CHARGE-EXCHANGE REACTIONS AND SPIN-ISOSPIN MODES

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CHARGE-EXCHANGE REACTIONS AND SPIN-ISOSPIN MODES

C. Gaarde

To cite this version:

C. Gaarde. CHARGE-EXCHANGE REACTIONS AND SPIN-ISOSPIN MODES. Journal de

Physique Colloques, 1984, 45 (C4), pp.C4-405-C4-416. �10.1051/jphyscol:1984431�. �jpa-00224097�

J O U R N A L D E PHYSIQUE

Colloque C4, suppl6ment a u n03, Tome 45, m a r s 1984 page C4-405

CHARGE-EXCHANGE REACTIONS AND SPIN-ISOSPIN MODES C. Gaarde

NieZs B o b I n s t i t u t e , University o f Copenhagen, DK-2100 Copenhagen

9,

Denmark

Resum6

-

Les r e a c t i o n s ( p , n ) e t ( 3 ~ e , t ) 2 e n e r g i e s i n t e r m g d i - a i r e s , r e p r g s e n t e n t d e s processus B une seule 6tape e t sont &x- trgmement s e l e c t i v e s aux t r a n s i t i o n s o ~ . La r g p a r t i t i o n d e 1 1 i n t e n s i t 6 d e s p i n d i p o l a i r e e s t d i s c u t g e d a n s l e c a s ' 2 ~ - 1 2 ~ .

La r e a c t i o n ( 3 ~ e , t ) 3 2 GeV r & v & l e d e t r g s f o r t e s e x c i t a t i o n s d e l a r s s o n a n c e A .

A b s t r a c t

-

The ( p , n ) and ( 3 ~ e , t ) r e a c t i o n s a t i n t e r m e d i a t e e n e r g i e s a r e o n e s t e p p r o c e s s e s and v e r y s e l e c t i v e f o r aT- t r a n s i t i o n s . The s p i n d i p o l e s t r e n g t h d i s t r i b u t i o n i s d i s - c u s s e d i n a s p e c i f i c c a s e , ' 2 ~ - 1 2 ~ . The ( 3 ~ e , t ) r e a c t i o n a t 2 GeV shows v e r y s t r o n g e x c i t a t i o n s o f A-resonance.

I

-

INTRODUCTION

Charge exchange r e a c t i o n s a t i n t e r m e d i a t e e n e r g i e s have r e c e n t l y been shown t o be v e r y u s e f u l s p e c t r o s c o p i c t o o l s . The ( p , n ) e x p e r i m e n t s performed a t t h e I n d i a n a U n i v e r s i t y C y c l o t r o n F a c i l i t y [ 1 , 2 ] have demonstrated a n extreme s e l e c t i v i t y f o r 0 7 - e x c i t a t i o n s , i . e . t r a n s i - t i o n s c h a r a c t e r i z e d by i s o s p i n and s p i n t r a n s f e r , and t h e s e e x p e r i - ments have l e d t o a major b r e a k t h r o u g h i n t h e u n d e r s t a n d i n g of i s o - s p i n - s p i n c o r r e l a t i o n s i n n u c l e i .

I n F i g . 1 we show a n e u t r o n spectrum f o r t h e 2 0 8 ~ b ( p , n ) r e a c t i o n a t Ep=200 MeV [ 2 ] . The spectrum i s s e e n t o be dominated by a s i n g l e peak.

208pb

(p,n)

; Ep

= 200

MeV ; B = O o h

En (MeV)

F i g . 1

-

Energy spectrum from t h e ( p , n ) r e a c t i o n a t 2 0 0 MeV.

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1984431

C4-406 J O U R N A L DE PHYSIQUE

The t r a n s i t i o n h a s A R = O and A s = l , and t h e peak i s i n t e r p r e t e d a s t h e G i a n t Gamow-Teller r e s o n a n c e , i . e . t h e c o l l e c t i v e s t a t e t h a t c a r r i e s a s i g n i f i c a n t p a r t of t h e t o t a l o r - s t r e n g t h . The spectrum t h e r e f o r e d i r e c t l y shows t h a t c o r r e l a t i o n s i n t h e o ~ - c h a n n e l i n s i d e t h e n u c l e u s a r e s t r o n g and b u i l d up c o l l e c t i v e s t a t e s .

The f u r t h e r a n a l y s i s shows t h a t t h e whole spectrum i n F i g . 1 ( i . e . t h e h i g h energy p a r t of t h e t o t a l n e u t r o n spectrum) i s a r e s u l t o f one s t e p p r o c e s s e s . I t s h o u l d t h e r e f o r e be p o s s i b l e t o c a l c u l a t e t h e spectrum u s i n g a D i s t o r t e d Wave Impulse Approximation t o c a c u l a t e a l l p o s s i b l e one p a r t i c l e - o n e h o l e t r a n s i t i o n s s t a r t i n g from t h e t a r g e t ground s t a t e . F. O s t e r f e l d h a s shown i n a paper 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 [ 3 ] t h a t t h i s i s r e a l l y t h e c a s e .

The s e l e c t i v i t y f o r o r - e x c i t a t i o n s i s d e m o n s t r a t e d i n F i g . 2 where p a r t s of s p e c t r a from t h e '+C ( p , n ) r e a c t i o n a r e shown a t d i f f e r e n t bombarding e n e r g i e s [ 4 ] .

