LOW ENERGY PIONS IN NUCLEAR PHYSICS

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LOW ENERGY PIONS IN NUCLEAR PHYSICS

Mannque Rho

To cite this version:

Mannque Rho. LOW ENERGY PIONS IN NUCLEAR PHYSICS. Journal de Physique Colloques,

1972, 33 (C5), pp.C5-155-C5-169. �10.1051/jphyscol:1972512�. �jpa-00215114�

JOURNAL DE PHYSIQUE C a l l o q u e C5, s u p p l e m e n t a u n o 8 - 9 , Tome 33, ~ o O t - S e p t e m b r e 1 9 7 2 , p a g e C5-155

LOW ENERGY PIONS I N NUCLFAR PHYSICS

Mannque RiiO

S e r v i c e d e P h y s i q u e T h e o r i q u e , CEN-Saclay

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o n t h e l o n g e s t r a n g e p a r t o f i t . T h u s t h e p i o n p l a y s a n e s s e n t i a l r o l e h e r e j u s t a s t h e s m a l l mass o f p i o n p l a y s a c r u c i a l r o l e i n t h e t h e o r i e s o f 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 . The a i m o f t h i s t a l k i s t o d i s c u s s t h e r e l e v a n c e o f p i o n s t o n u c l e a r p h y s i c s i n as u n i f i e d manner a s i t is p o s s i b l e t o - d a y . L e t me f i r s t e x p l a i n what I mean by a u n i f i e d ma.-iner. T h e p i o n is a p s e u d o s c a l a r o b j e c t , s p i n zero a n d p a r i t y - 1 a n d may b e d e s c r i b e d b e s i d e s i t s quantum numbers by t h e mmentum f o u r v e c t o r

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means s i m p l y t h a t i n my metric qL: i s a p o s i t i v e N u c l e a r P h y s i c s b a s d e v e l o p e d o n t h e c o n -

q u a n t i t y . N o w i f a l l t h e n u c l e o n s a r e i n s i d e a nu- c e p t o f p o t e n t i a l . Much o f low-energy p r o p e r t i e s

c l e u s ( i n o t h e r w o r d s , w i t h i n t h e F e r m i s e a ) , t h e n s t u d i e d i n n u c l e a r l a b o r a t o r i e s d e p e n d i n t i m a t e l y

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1972512

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we a r e i n t e r e s t e d i n t h e phenomena where t h e l o n g r a n g e one-pion-exchange p i c t u r e i s r e l e v a n t .

T h e r e h a s been a c o n s i d e r a b l e p r o g r e s s i n b o t h n u c l e a r and s u b n u c l e a r p h y s i c s i n d e s c r i b i n g t h e t h r e s h o l d p r o c e s s i n v o l v i n g n u c l e o n s s t a r t i n g from t h e s o f t - p i o n l i m i t . L i k e t h e s o f t - p h o t o n f o r which low-energy theorems a r e w e l l known, t h e s o f t p i o n l i m i t g i v e s u s a model-independent r e s u l t , q u i t e s i m i l a r i n many a s p e c t s t o t h e s o f t - p h o t o n r e s u l t s . The major p r o g r e s s c o n c e r n s t h e n t h e l i n k between t h i s p o i n t and t h e p h y s i c a l t h r e s h o l d . Now i t seems r e a s o n a b l e t o t h i n k t h a t i f one c a n go i n t h e q d i r e c t i o n int h e / q 4

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T h i s t a l k d e a l s t h u s on a same f o o t i n g t h e p i o n which i s exchanged between n u c l e o n s and t h e p i o n which i s p r o d u c e d o r c a p t u r e d o r s c a t - t e r s by n u c l e o n s o r n u c l e i , The major a d v a n t a g e d t e p i o n i n n u c l e a r p h y s i c s i s t h a t i t g e n e r a t e s t h e p o t e n t i a l which g o v e r n s a g r e a t d e a l of n u c l e a r dy- namics a s w e l l a s i t c a n b e u s e d a s a p r o b e , d i f f e - r e n t from t h e u s u a l n u c l e a r o r e f e c t r o m a g n c t i c pro- bes.

