o r t u n a t e l y , i n t h e high-energy n u c l e a r p h y s i c s t h e g e n e r a l p o s s i b i l i t i e s of t h i s method h a v e n o t been t h e s u b j e c t of s p e c i a l a n a l y s i s . No- wadays, when g r e a t e f f o r t s a r e b e i n g t a k e n i n many c o u n t r i e s toward t h e p r o v i s i o n of a p p r o p r i a t e t e c h - n i c a l equipment f o r n u c l e a r e x p e r i m e n t s , t h e s e q u e s t i o n s r e q u i r e s p e c i a l d i s c u s s i o n .

H e r e o n l y two examples a r e g i v e n i l l u s t r a - t i n g t h e i m p o r t a n c e of t h e employment o f t h i s me- t h o d i n t h e i n v e s t i g a t i o n s of t h e h a d r o n - n u c l e u s s c a t t e r i n g problem.

Example 1 : The n u c l e u s a s a s e l e c t o r of e l e m e n t a r y a m p l i t u d e s .

I t h a s l o n g been i n d i c a t e d [ 3 0 ] t h a t t h e measurement of t h e s u f f i c i e n t number of p a r t i a l t r a n s i t i o n s i n t o s e p a r a t e n u c l e a r l e v e l s i n i n e l a s - t i c and c h a r g e exchange h a d r o n - n u c l e u s s c a t t e r i n g e n a b l e s one t o o b t a i n good i n f o r m a t i o n a b o u t t h e hadron-nucleon i n t e r a c t i o n . T h i s problem r e m a i n s u r g e n t now a s t h e s p i n and i s o s p i n s t r u c t u r e of t h e

h a e o n - n u c l e o n a m p l i t u d e s a t e n e r g i e s above 1 GeV i s s t i l l p o o r l y u n d e r s t o o d .

However, t h e problem i s how t o s e p a r a t e t h e s e t r a n s i t i o n s e x p e r i m e n t a l l y a t h i g h e n e r g i e s of i n c i d e n t p a r t i c l e s . The s t u d y of t h e s p e c t r a o f t h e y - t r a n s i t i o n s i n d u c e d i n t h e t a r g e t n u c l e u s and i n d a u g h t e r n u c l e i by t h e h a d r o n - n u c l e u s i n t e r a c t i o n c a n c l a r i f y t h e mechanism of n u c l e a r e x c i t a t i o n a n d d i s s o c i a t i o n [31]. Y e t , t h i s method g i v e s o n l y t h e i n t e g r a l c h a r a c t e r i s t i c s of t h e p r o c e s s e s . The pos- s i b i l i t i e s o f t h i s method c a n g r e a t l y i n c r e a s e i f t h e Y-quanta s p e c t r u m is measured i n c o i n c i d e n c e w i t h a s c a t t e r e d p a r t i c l e . Many y e a r s a g o t h e ( p , p 1 y ) r e a c t i o n s i n t h e i n t e r m e d i a t e e n e r g y r e g i o n were q u i t e s u c c e s s f u l l y s t u d i e d j u s t i n t h i s way.

I n o r d e r t o d e t e r m i n e t h e optimum c o n d i t i o n s f o r s S x h a n e x p e r i m e n t w i t h high-energy p r o t o n s , Kara- p e t y a n , M i l e e v and T i t a r e n k o [ 2 6 ] have c a l c u l a t e d t h e t o t a l c r o s s s e c t i o n s f o r t h e e x c i t a t i o n o f se- p a r a t e l e v e l s of t h e l p - s h e l l n u c l e i and t h e c o r r e s - ponding ( p , y ) - a n g u l a r c o r r e i k a t i o n s . They i n d i c a t e d t h e most i n t e n s i v e t r a n s i t i o n s i n e a c h n u c l e u s a s w e l l a s t h e t r a n s i t i o n s whioh a r e most s e n s i t i v e t o t h e p o o r l y known component8 of t h e N-N a m p l i t u d e . Note added a f t e r t h e C o n f e r e n c e :

J. T h i r i o n and h i s c o l l a b o r a t o r s [ 5 2 ] p r e s e n t e d a t t h i s c o n f e r e n c e t h e p r e l i m i n a r y r e s a l t s i n measure- ments of e l a s t i c and i n e l a s t i c p r o t o n - n u c l e u s s c a t t e r i n g a t 1 GeV performed on " ~ a t u r n e " ( S a c l a y ) w i t h t h e e n e r g y r e s o l u t i o n 1 3 5 keV. T h i s r o r k seems t o open a wide f i e l d of d i r e c t i n v e s t i g a t i o n s i n t h e high-energy n u c l e a r s p e c t r o s c o p y .