4 2 0 Excitation Energy (XeV)

F i g . 2

-

S p e c t r a from t h e " + ~ ( ~ , n ) r e a c t i o n a t 4 bombarding e n e r g i e s . The a n a l y s e s of t h e ( p , n ) d a t a from I n d i a n a have f u r t h e r shown t h a t t h e z e r o d e g r e e spectrum t o a f a i r approximation d i r e c t l y g i v e s t h e G.T. s t r e n g t h f u n c t i o n , and we s h a l l show below t h a t t h e s p e c t r a a t l a r g e r a n g l e s g i v e t h e s t r e n g t h d i s t r i b u t i o n f o r t h e h i g h e r s p i n m u l t i p o l e s .

I n t h i s paper we s h a l l n o t go i n t o a d e t a i l e d d i s c u s s i o n of t h e R = O i s o s p i n - s p i n modes. We r e f e r t o a r e c e n t r e v i e w a r t i c l e [ 5 ] . We s h a l l b r i e f l y d i s c u s s t h e R = l s p i n modes and t a k e 1 2 ~ - 1 2 ~ a s a spe- c i f i c example.

The ( 3 ~ e , t ) r e a c t i o n i s a l s o a charge-exchange r e a c t i o n b u t h a s been c o n s i d e r e d v e r y c o m p l i c a t e d because of i m p o r t a n t two s t e p c o n t r i b u - t i o n s [ 6 ] . Recent ( 3 ~ e , t ) e x p e r i m e n t s a t i n t e r m e d i a t e e n e r g i e s p e r - formed a t S a t u r n e [ 7 ] show, however, t h a t a l s o t h e ( 3 ~ e , t ) r e a c t i o n a t t h e s e e n e r g i e s i s dominated by o n e s t e p p r o c e s s e s . I n F i g . 3 we compare ( p , n ) and ( 3 ~ e , t ) z e r o d e g r e e s p e c t r a f o r a bombarding energy of 2 0 0 MeV p e r nucleon w i t h ' O Z ~ a s t h e t a r g e t . We s e e a s t r i k i n g s i m i l a r i t y . The s e l e c t i v i t y f o r o r - e x c i t a t i o n s a l s o f o r t h e ⁽ 3 ~ e , t) r e a c t i o n i s demonstrated by t h e s m a l l n e s s of t h e t r a n s i t i o n t o t h e O + i s o b a r i c a n a l o g u e s t a t e .

We s h a l l b r i e f l y d i s c u s s t h e ( 3 ~ e , t ) r e a c t i o n below and show d a t a o b t a i n e d a t a bombarding e n e r g y of 2 GeV. A t t h i s energy we s e e a s t r o n g e x c i t a t i o n of t h e A-resonance, a d i r e c t e v i d e n c e f o r t h e o r - n a t u r e of t h i s e x c i t a t i o n .

F i g . 3

-

Energy s p e c t r a f o r t h e ( p , n ) and ( 3 ~ e , t ) r e a c t i o n s a t 200 MeV p e r nucleon.

I1 - SPIN DIPOLE STRENGTH

I n F i g . 4 we show s p e c t r a a t d i f f e r e n t a n g l e s f o r t h e '08pb ( p , n ) r e a c t i o n a t Ep=200 MeV [ 2 ] . The peak i n t h e 8=4.5O spectrum h a s an a n g u l a r distribution c o r r e s p o n d i n g t o ,P,=l. Such a peak i s observed f o r a l l heavy n u c l e i and i s i n t e r p r e t e d a s a m a n i f e s t a t i o n of s t r e n g t h c o r r e s p o n d i n g t o t h e o p e r a t o r

I 3 0 -

20 -

o - - , . .

120 160 200

En (MeV)

F i g . 4

-

S p e c t r a a t s e v e r a l a n g l e s f o r t h e 08pb (pin) r e a c t i o n .

C4-408 JOURNAL DE PHYSIQUE

I n F i g . 5 i s a l s o shown t h e s t r e n q t h d i s t r i b u t i o n from an RPA c a l c u - l a t i o n w i t h a z e r o r a n g e f o r c e f o r t h e p a r t i c l e - h o l e i n t e r a c t i o n i n t h i s c h a n n e l . The c a l c u l a t i o n s u g g e s t s t h a t t h e peak i s an envelope of s t a t e s w i t h s p i n p a r i t i e s a s g i v e n above, and w i t h a d e f i n i t e o r d e r i n g i n e n e r q y . A c a l c u l a t i o n performed by F. O s t e r f e l d e t a l .

181 g i v e s s i m i l a r r e s u l t s .

F i g . 5

-

The 6=4.5O spectrum i s shown t o g e t h e r w i t h t h e r e s u l t of a RPA c a l c u l a t i o n o f t h e s p i n d i p o l e s t r e n g t h d i s t r i b u t i o n [ 2 ] . The

"background" i s r a t h e r a r b i t r a r i l y drawn. The t o t a l a r e a under t h e peak ( i . e . w i t h no "background") i s p r o b a b l y due t o s p i n d i p o l e s t r e n g t h .