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T h i s d e s c r i p t i o n may b e t o o c r u d e a n d p e r h a p s t o o model-dependent f o r u s t o t a k e i t s e - r i o u s l y , But i t may be c o r r e c t a t l e a s t q u a l i t a t i - v e l y . How c a n we check t h e s e f e a t u r e s ? I f we d i s - t u r b weakly a two- o r many-nucleon system, i.e.

a n u c l e u s , t h e n f i r s t o f a l l some e f f e c t s may show t h e s e meson exchange phenomena and s e c o n d l y t h e y may b e s e n s i t i v e o n l y t o t h e one-pion exchange do- main. One o f s u c h e f f e c t s we know i s t h e meson- exchange c u r r e n t i n t h e e l e c t r o m a g n e t i c and weak p r o c e s s e s i n n u c l e i , I s h a l l t r y t o show you whe- t h e r we c a n combine a l l t h e s e c o n c e p t s ( s o f t - p i o n s , meson c l o u d

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d i p o l e t r a n s i t i o n . One c a n r e a d i n t e x t books t h a t t h e p r e s e n c e of exchange p o t e n t i a l s r e q u i r e s t h e p r e s e n c e of meson exchange m u l t i - p a r t i c l e c u r r e n t s . I n i t s a b s e n c e , t h e c u r r e n t would n o t s a t i s f y t h e c o n t i n u i t y e q u a t i o n . Thus t h e m a g n e t i c moment c a l - c u l a t e d w i t h t h e u s u a l s i n g l e - p a r t i c l e o p e r a t o r s i s e x p e c t e d t o d i f f e r from t h e t r u e v a l u e , t h e e x p e r i - m e n t a l l y measured d i p o l e moment. The same would be t r u e a l s o f o r t h e t r a n s i t i o n m a t r i x element.

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L e t u s c o n s i d e r t h e s i m p l e s t c a s e r e c e n t - l y s t u d i e d by R i s k a and Brown [2 ] namely t h e t h r e s h - o l d c a p t u r e of n e u t r o n

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A t low e n e r g i e s , t h i s p r o c e s s g o e s p r e d o m i n a n t l y v i a t h e i s o v e c t o r m a g n e t i c d i p o l e o p e r a t o r and b r i n g s o u t t h e main f e a t u r e we want t o s t u d y . F o r many y e a r s , a d i s c r e p a n c y of a b o u t 1 0 % i n t h e c r o s s - s e c - t i o n h a s been a g l a r i n g embarrassment t o t h e n u c l e a r t h e o r i s t s . More s p e c i f i c a l l y i f one t a k e s t h e conven- t i o n a l s i n g l e - p a r t i c l e o p e r a t o r and a s o p h i s t i c a t e d wave f u n c t i o n s e r i o u s l y , a l l t h a t t h e o r i s t s c a n do i s

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whereas e x p e r i m e n t a l i s t s t e l l u s t h a t i t i s

S o t h e r e i s a d i s a g r e e m e n t . Can t h i s 9.5% d i s c r e p a n - c y which one u s u a l l y a s c r i b e s t o t h s meson exchange c o r r e c t i o n be d e s c r i b e d by one-pion exchange and s o f t - p i o n d e s c r i p t i o n of t h e exchanged p i o n ? The c o r r e c t i o n c a l c u l a t e d by R i s k a and Brown which co- mes o u t t o be m i r a c u l o u s l y c l o s e t o t h e d i s c r e p a n c y

( i . e . 9.5%) a n s w e r s t h e s e q u e s t i o n s , t h e f i r s t a f f i r m a t i v e l y and t h e second more o r l e s s a l s o . H e r e i s how.

