Recent Aspects of the Nuclear Spin Isospin Response Function

The s u b j e c t o f my t a l k i s t h e r e s p o n s e f u c t i o n o f t h e n u c l e u s t o a s p i n i s o s p i n e x c i t a t i o n . I w i l l f o c u s on some r e c e n t a s p e c t s , n a m e l y t h e c o l l e c t i v e f e a t u r e s o f t h e l p l h r e s p o n s e i n t h e r e g i o n o f t h e q u a s i e l a s t i c peak and t h e r e s p o n s e due t o 2p2h e x c i t a t i o n s . A s a n a p p l i c a t i o n o f t h e s e p rob lems I w i l l f i n a l l y men t ion t h e s o c a l l e d EMC e f f e c t (European muon c o l l a b o r a t i o n ) . Cihat i s t h e i n t e r e s t o f t h e s e problems ; what a r e t h e open i s s u e s ? The q u e s t i o n o f c o l l e c t i v e e f f e c t s I n t h e r e g i o n of t h e q u a s i e l a s t i c peak i s an i n t e r e s t i n g s u b j e c t i n i t s e l f , b u t p a r t i c u l a r l y I n t h e s p i n i s o s p i n c h a n n e l b e c a u s e i t is i n t i m a t e l y l i n k e d t o t h e p i o n exchange f o r c e . I t w i l l t h u s s h e d l i g h t i n t h e e x i s t e n c e and t h e r o l e o f t h e p i o n i n n u c l e i which i s somet imes q u e s t i o n e d nowadays and f o r which a c o n v i n c i n g e v i d e n c e s h o u l d b e b u i l t . The q u e s t i o n of t h e 2p2h r e s p o n s e i s d i r e c t l y r e l a t e d t o t h e problem o f t h e h i g h e n e r g y t a i l o f t h e Gamow-Teller (G.T) s t r e n g t h f u c t i o n ; we w i l l a l s o d i s c u s s t h e problem of i t s quench ing . F i n a l y t h e EMC e f f e c t i n i t s p i o n i c i n t e r p r e t a t i o n o f f e r s a b e a u t i f u l a p p l i c a t i o n of t h e s e i d e a s i n a v e r y h i g h ene rgy expe r imen t . I n o r d e r t o f i x t h e n o t a t i o n s l e t m e remind you t h e d e f i n i t i o n o f t h e r e s p o n s e f u n c t i o n . I w i l l a d o p t t h r o u g h o u t t h i s work a n i n f i n i t e nuc l e a r m a t t e r d e s c r i p t i o n f o r which i t is c o n v e n i e n t t o work i n momentum s p a c e . I f an e x t e r n a l f o r c e U ( q , w ) i s a p p l i e d t o t h e n u c l e a r sys t em a t a momentum q and f r e q u e n c y w t h e n a d e n s i t y f l u c t u a t i o n 6n is induc e d The q u a n t i t y n is t h e p o l a r i z a t i o n p r o p a g a t o r . Its imag ina ry p a r t i s t h e r e s p o n s e f u n c t i o n o f t h e sys t em. I t is a q u a n t i t y of a g r e a t p r a c t i c a l i n t e r e s t s i n c e i t is p r o p o r t i o n a l t o t h e i n e l a s t i c c r o s s s e c t i o n f o r a p r o b e which c o u p l e s t o t h e s e d e n s i t y f l u c t u a t i o n s . I t is a l s o ( w i t h i n t r i v i a l f a c t o r s ) t h e c o r r e l a t i o n f u n c t i o n o f t h e sys t em. The r e s p o n s e o f t h e sys t em is l i n k e d t o i t s e x c i t a t i o n s . F o r a f r e e Fermi g a s t h e n u c l e o n s r e spond i n d i v i d u a l l y and t h e e x c i t a t i o n s a r e o f two t y p e s , t h e p u r e l y n u c l e a r o n e s a t low e n e r g i e s , wz q2/2mN and t h e Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1984439 C4-490 JOURNAL DE PHYSIQUE n u c l e o n i c ones a t h i g h e n e r g y , f o r a s p i n i s o s p i n e x c i t a t i o n m o s t l y due t o t h e A , w = w A + cf /2m A w i t h w A = 300 MeV. F o r a f i x e d v a l u e o f q t h e b e h a v i o r of n i s a s f o l l o w s . The re a r e two r e g i o n s of r e s p o n s e , one a t low e n e r g y and one a t h&gh e n e r g y , a s is shown i n P i g . 1 . Re n h a s a d i s p e r s i v e b e h a v i o r , Ren c h a n g i n g s i g n a t low e n e r g y w h i l e Reno c h a n g e s s i g n a t h i g h e n e r g y . I would l i k e t o draw your a t t e n t i o n t o t h e f a c t t h a t en^ ( a n d hence Re n o ) is n o t , a t f i x e d q , a smooth f u n c t i o n o f w i n t h e low e n e r g y s e c t o r o r e q u i v a l e n t l y , a t f i x e d w , i t is n o t a smooth f u n c t i o n of q . Moreover t h e r e is a n e a r cancellation between R e nN and Rex0 I n a c e r t a i n k i n e m a t i c a l domain ( s e e F i g . 1 ) . F i g . 