We have however n o t been a b l e s o f a r t o r e s o l v e t h i s broad peak i n i t s components, s o we do n o t know t h a t a c o l l e c t i v e s t a t e i s formed i n e . g . t h e 0--channel. We should a l s o mention t h a t t h e c o l l e c t i v e 1 - - s t a t e o f e l e c t r i c t y p e c o r r e s p o n d i n g t o t h e r Y 1 ~ - 1 s t r e n g t h i s l y i n g i n t h i s e n e r g y r e g i o n . We do n o t . e x p e c t , however, t h a t t h e c r o s s s e c t i o n c o n t r i b u t i o n i s v e r y l a r g e because of t h e non s p i n t r a n s f e r c h a r a c t e r o f t h e t r a n s i t i o n ( s e e F i g . 2 ) t 8 1 .

The e n e r g y and s t r e n g t h s y s t e m a t i c s we have oljserved f o r t h i s s p i n d i p o l e peak i s c o n s i s t e n t w i t h t h e s i m p l e R P A ' c a l c u l a t i o n s mentioned above. The p i c t u r e of t h e 0 - - c o r r e l a t i o n s c o Ild however be wrong.

"i

The c o n t r i b u t i o n from t h e 0 - - s t a t e s t o t h e bropd peak i s f a i r l y s m a l l .

I

I n F i g . 6 we g i v e s p i n d e n s i t i e s f o r some of t h e c o l l e c t i v e s t a t e s i n 2 0 8 ~ i . The f i g u r e s can be t h o u g h t of a s s n a p s h o t p i c t u r e s of v i b r a t i o n s i n O T - s p a c e . I n a l l c a s e s t h e r e i s a x i a l symmetry a b o u t

t h e Z-axis.

The s p i n d e n s i t y f o r t h e I f - c o l l e c t i v e s t a t e i s s e e n t o f o l l o w ( a l m o s t ) t h e nucleon d e n s i t y whereas t h e s p i n - d i p o l e v i b r a t i o n s a r e more s u r f a c e peaked.

11.1

-

S p i n d i p o l e s t r e n g t h i n

12c

I n t h e l i g h t e r systems t h e s p i n d i p o l e s t r e n g t h i s more fragmented, and we c o u l d hope t o u n d e r s t a n d t h e n a t u r e of t h e 0 - - s t a t e s t h r o u g h

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

I n F i g . 7 we g i v e t h e r e s u l t s of a Cohen-Kurath t y p e of s h e l l model c a l c u l a t i o n f o r t h e s p i n d i p o l e s t r e n g t h d i s t r i b u t i o n i n I 2 c - l 2 ~ [ 9 ] . Also shown i s t h e e l e c t r i c d i p o l e s t r e n g t h f o r t h e 1--spectrum. We

s e e t h a t most of t h i s l a t t e r s t r e n g t h i s c o n c e n t r a t e d on a s i n g l e s t a t e whereas t h e s p i n d i p o l e s t r e n g t h f o r t h e 1 - - s t a t e s i s s p r e a d

F i g . 6

-

S p i n d e n s i t i e s f o r t h e 4 c o l l e c t i v e i s o s p i n - s p i n s t a t e s i n '08pb a r e shown w i t h c u t s c o n t a i n i n g t h e z - a x i s e x c e p t f o r t h e 1--mode where t h e c u t c o n t a i n s t h e e q u a t o r p l a n e . I n a l l c a s e s t h e r e i s a x i a l symmetry. The c a l c u l a t i o n s a r e done by Toru Suzuki.

E x (MeV) 15 10 5 0

F i g . 7

-

S t r e n g t h d i s t r i b u t i o n s f o r t h e o p e r a t o r s r ( Y r a ) ~ - l and r Y 1 - c - I a r e c a l c u l a t e d f o r

12c.

Also shown a r e t h e c o r r e s p o n d i n g ( p , n ) c r o s s s e c t i o n s a t 160 MeV and 8 = 8 0 , s e p a r a t e f o r t h e 0-, 1- and 2 - s t a t e s and added,where e a c h s t a t e i s g i v e n a w i d t h of 1 . 6 MeV.

I n comparing w i t h t h e d a t a n o t e t h e f a c t o r o f 2 change i n s c a l e .

En (MeV)

o v e r many s t a t e s . The f i g u r e a l s o shows t h e c a l c u l a t e d c r o s s s e c t i o n f o r ( p , n ) t r a n s i t i o n s t o t h e s e s t a t e s f o r a s c a t t e r i n g a n g l e o f 8=8O, c o r r e s p o n d i n g t o t h e maximum i n t h e a n g u l a r d i s t r i b u t i o n .

C4-410 JOURNAL DE PHYSIQUE

The c a l c u l a t i o n s a r e done i n a DWIA u s i n g t h e i n t e r a c t i o n p o t e n t i a l s by Love and Franey [ l o ] and a r e d e r i v e d from NN p h a s e s h i f t d a t a . The c r o s s s e c t i o n f o r t h e t r a n s i t i o n t o t h e l + - g . s . i s w e l l d e s c r i b e d i n s u c h a n approach. The c r o s s s e c t i o n s f o r t h e 2 - - s t a t e s a r e

s t r i c t l y p r o p o r t i o n a l t o t h e s p i n s t r e n g t h . For t h e 1 - - s t a t e s we a l s o have c o n t r i b u t i o n from non-spin t r a n s f e r a m p l i t u d e s , and t h e above p r o p o r t i o n a l i t y i s n o t q u i t e f u l f i l l e d . The e f f e c t from non- s p i n t r a n s f e r i s however s m a l l . T h i s i s most c l e a r l y s e e n f o r t h e 1 - - s t a t e t h a t c a r r i e s most o f t h e r Y 1 ~ - 1 s t r e n g t h . The ( p , n ) c r o s s s e c t i o n f o r t h i s s t a t e i s o n l y s l i g h t l y l a r g e r t h a n e x p e c t e d from i t s s p i n s t r e n g t h . The g i a n t d i p o l e s t a t e "does n o t know" it i s s p e c i a l when examined w i t h t h e ( p , n ) r e a c t i o n , and a l m o s t p u r e a?- probe a t t h e s e e n e r g i e s .