I f t h e one-pion-exchange dominance makes s e n s e , t h e n i n t h e s m a l l photon momentum l i m i t ( o r i n t h e s o f t - p i o n l i m i t 1 one would e x p e c t t h a t o n l y t h e f i r s t two g r a p h s i n F i g . 5 c o n t r i b u t e s i g n i f i - c a n t l y and t h e l a s t two n e g l i g i b l y f o r t h e i s o v e c - t o r t r a n s i t i o n ( t h i s i s t h e consequence of low-ener- gy t h e o r e m s ) . I f t h e wave f u n c t i o n s f o r b o t h t h e bound and unbound s y s t e m s w e r e i n r e l a t i v e S s t a t e

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( i . e . 3~ and 1 So r e s p e c t i v e l y ) , t h e n F i g . 5 c d )

F i g . 5

V s t a n d s f o r a v e c t o r meson (p o r 0 ) and N* nu- c l e o n i s o b a r s . Note t h a t F i g . ( a ) c a n a l s o b e g i v e n by a p a i r graph.

where t h e ( 3 , 3 ) r e s o n a n c e ( h e r e a f t e r c a l l e d h ( 1 2 3 6 ) ) i s t a k e n f o r N* d o e s n o t c o n t r i b u t e and F i g . S ( c ) is s m a l l , s o t h e low e n e r g y theorem would be a v e r y good d e s c r i p t i o n . The 3 ~ 1 s t a t e o f d e u t e r o n i n v a - l i d a t e s scnewhat t h i s n i c e f e a t u r e . N o n e t h e l e s s e v e n w i t h t h e f u l l components of t h e wave f u n c t i o n , a l r e a d y 6.6% comes from t h e f i r s t two g r a p h s and t h e r e s t from F i g . S ( d ) . T h a t t h e n u c l e o n r e s o n a n c e A c o n t r i b u t e s non n e g l i g i b l y v i a t h e D - s t a t e i n d i - c a t e s t h a t i n such a s i t u a t i o n , t h e p i o n i s no l o n - g e r s o s o f t . T h i s i s n o t s u r p r i s i n g , s i n c e t h e D- s t a t e c a n b e g e n e r a t e d by t h e OPEP t e n s o r f o r c e , s o t h i s s o r t of c o n t r i b u t i o n amounts e s s e n t i a l l y t o a two-pion exchange, e a c h o f t h e p i o n s f a r from t h e s o f t - p i o n p o i n t . What c o u n t s h e r e i s t h a t t h i s c a n be c a l c u l a t e d a s shown by t h e r e s u l t . T h i s i s n o t always t h e c a s e however a s we w i l l s e e below.

b. L e s s S p e c t a c u l a r , b u t S t i l l I m p r e s s i v e The above s u c c e s s n a t u r a l l y s u g g e s t s t h a t o n e c o u l d e x p e c t s i m i l a r a g r e e m e n t s i n s t a t i c magne- t i c moments. The d e u t e r o n m a g n e t i c moment i s i s o - s c a l a r , s o i t i s t o o d i f f i c u l t from t h e p o i n t of view r am t a k i n g . The o t h e r n u c l e i e x t e n s i v e l y s t u - d i e d r e c e n t l y a r e t h e i s o d o u b l e t s 3~ and He 3

.

T r y i n g t o u n d e r s t a n d t h e m a g n e t i c moments of t h e s e two n u c l e i i s r e a l l y a n o l d problem. What m o t i v a t e s u s t o l o o k i n t o t h e s e a g a i n i s t h i s . The above exam- p l e s u g g e s t s t h a t t h e two-body c u r r e n t i s r e l i a b l y

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g i v e n by s o m e t h i n g l i k e F i g . 5 , g e n e r a l i z e d t o a r b i - t r a r y i n i t i a l and f i n a l two-body s t a t e s . I t a p p e a r s a l s o r e a s o n a b l e t o a p p r o x i m a t e t h e exchange c u r r e n t by a two-body c u r r e n t a l o n e even i n t h e t r i - n u c l e o n systcm. Then t h e mechanism s t u d i e d above, g e n e r a l i - z e d t o a n a r b i t r a r y s t a t e , must b e a p p l i c a b l e t o t h e t h r e e - n u c l e o n d o u b l e t s . F u r t h e r m o r e , t h e r e c e n t de- velopment of Faddeev t e c h n i q u e a l l o w s one t o o b t a i n r e l i a b l e t h r e e - n u c l e o n bound state wave f u n c t i o n s which were n o t p o s s i b l e b e f o r e .

