HAL Id: jpa-00226476
https://hal.archives-ouvertes.fr/jpa-00226476
Submitted on 1 Jan 1987
HAL is a multi-disciplinary open access
archive for the deposit and dissemination of
sci-entific research documents, whether they are
pub-lished or not. The documents may come from
teaching and research institutions in France or
abroad, or from public or private research centers.
L’archive ouverte pluridisciplinaire HAL, est
destinée au dépôt et à la diffusion de documents
scientifiques de niveau recherche, publiés ou non,
émanant des établissements d’enseignement et de
recherche français ou étrangers, des laboratoires
publics ou privés.
ON THE LONGITUDINAL CHARGE RESPONSE IN
THE QUASI ELASTIC PEAK REGION
J. Jaenicke, P. Schuck, U. Stroth, R. Hasse
To cite this version:
JOURNAL DE PHYSIQUE
Colloque C2, supplement
au
n o
6, Tome 48, juin 1987
ON THE LONGITUDINAL CHARGE RESPONSE IN THE QUASI ELASTIC PEAK REGION
J. JAENICKE,
P.
SCHUCK, U. STROTH'
and
R.
W.
HASSE"
Institut des Sciences Nuclbaires, 53, Avenue des Martyrs,
F-38026 Grenoble Cedex, France
' ~ a x
Planck Institut fiir Plasmaphysik, 0-8046 Garching, F.R.G.
" G S I ,
Postfach 110541, D-6100 Darmstadt 11, F.R.G.
RI5sumB Nous gI5nI5ralisons n o t r e t h i o r i e pour l a f o n c t i o n d e r e p o n s e d a n s l a r e g i o n d u p i c q u a s i P l a s t i q u e au c a s N
#
Z e t l ' a p p l i q u o n s pour e x p l i q u e r l e s m e s u r e s r P c e n t e s d e ( e , e ' ) s u r 2 3 8 ~ . 11 y a p e r s i s t a n c e du probleme d e l acharge manquantc
.
A b s t r a c t We g e n e r a l i s e o u r t h e o r y f o r t h e l i n e a r r e s p o n s e f u n c t i o n i n t h e q u a s i e l a s t i c peak r e g i o n t o t h e c a s e N
#
Z and a p p l y i t t o t h e r e c e n t l y measu- r e d e , e l c r o s s - s e c t i o n o f 2 3 8 ~ . We f i n d t h a t t h e problem of t h e m i s s i n g c h a r g e p e r s i s t s .We have r e c e n t l y f o r m u l a t e d and a p p l i e d a s e m i - c l a s s i c a l t h e o r y f o r t h e l i n e a r r e s p o n s e t o i n e l a s t i c e l e c t r o n s c a t t e r i n g on n u c l e i i n t h e q u a s i e l a s t i c peak r e g i o n [l]
.
We used t h e f u l l y a n t i s y m n e t r i s e d Gogny f o r c e which s h o u l d be v a l i d-1
f o r momentum t r a n s f e r s q ,( 1 . 6 fm i n t h e l o n g i t u d i n a l c h a r g e c h a n n e l . With no a d j u s t a b l e p a r a m e t e r s we f i n d q u i t e s a t i s f a c t o r y r e s u l t s o v e r a wide momentum range f o r 1 2 c ( s e e F i g . 1 ) .
For i n c r e a s i n g mass number t h i s agreement o f t h e o r y and e x p e r i m e n t drama- t i c a l l y d e t e r i o r a t e s . We g e n e r a l i s e d o u r t h e o r y f o r t h e N
#
Z c a s e t o a c c o u n t f o r t h e r e c e n t 2 3 8 ~ d a t a . I n F i g . 2 we show a t q = 1 . 5 2 fm-l t h e r e s u l t s f o r 5 6 ~ e and 2 3 8 ~ . We s e e a v e r y s t r o n g o v e r s h o o t i n g o f t h e t h e o r e t i c a l r e s u l t w i t h r e s p e c t t o t h e e x p e r i m e n t a l d a t a . For 2 3 8 ~ even more s o t h a n f o r 5 6 ~ e . A s t r o n g l y mass depen- d e n t e f f e c t must t h e r e f o r e be a t o p e r a t i o n which i s n o t t a k e n i n t o a c c o u n t w i t h i nRPA t h e o r y
.