The c r o s s s e c t i o n f o r t h e 0 - - s t a t e s i s a l m o s t a f a c t o r of 3 s m a l l e r t h a n 2 - - s t a t e s w i t h t h e same s p i n s t r e n g t h . T h i s i s d u e t o a de- s t r u c t i v e i n t e r f e r e n c e between t h e c e n t r a l and t e n s o r t e r m s i n t h e i n t e r a c t i o n . T h i s means t h a t it i s much more d i f f i c u l t t o l o c a t e t h e 0 - - s t a t e s t h a n t h e s p i n s t r e n g t h d i s t r i b u t i o n s u g g e s t s . I n t h e p r e s e n t c a s e t h e sum of a l l 0--cross s e c t i o n s i s o n l y 3 % of t h e s p i n - d i p o l e c r o s s s e c t i o n s . The s p e c i a l s t a t u s o f t h e 0 - - s t a t e s makes i t even more i n t r i g u i n g t o u n d e r s t a n d t h e p a r t i c l e - h o l e i n t e r a c t i o n i n t h i s c h a n n e l i n s i d e t h e n u c l e u s . I s a c o l l e c t i v e s t a t e i n heavy n u c l e i a t a l l formed?

I n F i g . 7 t h e c r o s s s e c t i o n s f o r a l l t h e s t a t e s a r e added, and t h e peaks a r e g i v e n a width of 1 . 6 MeV, t h e one found e x p e r i m e n t a l l y f o r t h e s t a t e around 4.2 MeV. I f we compare w i t h t h e observed ( p , n ) spectrum, we f i r s t n o t e t h a t t h e a n g u l a r d i s t r i b u t i o n s show t h a t t h e whole spectrum a t 8=8' and Ex=2-17 MeV i s c h a r a c t e r i z e d by R = l t r a n s - f e r . We s e e t h a t t h e 2 broad s t r u c t u r e s a r e w e l l reproduced i n t h e c a l c u l a t e d spectrum. The c r o s s s e c t i o n f o r t h e 4.2 MeV s t r u c t u r e , a c c o r d i n g t o t h e f i g u r e m o s t l y a 2 - - s t a t e , i s a f a c t o r of 2 t o o l a r g e .

The c a l c u l a t i o n s u g g e s t s t h a t most of t h e s p i n - d i p o l e s t r e n g t h i s c o l l e c t e d i n t h e 2 broad s t r u c t u r e s a t 4 and 7 MeV, predominantly 2- and 1 - - s t a t e s , r e s p e c t i v e l y . The ( p , n ) d a t a , however, show t h a t o n l y h a l f t h e c a l c u l a t e d s t r e n g t h i s i n t h i s r e g i o n , and t h a t t h e r e s t i s pushed u p i n energy. I f we i n t e g r a t e t h e t o t a l y i e l d a t 8 = 8 " up t o Ex%22 MeV, we e x h a u s t t h e c a l c u l a t e d s p i n - d i p o l e c r o s s s e c t i o n . Above t h i s e x c i t a t i o n energy we have c o n t r i b u t i o n s from h i g h e r m u l t i p o l e s and a comparison w i t h 1% c a l c u l a t i o n s a s t h e p r e s e n t o n e , becomes q u e s t i o n a b l e .

As t o t h e q u e s t i o n of m i s s i n g s t r e n q t h we n o t e t h a t t h e i n t e r a c t i o n used i n t h e p r e s e n t s h e l l model c a l c u l a t i o n i s an e f f e c t i v e i n t e r - a c t i o n . The c a l c u l a t i o n s r e p r o d u c e t h e measured B ( G T ) f o r t h e

' 2 ~ - + ' 2 ~ ( g . s . ) t r a n s i t i o n , whereas i n

"c-"N,

where a Garnow-Teller sumrule a p p l i e s , t h e measured GT s t r e n q t h i s quenched a f a c t o r of 0.65 r e l a t i v e t o t h e s h e l l model p r e d i c t i o n . I n c o n c l u s i o n : t h e q u e s t i o n o f m i s s i n g s p i n - d i p o l e s t r e n g t h c a n n o t be answered w i t h o u t a more model-independent surnrule.

For t h e 0 - - s t a t e s we c o n c l u d e t h a t t h e p r e s e n t ( p , n ) d a t a do n o t a l l o w a l o c a l i z a t i o n of t h e s e s t a t e s .