T h e s e two i n g r e d i e n t s were b r o u g h t t o g e - t h e r by H a r p e r , K i m , T u b i s and ~ h o f 3

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i n n i c e agreement w i t h ( 5 ) . The i s o s c a l a r exchange moment i s a d i f f i c u l t t h i n g t o c a l c u l a t e b e c a u s e i t i s small and g e t s i m p o r t a n t c o n t r i b u t i o n from heavy mesons, s o o u r number may n o t be very m e a n i n g f u l , b u t t h e agreement w i t h t h e i s o v e c t o r moment i s q u i t e s i g n i f i c a n t . One f i n d s t h a t t h e c o n t r i b u t i o n from F i g . J ( d ) becomes more s u b s t a n t i a l , amounting t o a b o u t 4% of t h e t o t a l exchange c o r r e c t i o n , t h a n i n t h e slow n e u t r o n c a p t u r e c a s e . The moral h e r e i s t h a t t h e one-pion-exchange p i c t u r e i s s t i l l good b u t

t h e low-energy theorem, i n p a r t i c u l a r , t h e s o f t - p i o n d e s c r i p t i o n seems weakencd a l i t t l e b e c a u s e o f

a p o s s i b l y s i z a b l e A c o n t r i b u t i o n ( s e e , however, t h e remark made i n t h e s u b s m r i o n d. ).

I n a n t i c i p a t i o n of what i s t o come, I ( 2 ) must s a y t h a t t h i s r e m a r k a b l e agreement f o r

6 p V i s more d i s t u r b i n g t h a n p l e a s i n g . The r e a s o n i s t h z t one would e x p e c t 6$) t o o v e r s h o o t t h e ex- p e r i m e n t a l d i s c r e p a n c y more t h a n t h e r e s u l t ( 6 ) .

c . S t i l l S u c c e s s f u l

Another p l a c e q h c r e t h e one-pion-exchange a p p r o x i m a t i o n seems t o work w e l l i s i n p r e d i c t i n g t h e anomalous o r b i t a l moment i n heavy n u c l e i . Long t i m e a g o ?5], i t was p r e d i c t e d on t h e b a s i s of t h e p i a n i c exchange c u r r e n t o f F i g . S ( b ) ( o t h e r s d o n o t c o n t r i b u t e ) t h a t a n u c l e o n i:: n u c l e u s h a s a n o r b i - t a l gyromagnetic r a t i o which i s d i f f e r e n t by a b o u t 10% from t h a t of a f r e e n u c l e o n : i . e . ,

e f f

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w i t h ge 1 and 6 g e g 0.1

.

.

Sge ( p r o t o n )

=

(81 Sge ( n e u t r o n )

=

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T h e r e a r e some c o n t r o v e r s i e s a s t o whether t h i s r e m a r k a b l e s u c c e s s of t h e one-pion-exchange t e r m i s n o t a c c i d e n t a l . F o r i n s t a n c e , F u j i t a e t a 1 [ 7 ] a r g u e th.zt t h e mesonic c o n t r i b u t i o n t o Sge s h o u l d be r e a l l y 0.2 r a t h e r t h a n 0.1 and what t h e cxperlmentersmeasure i s n o t t h e mesonic c o r r e c t i o n a l o n e b u t t h e mesonic c o r r e c t i o n p l u s a c o r r e c t i o n coming from s h o r t - r a n g e c o r r e l a t i o n which i s c l a i - med t o b e a b o u t -0.1

.

e x c h a n g e d , t h e r e is n o s y s t e m a t i c way o f d i s e n t a n - g l i n g s h o r t - r a n g e c o r r e l a t i o n a n d meson-exchange e f f e c t s , a p o i n t r e p e a t e d l y e m p h a s i z e d by J . S . B e l l

[81 .