Noble and S h a k i n C31 proposed a s w e l l i n g o f t h e n u c l e o n i n t h e n u c l e a r m a t t e r which l e a d s t o a m o d i f i c a t i o n o f t h e n u c l e o n form f a c t o r . We h e r e a r g u e f o r a n o t h e r p o s s i b i l i t y which c o u l d be g i v e n by t h e i n c l u s i o n of 2p-2h s t a t e s . I n d e e d t h e Uranium d a t a [4] d o n o t seem t o d r o p t o z e r o up t o t h e e n e r g i e s measuredJOURNAL
DE
PHYSIQUEF i g . I . The c h a r g e r e s p o n s e f o r '*C a t f i v e momentum t r a n s f e r s : t h e f r e e r e s p o n s e and t h e i n t e r a c t i n g one ( f u l l l i n e s ) a r e compered t o d a t a from Barreau e t a 1 [ 2 ]
.
The d e c o m p o s i t i o n of t h e i n t e r a c - t i n g r e s p o n s e i n t o i s o s c a l a r and i s o v e c t o r c o n t r i b u t i o n s i s g i v e n by t h e dashed l i n e s .and 5 6 ~ e a s w e l l a s 2 3 8 ~ show a p r o n o u n c e d p l a t e a u s t r u c t u r e a t q = 1 . 5 2 fm-l ( t h i s i s t h e r e a s o n why we c h o s e t h i s v a l u e ) w h i c h i s a b s e n t f o r I 2 c . W i t h i n o u r t h e o r y t h i s p l a t e a u c o u l d p o s s i b l y be e x p l a i n e d by t h e f a c t t h a t t h e Gogny f o r c e i n t h e i s o s c a l a r c h a n n e l i s a t t r a c t i v e i n t h e s u r f a c e b u t r e p u l s i v e i n t h e b u l k . The 2p-2h s t a t e s would t h e n p r i m a r i l y s m e a r o u t t h e i s o v e c t o r p a r t o f t h e r e s p o n s e . T h a t s u c h a s c e n a r i o c a n o c c u r h a s r e c e n t l y b e e n shown by Drozdz e t a l . [ S ]
.
On t h e o t h e r hand t h e d e n s i t y o f 2p-2h s t a t e s i s s u r e l y v e r y s t r o n g l y mass d e p e n d e n t a s we show i n F i g . 3 . P i g . 3. 2p-2h l e v e l d e n s i t i e s a t f i x e d e x c i - t a t i o n e n e r g y a s a f u n c t i o n o f mass number f o r a h a r m o n i c o s c i l l a t o r p o t e n t i a l . I n c o n c l u s i o n we c a n s a y t h a t t h e m i s s i n g c h a r g e p r o b l e m shows up v e r y s t r o n g l y a l s o i n t h e r e c e n t l y measured c h a r g e r e s p o n s e o f 2 3 8 ~ . We c a n n o t a c c o u n t f o r t h e d e t a i l e d s h a p e o f t h e c r o s s s e c t i o n e v e n w i t h a m o d i f i e d n u c l e o n form f a c - t o r . We however g i v e a r g u m e n t s t h a t t h e i n c l u s i o n o f 2p-2h s t a t e s c a n p l a y a n i m p o r t a n t r o l e i n t h e q u a s i e l a s t i c peak r e g i o n .ACKNOWLEDGEMENTS. We a r e g r a t e f u l t o G. C h a n f r e y f o r h i s he1.p i n g e n e r a l i s i n g li- n e a r r e s p o n s e t h e o r y t o t h e N
#
Z c a s e .REFERENCES
1 U. STROTH, R.W. HASSE and P. SCHUCK, Nucl. Phys. A462 ( 1 9 8 7 ) 45
2 P. BARREAU e t a l . , N u c l . Phys. A 402 ( 1 9 8 3 ) 5 1 5 and n o t e CEA N-2334,1983 3 J. NOBLE, P h y s . Rev. L e t t . 46 ( 1 9 8 1 ) 412;
C.M. SHAKIN, N u c l . P h y s . A 446 ( 1 9 8 5 ) 323C 4 C.C. BLATCHLEY e t a l . , P h y s . Rev. C34 ( 1 9 8 6 ) 1 2 4 3