1 Imag ina ry p a r t s ( d o t d a s h e d l i n e s ) and Rea l p a r t s o f n and no ( c o n t i n u o u s l i n e s ) and of no = + n A ( d a s h e d l i n e ) . When t h e i n t e r a c t i o n between t h e nuc leons is s w i t c h e d on t h e nuc leons no l o n g e r r e spond i n d i v i d u a l l y . The e x t e r n a l f o r c e c a n b e t r a n s m i t t e d t o t h e n e i g h b o u r s th rough a c o h e r e n t s u p e r p o s i t i o n o f l p l h s t a t e s and t h e l p l h r e s p o n s e becomes where V i s thep.h . i n t e r a c t i o n . T h i s e x p r e s s i o n sums t h e f o l l o w i n g series o f b u b b l e g r a p h s . The e x p r e s s i o n (1) r e p r e s e n t s t h e random phase a p p r o x i m a t i o n , RPA, more e x a c t l y a s i m p l i f i e d v e r s i o n o f i t where t h e a n t i s y m m e t r i s a t i o n is om i t t e d . Although o v e r s i m p l i f i e d a s compared t o t h e e x a c t RPA, e x p r e s s i o n (1) is a u s e f u l g u i d e l i n e t o s t u d y t h e c o l l e c t i v e f e a t u r e s of t h e r e s p o n s e , embodied i n t h e RPA d e n o m i n a t o r , and t o p r e d i c t what k i n d o f f e a t u r e s s h o u l d b e e x p e c t e d . T h i s a p p r o x i m a t i o n g i v e s f o r t h e r e s p o n s e The c o l l e c t i v e e f f e c t s i n f l u e n c e t h e r e s p o n s e i n a way which depends on t h e s i g n o f t h e p r o d u c t V ( q , w) R e n o (q,cu). F o r what c o n c e r n s t h e p .h . f o r c e t h e p i o n which c o u p l e s t o t h e nuc leo n i c s p i n and i s o s p i n i s an e f f e c t i v e a g e n t t o c a r r y t h e s p i n e x c i t a t i o n . T h i s makes pn$ o f t h e i n t e r e s t i n g a s p e c t s o f t h e f i e l d . However t h e p i o n h a s a a . q t y p e o f c o u p l i n g . Consequen t ly i t c a n a c t o n l y ( i n nuC4-492 JOURNAL DE PHYSIQUE c l e a r m a t t e r ) i f t h e e x c i t i n g f i e l d i t s e l f h a s a s i m i l a r c o u p l i n g , i . e . , i f i t p r o b e s t h e component o f t h e m a g n e t i z a t i o n a l o n g t h e + d i r . e c t i o n o f t h e momentum. I f t h e p robe c o u p l e s i n a t r a n s v e r s e way ( a x ̂ q) t h e n i n n u c l e a r m a t t e r i t i s t o t a l l y b l i n d t o t h e p i o n exchange f o r c e , a t l e a s t f o r t h e d i r e c t p i e c e b u t remember t h a t w e i g n o r e a n t i s y m m e t r i s a t i o n i n o u r s i m p l e a p p r o x i m a t i o n . T h i s p a r t i c u l a r f e a t u r e t u r n s o u t t o b e o f g r e a t v a l u e . By t u r n i n g t h e d i r e c t i o n o f t h e m a g n e t i z a t i o n t h a t we e x p l o r e w e c a n s w i t c h on and o f f t h e p i o n i c component of t h e f o r c e , e n a b l i n g t h u s t h e d i s p l a y o f t h i s component. I n p r a c t i c e t h i s i s n o t s o e a s y t o c a r r y th rough b u t t h e p o s s i b i l i t y i s t h e r e and i t s h o u l d b e e x p l o i t e d . What it means i n p r a c t i c e i s t h a t t h e f o r c e and hence t h e c o l l e c t i v e f e a t u r e s t h a t t h i s f o r c e g e n e r a t e s a r e d i f f e r e n t i n t h e s p i n l o n g i t u d i n a l and i n t h e s p i n t r a n s v e r s e c h a n n e l s (1). B e s i d e p i o n exchange t h e f o r c e c o n t a i n s s h o r t r a n g e components which a r e p a r a m e t r i z e d phenomeno log ica l ly by t h e Landau-Migdal p a r a m e t e r g o , which represents t h e r e p u l s i v e s h o r t r a n g e component. The t o t a l f o r c e V L i n t h e s p i n l o n g i t u d i n a l c h a n n e l is t h u s Where f is t h e n N c o u p l i n g c o n s t a n t ( f 2 = 1). The p i o n exchange p i e c e g e n e r a t e s a r a p i d v a r i a t i o n i n momentum due t o t h e s m a l l v a l u e of t h e p i o n mass. I n t h e s p i n t r a n s v e r s e c h a n n e l t h e r e i s no p i o n exchange and t h e f o r c e VT h a s a s low v a r i a t i o n i n ¶(maybe due t o p exchange ) r e m a i n i n g r e p u l s l v e o v e r a l a r g e r r a n g e o f momenta. The two f o r c e s a r e r e p r e s e n t e d i n F i g . 2 f o r a t y p i c a l v a l u e g t = 0 . 7 .