d. D i s a s t e r : Gamow-Teller Matrj.,: E l e m e n t T h i n g s a r e n o t a l w a y s as r o p y a s t h e y l o o k e d a b o v e . L e t u s r e p l a c e t h e e l e c t r o m a g n e t i c c u r r e n t by t h e weak a x i a l c u r r e n t w i t h a s m a l l f o u r momentum k as a n e x t e r n a l d i s t u r b a n c e . T h i s i s t h e c a s e f o r e d e c a y , more p r e c i s e l y a Gamow-Teller m a t r i x e l e m e n t . I f t h e a x i a l c u r r e n t i s r e p r e s e n t e d b y t h e w i g g l y l i n e i n F i g . 5 ( w i t h no r e s t r i c t i o n s o n t h e i n i t i a l a n d f i n a l s t a t e s ) , t h e n t h e g r a p h ( b ) d o e s n o t c o n t r i b u t e a n d ( a ) i s n e g l i g i b l e , s o t h e c o n t r i b u t i o n s come m a i n l y f r o m t h e g r a p h s ( c ) a n d ( d ) . I t s h o u l d b e p o i n t e d o u t t h a t t h e r e i s a g r e a t d e a l o f d i f f e r e n c e b e t w e e n t h e a x i a l c u r r e n t a n d t h e e l e c t r o m a g n e t i c c u r r e n t : w h e r e a s F i g s . S ( c ) a n d ( d ) a p p e a r a s c o r r e c t i o n s t o t h e s o f t - p i o n r e - s u l t s i n t h e e l e c t r o m a g n e t i c c a s e , t h e y c o n s t i t u t e some o f t h e main c o n t r i b u t i o n s g i v e n by t h e s o f t - p i o n t h e o r e m i n t h e a x i a l c a s e . One c a n d e m o n s t r a t e t h i s u s i n g t h e PCAC h y p u t h e s i s t h a t we s h a l l n o t g o i n t o [9]. L e t me j u s t m e n t i o n t h a t what i s n e e d e d i s s o m e t h i n g l i k e (-

a

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p r o d u c t i o n a m p l i t u d e i n N-N c o l l i s i o n . I t t h u s r e q u i r e s a p-wave a m p l i t u d e . I n t h e a p p r o x i m a - t i o n of o n e - p i o n e x c h a n g e , t h i s i n v a l v e s s i m p l y t h e p-wave x-N s c a t t e r i n g a m p l i t u d e . Or i n t e r m s o f p i o n p r o d u c t i o n v i a a n a x i a l c u r r e n t , t h e m a i n c o n - t r - ; b u t i o n comes f r o m F i g s . S ( c ) a n d ( d ) . T h u s i f o n e c o n f i n e s o n e s e l f t o o n e - n i o n e x c h a n g e a n d i f t h e p i o n c a n be c o n s i d e r e d t o b e s o f t , t h e n F i g s . 5 c c ) a n d ( d ) a r e a m o d e l - i n d e p e n d e n t d e s c r i p t i o n o f t h e m e s o n i c c u r r e n t s i n t h e Gamow-Teller m a t r i x e l e m e n t .

An a p p l i c a t i o n o f t h i s t h e o r y t o t h e t r i t o n e d e c a y

was made by F i s c h b a c h , H a r p e r , Kim, T u b i s a n d Cheng [ l o ] , u s i n g t h e same F a d d e e v s o l u t i o n w h t c h p r o v e d t o b e s u c c e s s f u l f o r t h e m a g n e t i c moment. T h e d i s - c r e p a n c y b e t w e e n t h e e x p e r i m e n t a l G-T m a t r i x e l e - ment a n d t h e s i n g l e - p a r t i c l e o p e r a t o r v a l u e i s kn3wn t o b e

G ~

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b a s e d o n t h e g r a p h s o f F i g . S ( c ) w i t h V r p a n d

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Even g r a n t i n g a l a r g e e r r o r t o t h e e x p e r i m e n t a l m a t r i x e l e m e n t w h i c h i s i t s e l f somewhat c o n t r o v e r - s i a l , b c 2 ) o f 15% seems r i d i c u l o u s l y huge. S i n c e i t i s t h e A w h i c h i s r e s p o n s i b l e , t h e r e m u s t b e s o m e t h i n g wrong i n t r e a t i n g t h i s o b j e c t .