I11

-

MISSING GAMOFT-TELLER STRENGTH

Very u s e f u l sumrules a p p l y t o c h a r g e exchange modes. S p e c i f i c a l l y f o r GT t r a n s i t i o n s we f i n d [ 6 ]

Sge

-

Sa+ = 3 (N-2)

The d i f f e r e n c e between t h e t o t a l 6-- and B + - s t r e n g t h from a g i v e n s t a t e i s 3 ( N - 2 ) . The o n l y assumption i s t h a t t h e o p e r a t o r s a and T

a r e one body o p e r a t o r s .

The a n a l y s i s of t h e t o t a l GT s t r e n g t h a s o b t a i n e d from t h e ( p , n ) e x p e r i m e n t s i n I n d i a n a n e v e r t h e l e s s shows t h a t o n l y between 0.5 and 0.65 of t h e sumrule s t r e n g t h i s found i n t h e expected r e g i o n of t h e spectrum. Two d i f f e r e n t e f f e c t s have been d i s c u s s e d a s p o s s i b l e e x p l a n a t i o n s o f t h e m i s s i n g s t r e n g t h . i ) I n c l u s i o n of t h e i n t e r n a l d e g r e e s of freedom of t h e nucleon [ l l ] , s p e c i f i c a l l y t h e A , removes

s t r e n g t h from t h e low l y i n g r e g i o n o r w i t h o t h e r words l e a d s t o a r e n o r m a l i z a t i o n of a l l o r - m a t r i x e l e m e n t s . The above sumrule i s m o d i f i e d . ii) Coupling t o 2p-2h s t a t e s removes s t r e n g t h and s p r e a d s i t t h i n l y o v e r a l a r g e e n e r g y r e g i o n [121.

E x p e r i m e n t a l l y we c a n n o t r u l e o u t t h e l a t t e r p o s s i b i l i t y .

F i g . 8

-

S p e c t r a a t d i f f e r e n t a n g l e s f o r t h e ( p , n ) and ( 3 ~ e , t ) r e a c t i o n s on

12c

a t 200 MeV p e r n u c l e o n .

I V

-

THE ( 3 ~ e , t ) REACTION

The ( 3 ~ e , t ) d a t a a r e o b t a i n e d w i t h t h e magnetic s p e c t r o m e t e r SPESIV [131 a t S a t u r n e . The s p e c t r o m e t e r i s a D5Q6 i n s t r u m e n t w i t h 35 m between t a r g e t and f o c a l p l a n e . I n t h e e x p e r i m e n t s d e s c r i b e d h e r e t h e momentum r a n g e Ap/p was 7% and t h e r e s o l u t i o n 6p/p %(0.5-&lo-3.

The s o l i d a n g l e was 0.1 m s r and w i t h t a r g e t s around 50 mg/cm2 it t y p i c a l l y t a k e s 10 min. t o g e t a spectrum. The s p e c t r o m e t e r a l l o w s measurements a t 8 = 0 ° , and t h e background c o n d i t i o n s a r e i n g e n e r a l e x t r e m e l y good. T h i s c a n be i l l u s t r a t e d by n o t i n g t h a t t h e f i r s t 1 0 MeV o f e x c i t a t i o n energy i n ' 3 c a n b e s t u d i e d t h r o u g h t h e ~ 1%

13c

abundance i n a n a t u r a l c a r b o n t a r g e t used i n o u r experiment ( s e e F i g . 8 ) .

We have d a t a a t 600 MeV, 1 . 2 , 1 . 5 and 2 GeV f o r t a r g e t s 4 0 ~ a , 5 4 ~ e , 9 0 ~ r , '08pb a t a n g l e s between 0' and 6'.

Ep = 200 MeV 5 ^-

4 ^~

-

I n F i g . 8 we show s p e c t r a f o r t h e ( p , n ) and ( 3 ~ e , t ) r e a c t i o n s on

I 2 c .

W e s e e t h a t t h e s p e c t r a a r e v e r y s i m i l a r . A t forward a n g l e s we s e e /&,I -

5 - ^{4* -}

o r 1 ^{' ' !} " ^{1 . 1}

120 160 200 560 600

E (MeV)

C4-4 12 JOURNAL DE PHYSIQUE

i n b o t h r e a c t i o n s s t r o n g e x c i t a t i o n s of t h e 1+ 9 . s . and t h e 2 broad s t r u c t u r e s a t 4 and 7 MeV e x c i t a t i o n energy d i s c u s s e d above. We n o t e e . g . t h a t t h e 8=4.5' and 8=1.5' s p e c t r a f o r t h e ( p , n ) and ( 3 ~ e , t ) r e a c t i o n s , r e s p e c t i v e l y , l o o k t h e same; t h e two a n g l e s c o r r e s p o n d t o t h e same momentum t r a n s f e r . We have a t t e m p t e d an a n a l y s i s i n t h e impulse a p p r o x i m a t i o n . I n a momentum r e p r e s e n t a t i o n t h e f o r m f a c t o r f a c t o r i z e s [ 1 4 ]

The i n t e r a c t i o n v ( q ) i s t h e n t a k e n a s t h e NN i n t e r a c t i o n a s e . g . p a r a m e t r i z e d by Love and Franey. The t r a n s i t i o n d e n s i t i e s f o r t h e p r o j e c t i l e and t a r g e t a r e o b t a i n e d from some model c a l c u l a t i o n o r from e l e c t r o n s c a t t e r i n q d a t a . I n t h i s f o r m u l a t i o n t h e o n l y d i f f e - r e n c e between n u c l e o n s c a t t e r i n g and composite p a r t i c l e s ~ a t t e r i n g i s p p ( q ) . For t h e 3 ~ e - p r o j e c t i l e we have used p =e-0-42q d e r i v e d from t h e d a t a o n t h e maqnetic f o r m f a c t o r . T h i s means P w e o n l y con- s i d e r t h e S-wave p a r t of t h e wave f u n c t i o n and t h e 3 ~ e - p r o j e c t i l e i s t h e n l i k e a f e r m i o n w i t h a f o r m f a c t o r , e . g . a n e u t r o n h o l e i n t h e 4 ~ e c l o s e d s h e l l .