Example 2 : On t h e s t u d y of h i g h l y e x c i t e d q u a s i - s t a t i o n a r y s t a t e s i n n u c l e i under t h e c o n d i t i o n s o f a l l t i - q u a s i e l a s t i c k i n e - mat i c s

.

I t was p r o p o s e d e a r l i e r [ 3 2 ] to u s e knock- o u t r e a c t i o n s under t h e c o n d i t i o n s of s o - c a l l e d a n t i q u a s i e l a s t i c k i n e m a t i c s f o r s t u d y i n g h i g h l y e x c i t e d q u a s i s t a t i o n a r y s t a t e s i n n u c l e i . T h i s means t h a t a n e j e c t e d p a r t i c l e s h o u l d be d e t e c t e d i n c o i n c i d e n c e w i t h a s c a t t e r e d p a r t i d l e i n t h e d i - r e c t i o n o p p o s i t e t o t h e v e c t o r of momentum t r a n s f e r . I n ~ e f . [ 3 3 ] t h e ( e , e V ) a n d ( p , p ' ) r e a c t i o n s on

HADRON AND NUCLEUS SCATTERING

...

h a v e b e e n c o n s i d e r e d . As c a n b e s e e n f r o m F i g . 8 , i n t h e c a s e o f a n t i q u a s i e l a s t i c k i n e m a t i c s t h e lar- g e b a c k g r o u n d o f t h e direct q u a s i e l a s t i c s c a t t e r i n g p r o c e s s e s a l m o s t d i s a p p e a r s a n d t h e q u a s i s t a t i o n a r y

s t a t c s a r e d i s t i n c t l y v i s i b l e .

N o t e a d d e d a f t e r t h e C o n f e r e n c e :

A t t h i s C o n f e r e n c e G.A. L e k s i n f r o m t h e Moscow I n s - t i t u t e of T h e o r e t i c a l a n d E x p e r i m e n t a l P h y s i c s i n f o r m e d t h a t h i s g r o u p h a s t r i e d t o u s e t h e a n t i - q u a s i e l a s t i c g e o m e t r y i n t h e i r l a s t work o n p i o n - n u c l e u s i n e l a s t i c s c a t t e r i n g [ 5 3 ]

.

11.5

-

T h o d e s c r i p t i o n o f h a d r o n - n u c l e u s back- w a r d s c a t t e r i n g r e q u i r e s a d i f f e r e n t a p p r o a c h t o

t h a t o f t h e d i f f r a c t i o n model.

T h e q u e s t i o n a b o u t mechanism o f t h e back- ward s c a t t e r i n g i s s t i l l u n r e s o l v e d e v e n i n t h e s i m p l e s t c a s e of p-d s y s t e m . T h e e x c h a n g e p r o c e s s e s seem t o p l a y a n i m p o r t a n t r o l e h e r e . However i t i s known t h a t t h e n u c l e o n p i c k - u p model i s i n c o n s i s - t e n t a t t h e e n e r g i e s n e a r 1 GeV. Kerman a n d K i s s l i n - g e r [34 ] p u t f o r w a r d a n i d e a o f t h e r e g g e o n e x c h a n g e mechanism. R e c e n t l y Sharma, B h a s i n a n d Mitra [ 3 5 ] , p r o c e e d i n g f r o m t h i s i d e a , h a v e c o n s t r u c t e d t h e p-d b a c k w a r d s c a t t e r i n g a m p l i t u d e t a k i n g i n t o a c - c o u n t a set o f n u c l e o n i s o b a r s f r o m PI1(1470) t o

T h e r e s u l t s o f c a l c u l a t i o n s i n terms o f t h i s model a r e shown i n F i g . 9

Backward p-d s c a t t e r i n g a t 1 GeV f r o m Ref. [35] ; a ) N+N* e x c h a n g e c o n t r i b u t i o n ; b ) N e x c h a n g e c o n t r i b u t i o n o n l y .