e. A Way Out

G r e e n a n d S c h u c a n [11 ] p r o p o s e d a way o u t o f t h i s d i f f i c u l t y by making t h e f o l l o w i n g o b s e r v a - t i o n . A l t h o u g h i t l i e s 300 MeV a b o v e t h e n u c l e o n , A i s a n e x c i t e d s t a t e o f t h e l a t t e r . T h e r e f o r e i n c a l c u l a t i n g m e s o n i c c o r r e c t i o n s , b o t h s h o u l d b e t r e a t c d on a same f o o t i n g . Not o n l y F i g . 5 ( d ) i n whicit t h e A c o o r d i n a t e i s e s s e n t i a l l y t r a n s f o r m e d away, b u t a l s o t e r m s f r o m w h i c h i t c a n n o t b e t r a n s - f o r m e d away s h o u l d b e t a k e n i n t o a c c o u n t e x p l i c i t l y . A s a c o n s e q u e n c e , t h e e f f e c t i v e c u r r e n t s h o u l d b e r e n o r m a l i z e d a c c o r d i n g l y . They d e m o n s t r a t e t h e i r p o i n t by a s i m p l e model i n w h i c h t h e A d e g r e e of f r e e d o m i s p u t i n a g e n e r a l i z e d wave f u n c t i o n . T h i s s h o u l d t h e c c u t down t h e A c o n t r i b u t i o n .

A n e e d f o r s u c h r e n o r m a l i z a t i o n i s c l c a r . B u t u n f o r t u n a t e l y a s i m p l e model c o n s i d e r a t i o n i s n o t good e n o u g h f o r a q u a n t i t a t i v e c a l c u l a t i o n o f s m a l l e f f e c t s . I t i s n o t c l e a r how t o d o t h i s f o r t h e e f f e c t i v e two-body c u r r e n t i n a s a t i s f a c t o r y way. T h e C u t k o s k y model c o n s i d e r e d a b o v e t a k e s c a r e o f t h i s p r o b l e m f o r t h e d e u t e r o n , b u t a g e n e r a l i z a - t i o n t o many-body s y s t e m s h a s n o t b e e n s t u d i e d y e t . Any a t t e m p t f o r a s a t i s f a c t o r y t h e o r y s h o u l d l e a v e t h e m a g n e t i c moment r e l a t i v e l y u n t o u c h e d , w h i l e re- d u c i n g by a l a r g e amount t h e & d e c a y m a t r i x e l e m e n t . T h i s i s n o t a c h i e v e d i n t h e G r e e n - S c h u c a n p i c t u r e .

f . E x p e r i m e n t a l P r o b e o f E x c h a n g e C u r r e n t s A s a way o f j u s t i f y i n g my d i s c u s s i o n o f t h e v i r t u a l p i o n e f f e c t s i n t h i s c o n f e r e n c e a n d a l s o c o n n e c t i n g t h e a b o v e domain t o t h e r e a l p i o n w o r l d , l e t u s see w h e t h e r t h e r e are a n y e x p e r i m e n t s w h i c h b e a r d i r e c t l y on t h e e f f e c t s t h a t I h a v e b e e n t a l k i n g a b o u t . I t s e e m s f a i r t o s a y t h a t a t t h i s moment t h e r e e x i s t s n o s u c h e x p e r i m e n t w h i c h i s c o n -

LOW ENERGY PIONS

...

v i a c i n g enough. But t h e r e i s some i n d i c a t i o n t h a t w i t h i m a g i n a t i o n and h a r d work, one might f i n d some.

An i n s t r u c t i v e example i s t h e anomalous gyromagnetic r a t i o

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where z l ( w ) i s t h e n u c l e a r d i p o l e p h o t o a b s o r p t i o n

Y

c r o s s s e c t i o n . The o r i g i n of t h i s f o r m u l a i s t h e Bethe-Levinger d i p o l e sum r u l e . The exchange c o r r e c - t i o n ( t o t h e TKR sum r u l e ) i n t h i s sum r u l e i s found t o b e r e l a t e d t o t h e q u a n t i t y 2bge

.

where

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p r o d u c t i o n o f p i o n s from p and n r e s p e c t i v e l y and

$ p h o t o a b s o r p t i o n c r o s s - s e c t i o n i n n u c l e u s A

=

and

IEl

The r i g h t hand s i d e of Eq. ( 1 0 ) i s of c o u r - s e known, t h e i n t e g r a l b e i n g f a i r l y w e l l s a t u r a t e d by t h e g i a n t d i p o l e r e s o n a n c e . Eq.(lO) would t h u s l e a d t o b g e s 0 . 2 a l r e a d y mentioned above. The r i g h t - h a n d s i d e of E q . ( l l ) a s i t s t a n d s d o e s n o t seem t o b e m e a s u r l b l e . But i t i s s u g g e s t i v e of t h e k i n d of sum r u l e o n e c a n w r i t e down.