The t r a n s i t i o n a m p l i t u d e i s f u r t h e r w r i t t e n a s

a p r o d u c t of a d i s t o r t i o n - and f o r m - f a c t o r F ( g ) , t h e F o u r i e r t r a n s - form of F

( 4 ) .

The ( 3 ~ e , t ) t r a n s i t i o n t o t h e g . s . i n "N h a s been c a l c u l a t e d i n t h i s approximation [ 7 ] and good agreement i s o b t a i n e d w i t h t h e d a t a . I n t h i s c o n n e c t i o n we mention t h a t a l s o t h e e l a s t i c s c a t t e r i n g p o t e n t i a l i s c a l c u l a t e d i n t h i s a p p r o x i m a t i o n . There a r e no d a t a on e l a s t i c s c a t t e r i n g a t t h e s e e n e r g i e s .

We a l s o have d a t a f o r t h e ' 2 ~ ( 3 ~ e , t ) r e a c t i o n a t 1 . 2 , 1 . 5 and 2 GeV, and t h e a n a l y s i s i n t h e DWIA g i v e s s i m i l a r agreement a s o b t a i n e d a t 6 0 0 MeV. The u n c e r t a i n t i e s on t h e a b s o l u t e c r o s s s e c t i o n s a r e how- e v e r a t p r e s e n t r a t h e r l a r g e , around 25%.

I n F i g . 9 we show z e r o d e g r e e s p e c t r a f o r a number of t a r g e t s a t a bombarding energy o f 1 . 5 GeV. Comparison w i t h ( p , n ) d a t a f o r t h e s e n u c l e i shows t h a t a l s o a t t h i s energy t h e s p e c t r a a r e t o t a l l y domi- n a t e d by t h e c o l l e c t i v e Gamow-Teller r e s o n a n c e s .

We c o n c l u d e t h i s s e c t i o n on t h e ( 3 ~ e , t ) r e a c t i o n a t i n t e r m e d i a t e e n e r g i e s by n o t i n g : i ) e x p e r i m e n t a l l y t h e r e a c t i o n i s v e r y a t t r a c - t i v e . The s p e c t r a a r e v e r y c l e a n , and t h e c r o s s s e c t i o n s a r e v e r y l a r g e ; ii) t h e r e a c t i o n i s a one s t e p p r o c e s s . A n a l y s i s i n a n impulse approximation l o o k s promising; iii) t h e r e a c t i o n i s domi- n a t e d by o ~ - t r a n s i t i o n s i n t h e whole energy r e g i o n between 6 0 0 MeV and 2 GeV.

V

-

A-EXCITATION

I f we t h i n k of t h e A a s a U T - e x c i t a t i o n o f t h e nucleon we would e x p e c t t o s e e a s t r o n g A - e x c i t a t i o n i n ( p , n ) and ( 3 ~ e , t ) r e a c t i o n s a t s u f f i c i e n t l y h i g h bombarding e n e r g y . That t h i s i s indeed t h e c a s e i s d e m o n s t r a t e d i n F i g . 1 0 , where t h e t r i t o n spectrum from t h e n a t ~ ( ~ H e , t ) r e a c t i o n a t 2 GeV i s shown. I n F i g . 11 we show t h e spectrum w i t h t h e p r o t o n a s t h e t a r g e t . The spectrum i s o b t a i n e d a s a d i f f e r e n c e between y i e l d s from C- and CH2-targets. The l a t t e r spectrum shows t h a t t h e ( 3 ~ e , t ) r e a c t i o n i s t h e i d e a l way t o produce

a beam o f A's. A problem a s a beam, i s t h a t t h e A , w i t h a w i d t h o f 1 2 0 MeV, o n l y t r a v e l s 1-2 fm.

( 3 ~ e , t )

TSHe

=

1.5 GeV

8 -

^0"

- Q ( M e V )

F i g . 9

-

Zero d e g r e e s p e c t r a f o r t h e ( 3 ~ e , t ) r e a c t i o n a t 1 . 5 GeV.

TaHs = 2 GeV 8 = 0"

16 18 2 0

T,,.,, (GeV)

F i g . 1 0

-

T r i t o n spectrum a t 2 GeV. The dashed c u r v e c o r r e s p o n d s t o t h e 3 ~ e f o r m f a c t o r p a r a m e t r i z e d a s e-0 - 8 4 q ; ( a r b i t r a r y s c a l e )

.