A n o t h e r model a l o n g t h e s e l i n e s was p r o p o s e d by C r a i g i e a n d W i l k i n [ 3 6 ] who p o i n t e d o u t t h a t a t p r o t o n e n e r g i e s belov! 1 GeV some p i o n i n t e r m e d i a t e s t a t e s may b e i m p o r t a n t :

Now t h i s model i s b e i n g i n t e n s i v e l y e l a b o r a t e d by K o l y b a s o v a n d S m o r o d i n s k a y a [ 3 7 1.

V. V. BALASHOV

R e c e n t l y Komarov, Kosyrev, R e s h e t n i k o v and Savchenko [38 ] i n Dubna h a v e measured t h e e n e r - gy dependence for e l a s t i c p-d s c a t t e r i n g i n t h e i n - c i d e n t p r o t o n e n e r g y r a n g e 360-670 MeV

.

One c a n h a r d l y e x p e c t t h a t i n a broad e n e r g y i n t e r - v a l t h e r e e x i s t s one dominant s c a t t e r i n g mechanism.

As f o r t h e C r a i g i e - X i l k i n mechanism, a t a p r o t o n e n e r g y of a b o u t 700 MeV t h e momentum of t h e i n t e r - m e d i a t e p i o n c o r r e s p o n d s t o t h e (3-3) resonance.

T h i s s i n g u l a r i t y c a n p r o b a b l y c a u s e a dominant con- t r i b u t i o n from t h i s mechanism i n t h i s r e g i o n ( s e e F i g . 10).

Note added a f t e r t h e C o n f e r e n c e :

The problem of t h e backward p-d s c a t t e r i n g h a s been d i s c u s s e d i n t h e c o n t r i b u t i o n s [54,55] t o t h i s Con- f e r e n c e .

F i g . 1 0

E n e r dependence of t h e backward p-d s c a t t e r i n g f r o m Ref. E B ] . The e x p e r i m e n t a l d a t a a r e t a k e n from a num- b e r of p a p e r s . The d a s h e d l i n e c o r r e s p o n d s t o t h e c a l - c u l a t i o n a c c o r d i n g t o t h e C r a i g i e - W i l k i n model.

The problem of backward p-d s c a t t e r i n g i s c l o s e l y c o n n e c t e d w i t h t h e problem of q u a s i e l a s t i c knock-out of f a s t d e u t e r o n s i n t h e f o r w a r d d i r e c t i o n i n t h e p r o t o n - n u c l e u s i n t e r a c t i o n s [39]. S p e c i a l c o i n - c i d e n c e e x p e r i m e n t s on t h e measurement of " f o r b i d d e n "

t r a n s i t i o n s r e s u l t i n g from s u c h exchange p r o c e s s e s (e.g. t h e t r a n s i t i o n s w i t h AT= 1 i n t h e ( p , p d ) r e a c - t i o n ) a r e of e x t r e m e i m p o r t a n c e , i n p a r t i c u l a r , f o r

t k d i n a n c n t of t h e c o n c e p t of c l u s t e r e f f e c t i v e num- b e r s .

I 1 1

-

Wide e x p e r i m e n t a l i n v e s t i g a t i o n s of nu- c l e u s - n u c l e u s c o l l i s i o n s a t h i g h e n e r g i e s have be- come p o s s i b l e w i t h t h e r e a l i z a t i o n of t h e methods f o r o b t a i n i n g beams o f r e l a t i v i s t i c d e u t e r o n s and h e a v i e r i o n s i n a number of l a b o r a t o r i e s (Dubna, P r i n c e t o l l , B e r k e l e y ) [40]. The main o b j e c t i v e of