S i m i l a r a p p r o a c h e s a r e p o s s i b l e f o r meso- n i c c o r r e c t i o n s i n Gamow-Teller m a t r i x e l e m e n t s . One s u g g e s t i o n [ 1 3 ] i s t o r e l a t e t h e p r o c e s s (now you s e e t h e r e l e v a n c e of t h i s t a l k )

t o t h e two-body d e c a y p r o c e s s

which may n o t b e r e a l i z e d i n l a b o r a t o r i e s b u t i s known t o i n i t i a t e t h e "hydrogen burningt' i n s t a r s ( t h e f i r s t s t e p i n p r o d u c i n g h e l i u m from hydrogen)

and from which one c a n e x t r a c t an e f f e c t i v e two- body o p e r a t o r c o r r e s p o n d i n g t o t h e exchange c u r r e n t . The argument needed i n r e l a t i n g ( 1 2 ) t o ( 1 3 ) i n v o l - v e s PCAC and low-energy t h e o r e m s , s o we s h a l l n o t e l a b o r a t e on t h e method. The e s s e n t i a l p o i n t i s t h a t one c a n e x t r a c t t h e f u l l m a t r i x e l e m e n t s (mea- n i n g one- and two-body c u r r e n t m a t r i x e l e m e n t s ) of t h e p r o c e s s ( 1 3 ) from a p r e c i s e knowledge of t h e p r o c e s s ( 1 2 1 , a l t h o u g h t h e c o n n e c t i o n i s n o t a s d i - r e c t a s B l i n - S t o y l e e t a l o r i g i n a l l y t h o u g h t ( t h e r e i s a n e x t r a c o r r e c t i o n t o t h e r e s u l t of B l i n - S t o y l e e t a 1 i f one u s e s j u d i c i o u s l y t h e low-energy t h e o - rem a s s o c i a t e d w i t h PCAC [14]). I t s h o u l d b e c l e a r by now t h a t once we know t h e a m p l i t u d e f o r (131, i t c a n a l s o b e u s e d a s a n e f f e c t i v e c u r r e n t f o r h e a v i e r n u c l e i . U n f o r t u n a t e l y , t h e l a c k of p r e c i s e low- e n e r g y d a t a on ( 1 2 ) d o e s n o t a l l o w t h i s interesting a p p l i c a t i o n y e t .

A n o t h e r i n t e r e s t i n g way of c o n f r o n t i n g t h e mesonic c o r r e c t i o n w i t h h i g h e n e r g y e x p e r i m e n t s was s u g g e s t e d by M. E r i c s o n [15]. Using a d i s p e r s i o n r e l a t i o n f o r t h e x - n u c l e a r s c a t t e r i n g a m p l i t u d e (AK+ - A -) and making some a p p r o x i m a t i o n s , s h e ma-

x

nnged t o w r i t e a sum r u l e

H e r e f x i s t h e c h s r g e d p i o n d e c a y c o n s t a n t , w i s some v a l u e above t h r e s h o l d (m )

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t h e r i g h t - h a n d s i d e g o e s o v e r and above t h e ( 3 , 3 ) r e s o n a n c e r e g i o n , s o c o n t a i n s no low-energy ( 1 . e . t h r e s h o l d ) c o n t r i b u t i o n . T h i s f A h a s t h e p r o p e r t y 2 t h a t i f t h e r e were n o exchange c u r r e n t e f f e c t , i t wo:~ld b e t h e same a s t h e one n u c l e o n v a l u e , namely

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.