The ( 3 ~ e , t ) r e a c t i o n seems t o be a b e t t e r probe f o r t h e s t u d y of A's i n n u c l e i , t h a n t h e ( p , n ) r e a c t i o n . I n t h e l a t t e r we have c o n t r i b u - t i o n s from t h e p r o j e c t i l e e x c i t a t i o n i n t o A w i t h subsequent decay i n t o n e u t r o n and ^{T .} For t h e ( 3 ~ e , t ) r e a c t i o n t h e c o r r e s p o n d i n g a m p l i t u d e i s v e r y much s u p p r e s s e d because t h e ^{g . s .} o f t h e t r i t o n , t h e observed p a r t i c l e i s o n l y one among many decay c h a n n e l s .

J O U R N A L D E PHYSIQUE

T-direct 3He+p-t+Ai*

b,, = 2 GeV

F i g . 11

-

T r i t o n spectrum from a p r o t o n t a r g e t . The u n c e r t a i n t y i s ( a t p r e s e n t ) around 30%. The c u r v e s a r e c a l c u l a t e d c r o s s s e c t i o n s and e x p l a i n e d i n t h e t e x t .

I n F i g . 11 we show t h e c a l c u l a t e d c r o s s s e c t i o n f o r A-production i n a p l a n e wave a p p r o x i m a t i o n . The c r o s s s e c t i o n i s a p r o d u c t o f t h e

3 ~ e - f o r m f a c t o r and t h e i n t e r a c t i o n , t a k e n a s one boson exchange p o t e n t i a l s f o r T-and p-exchange. The f i g u r e shows a d e s t r u c t i v e i n t e r f e r e n c e between t h e two c o n t r i b u t i o n s i n d i c a t i v e of t h e t e n s o r c h a r a c t e r of t h e i n t e r a c t i o n . The momentum t r a n s f e r i s around 1.2 fm-1 i n t h e A-energy r e g i o n and a s c a t t e r i n g a n g l e of z e r o d e g r e e s . The c r o s s s e c t i o n g i v e n i n t h e , f i g u r e c o r r e s p o n d s t o a f o r m f a c t o r f o r 3 ~ e g i v e n a s p ( q ) = e-Oe6qV. T h i s i s t h e f o r m f a c t o r o b t a i n e d a s t h e Fadeev s o l u t i o n o f t h e 3-body system, whereas d a t a from magnetic e l e c t r o ~ s c a t t e r i n g ( f o r q 2 < 1 0 f m 2 ) c a n be p a r a m e t r i z e d a s p ( q ) = e-0-42q

.

^{[ 1 5 ]}

The ( 3 ~ e , t ) r e a c t i o n on t h e p r o t o n should t h e r e f o r e d i s t i n g u i s h be- tween t h e 2 f o r m f a c t o r s . The main e f f e c t i n t h e e l e c t r o m a g n e t i c c a s e f o r t h e d i f f e r e n c e i s a s i g n i f i c a n t e f f e c t from meson-exchange c u r r e n t s . T h i s e f f e c t should n o t be p r e s e n t i n t h e hadron c a s e , and we would t h e r e f o r e e x p e c t t h e Fadeev s o l u t i o n t o b e t h e b e t t e r

c h o i c e . The p r e s e n t d a t a , c r o s s s e c t i o n s between 0 = 0' and 4 ' , a r e n o t a c c u r a t e enough t o d e t e r m i n e t h e f o r m f a c t o r t o be used f o r t h e

( 3 ~ e , t ) r e a c t i o n .

Comparison between F i g u r e s 1 0 and 11 shows a s h i f t i n energy o f t h e A-peak. T h i s c a n be e x p l a i n e d a s an e f f e c t of t h e Fermi motion i n t h e c a r b o n t a r g e t . The motion g i v e s r i s e t o a broadening of t h e A-resonance ( a s observed e . g . i n t h e l a b . s y s t e m ) . The f o l d i n g w i t h t h e 3 ~ e - f o r m f a c t o r t h e n g i v e s an a p p a r e n t s h i f t of t h e r e s o n a n c e . Such a d e s c r i p t i o n c o r r e s p o n d s t o q u a s i f r e e A-production.

The observed r e s o n a n c e c a n a l s o be d e s c r i b e d d i f f e r e n t l y . The r e s o - nance may b e c o n s i d e r e d a s an e n v e l o p e of s e v e r a l A-nucleon h o l e s t a t e s w i t h d i f f e r e n t s p i n p a r i t i e s . The observed energy s h i f t i s i n t h i s d e s c r i p t i o n a p u r e l y k i n e m a t i c e f f e c t . The i m p o r t a n t que- s t i o n i s now, whether

AN-^

i n t e r a c t i o n s g i v e r i s e t o c o r r e l a t i o n s f o r t h e AN-1 s t a t e s , r e s u l t i n g e . g . i n s h i f t s i n e n e r g y .

T h i s q u e s t i o n i s s t i l l open, b u t f u r t h e r a n a l y s i s o f t h e r a t h e r e x t e n s i v e d a t a should h o p e f u l l y h e l p i n t h e u n d e r s t a n d i n g of A ' s i n n u c l e i .

We have d a t a a t 2 GeV f o r a number o f t a r g e t s , 4 0 ~ a , 5 4 ~ e , and '08pb. We o b s e r v e i n a l l c a s e s a s t r o n g e x c i t a t i o n o f t h e A-reso- nance. The e n e r g i e s a r e ( w i t h i n u n c e r t a i n t i e s ) t h e same f o r a l l t h e n u c l e i . The c r o s s s e c t i o n s i n c r e a s e l i k e ~ ~ up t o A=90 / 3

,

b u t ~r and '08pb have r o u g h l y t h e same c r o s s s e c t i o n s .