t h e c u r r e n t i n v e s t i g a t i o n s i n t h i s f i e l d is t o e l u - c i d a t e t h e q u a l i t a t i v e a s p e c t s of t h e mechanism of n u c l e u s - n u c l e u s c o l l i s i o n p r o c e s s e s a n d t o e l a b o r a t e t h e program of i n v e s t i g a t i o n s . A t p r e s e n t a t t e n t i o n i s c o n c e n t r a t e d on s u c h q u e s t i o n s which a r e c o n c e r - ned w i t h p o s s i b l e n o v e l p h y s i c a l phenomena i n nu- c l e a r c o l l i s i o n s . I n p a r t i c u l a r c o l l i s i o n s of r e l a - t i v i s t i c n u c l e i i n v o l v e t h e p o s s i b i l i t y of e f f e c t s of t h e a c c u m u l a t i o n of a l a r g e p o r t i o n of t h e i n c i - d e n t n u c l e u s e n e r g y on some hadron-product of r e a c - t i o n [41 ] ( r e c e n t l y i n Dubna [42 1 measurements were made of t h e p i o n s p e c t r u m under bombardment of cop- p e r n u c l e i by r e l a t i v i s t i c d e u t e r o n s ; t h e e n e r g y of s e c o n d a r y p a r t i c l e s e x c e e d s t h e k i n e m a t i c boundary c o r r e s p o n d i n g t o p i o n p r o d u c t i o n by a s i n g l e d e u t e - r i u m n u c l e o n k N e v e r t h e l e s s , c o m p r e h e n s i v e measure- ments of t h e t o t a l c r o s s s e c t i o n s f o r t h e i n t e r a c - t i o n of complex p a r t i c l e s w i t h n u c l e i and of t h e d i f f e r e n t i a l e l a s t i c s c a t t e r i n g c r o s s s e c t i o n s i n a wide r a n g e of a n g l e s seem t o b e t h e a b s o l u t e l y ne- c e s s a r y s t a k e of development of t h e p h y s i c s of r e l a - t i v i s t i c n u c l e i .

111.1

-

I n 1957, A k h i e z e r and S i t e n k o [ 4 3 ] e l a b o - r a t e d t h e t h e o r y of f a s t d e u t e r o n i n t e r a c t i o n w i t h complex n u c l e i . Even a t p r e s e n t i t c a n b e u s e d a s a s i m p l e g u i d e f o r t h e q u a l i t a t i v e d e s c r i p t i o n of n u c l e u s - n u c l e u s d i f f r a c t i o n a t h i g h e n e r g i e s .

The A k h i e z e r - S i t e n k o model assumes t h e m c l e u s a s absolutely b l a c k f o r e a c h of t h e bombarding n u c l e- ons. I t i s i n t e r e s t i n g t o examine t h e c o n n e c t i o n between t h i s model and t h e g e n e r a l e x p r e s s i o n f o r t h e d e u t e r o n s c a t t e r i n g a m p l i t u d e c o n s t r u c t e d by gene- r a l i z i n g t h e G l a u b e r model i n t h e way of E q . ( 6 ) .

NADROFION AND NUCLEUS SCATTERING

. . .

Tekou h a s s h o w [ 4 4 ] t h a t t h e Akhiezer-Sitenko lao- d e l d o e s n o t i n c l u d e a p o r t i o n of v i r t u a l n u c l e a r e x c i t a t i o n of a s p e c i a l kind when e x c i t a t i o n I S cau- s e d by one of the deuteron nucleons and e l i m i n a t e d by t h e o t h e r . I f t h e corresponding c o r r e c t i o n s a r e n e g l e c t e d t h e Glauber model t u r n s i n t o Akhiezer- S i t e n k o ' s d i f f r a c t i o n model. U n f o r t u n a t e l y , t h e c l e a r l i m i t s of a p p l i c a b i l i t y of both models have n o t been f m n d , however.

Some a u t h o r s performed d i r e c t c a l c u l a t i o n s of t h e high-energy deuteron-nucleus s c a t t e r i n g ba- s e d on t h e g a n e r a l i z e d e l a u b e x model ( s e e e.g. Ref.

t453). The comparison with experiment rloes not show any unexpected f e a t u r e s of t h e p r o c e s s , However t h e e x i s t i n g experimental d a t a a r e t o o poor t o make d e f i n i t e conclusions.