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i n d i v i d u a l t r a n s i t i o n s we a r e p a r t i c u l a r l y i n t e r e s - t e d i n . A l s o t h e r e l a t i o n t o Gamow-Teller m a t r i x e l e m e n t s i s o b t a i n e d t h r o u g h PCAC which may b e i n c o n s i d e r a b l e e r r o r i n n u c l e i . T h e p r e s e n c e o f ano- malous t h r e s h o l d s makes t h e n a i v e C o l d b e r g e r - T r e i - man r e l a t i o n h i g h l y d o u b t f u l i n n u c l e i , a l t h o u g h t h e y c a n b e t r e a t e d a p p r o p r i a t e l y [16

1.

g. Summary

T h i s is t h e n how t h e s i t u a t i o n i s w i t h t h e v i r t u a l p i o n i n n u c l e i . U n l i k e t h e s t r u c t u r e o f hadronswhere i n f i n i t e numbemof v i r t u a l p a r t i c l e s seem t o b e needed t o d e s c r i b e i t , it seems t o r e - q u i r e o n l y one-pion-exchange t o d e s c r i b e a l o t of low-energy p r o p e r t i e s of n u c l e i i n which t h e mesonic d e g r e e o f freedom i s e x p l i c i t l y needed. The v e r t i - c e s needed f o r s u c h d e s c r i p t i o n s e e m t o b e g i v e n r a t h e r w e l l i n terms of s o f t - p i o n a m p l i t u d e s . A l s o it l o o k s f e a s i b l e i n t h e nbar f u t u r e t o "measure"

t h e v i r t u a l meson e f f e c t s w i t h h i g h e n e r g y p a r t i c l e s which w i l l become a v a i l a b l e i n t h e meson f a c t o r i e s b e i n g c o n s t r u c t e d .

I V

-

-

.

a. P i o n P r o d u c t i o n i n Nucleon-Nucleus C o l l i - s i ~ n

I t was f o u n d t o b e p r o f i t a b l e i n t h e d i s -

c u s s i o n s g i v e n above t o t h i n k n u c l e o n s ( f r e e o r bound) c a r r y i n g t h e i r own ( v i r t u a l ) meson c l o u d s . They a r e v i r t u a l i n t h e s e n s e t h a t t h e y a r e o f f t h e m a s s - s h e l l . But would it n o t b e p o s s i b l e t o s t r i p o n e o f f and p u t i t on t h e m a s s - s h e l l by sup- p l y i n g a p p r o p r i a t e e n e r g y and momentum ? '$Tore spe- c i f i c a l l y , o n e might i m a g i n e t h e p i o n p r o d u c t i o n as s o m e t h i n g l i k e a s t r i p p i n g similar t o t h e fami- l i a r ( d , p ) r e a c t i o n . C o n s i d e r t h e p r o c e s s

a t t h e e n e r g y r e g i o n a p p r o p r i a t e f o r t h r e s h o l d p i o n p r o d u c t i o n . Can o n e p i c t u r e t h e o u t g o i n g p i o n a s p l a y i n g a s i m i l a r r o l e a s t h e p r o t o n i n ( d , p ) r e a c - t i o n ? T h i s i s p r o b a b l y n o t t h e q u e s t i o n i n mind when D a h l g r e n e t a 1 a t U p p s a l a performed t h e expe- r i m e n t s [ I ? ]

w i t h 185 MeV p r o t o n s , b u t i t is c e r t a i n l y a n appro- p r i a t z q u e s t i o n t o a s k when o n e l o o k s a t t h e expe- r i m e n t a l r e s u l t s . L e t me show you a d i f f e r e n t i a l c r o s s - s e c t i o n c u r v e which t h e y o b t a i n e d a t 40° l a - b o r a t o r y a n g l e ( F i g . 6 ) . T h i s I c o n s i d e r i s r a t h e r i m p r e s s i f e i n i t s s i m p l i c i t y . Some s t a t e s a r e e x c i - t e d c l e a r l y and some states n o t a t a l l . Thus b e s i - d e s t h e s i m p l e n a t u r e of e x c i t a t i o n mech%nis:n, t h e - r e inust be some s o r t o f s t r o n g s e l e c t i v i t y o p e r a t i v e i n t h e r e a c t ion.

- LOO -

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The e x p e r i m e n t a l d i f f e r e n t i a l c r o s s - s e c t i o n

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f o r dl85 M ~ V ) + 12c( a . s ) + x+ + ^I3c* a t dn dE 45O s c a t t e r i n g a n g l e ( ~ e f .[ 171).