W e s h a l l n o t go i n t o a d e t a i l e d d i s c u s s i o n h e r e , b u t r e f e r t o r e f e - r e n c e s [ 7 ] and [ 1 6 1 .

V I

-

^SUMMARY

W e have d i s c u s s e d t h e ( p , n ) and ( 3 ~ e , t ) r e a c t i o n s a t i n t e r m e d i a t e e n e r g i e s . The s p e c t a c u l a r s e l e c t i v i t y f o r O T - e x c i t a t i o n s h a s been e x p l o i t e d i n s t u d y i n g t h e s p i n - d i p o l e s t r e n g t h d i s t r i b u t i o n s . I n a s p e c i f i c c a s e , 1 2 ~ - 1 2 ~ , we have shown t h a t t h e n e u t r o n spectrum a t c e r t a i n a n g l e s d i r e c t l y g i v e s t h e r e s p o n s e f u n c t i o n f o r t h e s p i n - d i p o l e o p e r a t o r . The ( 3 ~ e , t ) r e a c t i o n i s e x p e r i m e n t a l l y v e r y a t t r a c - t i v e , and t h e a n a l y s i s o f t h e d a t a i n t e r m s of a DWIA seems pro- m i s i n g . Also f o r t h e s t u d y of A ' s i n n u c l e i t h e ( 3 ~ e , t ) r e a c t i o n c o u l d be u s e f u l . The r e a c t i o n w i t h t h e p r o t o n a s t h e t a r g e t g i v e s a v e r y c l e a n spectrum o n l y c o n t a i n i n g t h e A . For a l l n u c l e i t h e

( 3 ~ e , t ) s p e c t r a a t 2 GeV and forward a n g l e s show e x c i t a t i o n s of A ' s w i t h v e r y l a r g e c r o s s s e c t i o n s .

Acknowledgements

The m a t e r i a l p r e s e n t e d h e r e i s a r e s u l t of a c o l l a b o r a t i o n w i t h many p e o p l e . From t h e ( p , n ) work, I want t o e s p e c i a l l y t h a n k t h e f o l l o w - i n g : C.C. F o s t e r , C.D. Goodman C..A. Goulding, D.J. Horen, J.S.

Larsen, T. Masterson, J. Rapaport, E. Sugarbaker and T. Taddeucci.

The ( 3 ~ e , t ) s t u d y i s a French-Scandinavian c o l l a b o r a t i o n , and I want t o thank p a r t i c u l a r l y t h e f o l l o w i n g : D. B a c h e l i e r , M. B e d j i d i a n , I. B e r g q v i s t , M . B o i v i n , J . L . Boyard, L. C a r l g n , M. Chamcham, P . Ekstram, C . E l l e g a a r d , C . Goodman, J . Y . G r o s s i o r d , A. Guichard, M.

Gusakow, R . IIaroutunian, T. Hennino, B. J a k o b s s o n , J . C . J o u r d a i n , J . S . L a r s e n , J . L y t t k e n s , J . R . P i z z i , P. Radvanyi and M. Roy-Stephan.

R e f e r e n c e s

111 Bainum D.E., Rapaport J . , Goodman C.D., Horen D . J . , F o s t e r C.C., G r e e n f i e l d M.B., and Goulding C . A . , Phys. Rev. L e t t .

44

⁽¹⁹⁸⁰⁾

1751.

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Sugarbaker E . , Nucl. Phys. (1981) 258.

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C26

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183 O s t e r f e l d ,F Krewald S . , Dermawan H., and S p e t h J., Phys. L e t t . 105B (1981) 257.

C4-416 JOURNAL DE PHYSIQUE

G a a r d e C., L a r s e n J . S . , Sagawa H . , O h t s u k a N . , R a p a p o r t J., T a d d e u c c i T., Goodman C.D., F o s t e r C.C., G o u l d i n g C.A., Horen D . , M a s t e r s o n T., a n d S u g a r b a k e r E . , N u c l . Phys. A ( t o b e p u b l i s h e d ) Love W.G. a n d F r a n e y M . A . , P h y s . Rev.

C24

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E r i c s s o n M . , Ann. o f P h y s ,

63

( 1 9 7 1 ) 562; ~ r i c s s o n M . , F i g u r e a u A . , a n d T h e v e n e t C . , P h y s . L e t t . 45B ( 1 9 7 3 ) 1 9 ; O s e t E. a n d Rho M . , P h y s . Rev. L e t t .

42

( 1 9 7 9 ) 47;niipfer W . , D i l l i g M . , a n d R i c h t e r A . , P h y s . L e t t . 95B ( 1 9 8 0 ) 349; T o k i H . a n d W e i s e W . , P h y s . L e t t . ( 1 9 8 0 ) 1 T ~ o h r A . a n d M o t t e l s o n B . , P h y s . L e t t . lOOB ( 1 9 8 1 ) 1 0 ; B e r t s c h G . , N u c l . P h y s . A354 ( 1 9 8 1 ) 1 5 7 ; Brown

G.E.

a n d Rho M . , N u c l . P h y s . ( 1 9 8 1 ) m .

B e r t s c h G.F. a n d Hamamoto I . , P h y s . Rev.

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