One of t h e important p r a c t i c a l t a s k s of t h e t h e o r y of nucleus-nucleus d i f f r a c t i o n s c a t t e r i n g i s t o s t u d y t h e c o n d i t i o n s i n which ono of t h e c o l - l i d e d n u c l e i may b e considered a s an elementary

p a r t i c l e . Barashenkov a t a l . [46] exanined t h i s problem i n connection with t h e descriptfron of t o - t a l i n e l a s t i c c r o s s - s e c t i o n s f o r a-particle-nucleus i n t e r a c t i o n s . The e f f e c t s of simultaneous i n t e r a c - t i o n of two o r more a - p a r t i c l e nucleons with d i f f e - r e n t nucleons of t h e t a r g e t nucleus have proved t o b e n e g l i g i b l e i n t h e c a s e R >> R,

.

The P a u l i e x c l u s i o n p r i n c i p l e f o r b i d s t h e c l o s e approach of two n u c l e i . One c a n t a k e t h i s re- p u l s i o n i n t o account i n a p u r e l y phenomenological manner by i n t r o d u c i n g a r e p u l s i v e c o r e i n t o t h e l o - c a l o p t i c a l p o t e n t z a l . However, t h e problem c a n a l s o b e s o l v e d i n a n o t h e r way.

I n Ref. [49 1 t h e e f f e c t i v e nucleus-nucleus i n t e r a c t i o n p o t e n t i a l was c o n s t r u c t e d a s t h e susa of two terms :

Were Vo is t h e u s u a l p o t e n t i a l c o r r e s p o n d i n g t o t h e a v e r a g e p o t e n t i a l of t h e two-body i n t e r a c t i o n between nucleons of t h e two n u c l e i . The second term is included i n t h e Hamiltonian i n o r d e r t o remove t h e s t a t e s f o r b i d d e n by t h e P a u l i p r i n c i p l e :

The requirement of the o r t h o g o n a l i t y of t h e two- nucleus wave f u n c t i o n t o t h e wave f u n c t i o n s / p k ) of f o r b i d d e n s t a t e s t u r n s o u t t o be very r i g i d and p r a c t i c a l l y f i x e s t h e phase s h i f t s f o r nucleus- nucleus b c a t t e r i n g i n a r a t h e r wide energy region.

When t h e f u n c t i o n s

IqA)

o b t a i n e d w i t h t h e ' r e s o n a t i n g - ~ o u p metbod.

Neudatchin and h i s c w r k e r s [ 5 0 3, s t a r t i n g from t h e work by S a i t o 1491, have pus forward a n a t - in photoemisslon~ ^& similar Abul-Magd t r a c t i v e i d e a about t h e p o s s ~ b i l i t y of d e s c r i b i n i :

t h e systems a-a

,

n u c l e i w i t h a l o c a l o p t i c a l p o t e n t i a l . I n i t s cons- a n t i d e u t e r o n a b s o r p t i o n by n u c l e i .

t r u c t i o n t h e y proceeded from t h e f a c t t h a t i n t h e

111.2

-

I n r e c e n t y e a r s many a t t e m p t s have been made t o c o n s t r u c t a phenornenoltagical o p t i c a l poten-

t i a l f o r deuteron-nucleus and %e-nucleus s c a t t e - r i n g ( s e e f o r example Ref. 1481). What a r e t h o f~alrr

*Cures of t h i s p o t e n t i a l ?

c a s e of i n t e r a c t i o n between two n u c l e i t h e number of t h e f o r b i d d e n s t a t e s i s g r e a t . T h i s f o r b i d d a n c e determines t h e b a s i c f e a t u r e s of t h e l o c a l p o t e n t i 8 1 : i t is very deep. F o r s c a t t e r i n g t h e optimum parameters of t h e r e a l p a r t of t h e p o t e n t i a l a r e : V = ^{125 MeV ; R} 0 ^{T 1.76 fm ; a} = ^{0.66 fro}

.

The u s e of t h e deep l o c a l p o t e n t i a l i s e q u i v a l e n t t o a g r e a t e q e n t t o t h e u s e of s h a l l o w p o t e n t i a l s with t h e a d d i t i o n a l requirement of t h e o r t h o g o n a l i t y of t h e continuum wave f u n c t i o n t o t h e