MICROSCOPIC CALCULATIONS OF THE BACKGROUND BELOW GIANT RESONANCES

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MICROSCOPIC CALCULATIONS OF THE BACKGROUND BELOW GIANT RESONANCES

F. Osterfeld, A. Schulte

To cite this version:

F. Osterfeld, A. Schulte. MICROSCOPIC CALCULATIONS OF THE BACKGROUND BE- LOW GIANT RESONANCES. Journal de Physique Colloques, 1984, 45 (C4), pp.C4-13-C4-24.

�10.1051/jphyscol:1984402�. �jpa-00224067�

30URNAL DE PHYSIQUE

Colloque C4, supplément au n°3, Tome 45, mars 1984 page C4-13

MICROSCOPIC CALCULATIONS OF THE BACKGROUND BELOW GIANT RESONANCES F. O s t e r f e l d and A. S c h u l t e

Institut fuv Kernphysik, Kevnforschungsa.n~la.ge Juliah, D-5170 JUlieh, F.R.G.

Résumé - En appliquant un modèle microscopique à 1 p a r t i c u l e - 1 t r o u "doorway"

pour des é t a t s nucléaires e x c i t é s , nous montrons que les spectres d ' é n e r g i e continue des réactions d'énergie i n t e r m é d i a i r e (p,n) en d i r e c t i o n avant sont essentiellement un r é s u l t a t des processus à un pas. Le modèle est appliqué aux réactions H OCa(p,n) à une énergie i n c i d e n t e de 160 MeV et ^ V r ( p , n ) à 200 MeV. Dans l e cas du Zr nous trouvons qu'une p a r t i e importante de la f o r c e Gamow-Teller est l o c a l i s é e dans l a région de haute énergie d ' e x c i t a t i o n , 15«E <50 MeV. I l y a des i n d i c a t i o n s que l a force de t r a n s i t i o n du d i p o l e géant résonnant " s p i n - f l i p " ( A L = 1 , A S = 1 , A T = 1 ) est r é d u i t e d ' e n v i r o n 50 %.

Abstract - Using a microscopic 1 p a r t i c l e - 1 hole doorway model f o r nuclear e x c i t e d states we show t h a t the continuous forward angle energy spectra of medium energy ( p . n ) - r e a c t i o n s are mainly a r e s u l t of d i r e c t one-step proces- ses. The model i s a p p l i e d t o the reactions 4 8Ca(p,n) at 160 MeV and t o

9 0Z r ( p , n ) at 200 MeV i n c i d e n t energy. In case of 9 0Z r ( p , n ) we f i n d t h a t a large f r a c t i o n of Gamow-Teller strength i s located i n the high e x c i t a t i o n energy region 15<E <50 MeV. There are i n d i c a t i o n s t h a t the t r a n s i t i o n strength of the s p i n - f l i p giant d i p o l e (AL=1, A S = 1 , A T = 1 ) resonance i s quenched by roughly 50 %.

I - INTRODUCTION

One of the most serious problems i n the analysis of giant resonance states which ap- pear e n e r g e t i c a l l y i n the continuum region of the nuclear e x c i t a t i o n spectrum i s the decomposition of the spectra i n t o resonance and the u n d e r l y i n g physical background.

This i s p a r t i c u l a r l y t r u e f o r the e x c i t a t i o n of giant resonances by i n e l a s t i c hadron s c a t t e r i n g / l / where the resonances are located on top of a large continuum (back- ground) whose shape and magnitude is not known and whose nature depends on the probe used. U n c e r t a i n t i e s i n the decomposition of the spectra i n t o resonance and back- ground s e r i o u s l y l i m i t the accuracy w i t h which the amount of sum r u l e strength ex- hausted by the giant resonance states can be determined.

The nature of the background i s e s p e c i a l l y complicated i n reactions induced by p r o - j e c t i l e s ( p r o t o n s , deuterons, a - p a r t i c l e s ) w i t h r e l a t i v e l y low i n c i d e n t energy

(energy/nucleon < 100 MeV). In t h i s case m u l t i s t e p processes produce the dominant c o n t r i b u t i o n (75 %) t o the background cross section as has been reported by various authors / 2 - 5 / . For composite p a r t i c l e s c a t t e r i n g a d d i t i o n a l d i f f i c u l t i e s a r i s e be- cause of the p o s s i b i l i t y of the p r o j e c t i l e breakup combined w i t h other reaction mechanisms / 6 / . The s i t u a t i o n should be much s i m p l e r , however, f o r proton s c a t t e r i n g at high i n c i d e n t energy (E > 100 MeV) where the energy dependent p r o j e c t i l e - t a r g e t nucleon coupling p o t e n t i a l becomes weak / 7 / and the r e a c t i o n mechanism t h e r e f o r e dominantly d i r e c t . That t h i s supposition i s , indeed, c o r r e c t was r e c e n t l y shown by

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1984402

C4-14 J O U R N A L DE PHYSIQUE

Chiang and Hufner /8/, by B e r t s c h and Scholten /9/, and a l s o by one o f t h e p r e s e n t a u t h o r s

/lo/.

I n t h e l a t t e r p u b l i c a t i o n

/ l o /

a m i c r o s c o p i c background model was de- veloped which a l l o w e d t o c a l c u l a t e t h e c o n t i n u o u s spectrum o f h i g h energy (p,n)- s p e c t r a w i t h an accuracy o f 30 %. The model i s o n l y a p p l i c a b l e f o r f o r w a r d a n g l e s p e c t r a and f o r e x c i t a t i o n e n e r g i e s which a r e s m a l l e r t h a n h a l f t h e i n c i d e n t p r o j e c - t i l e energy. To d e s c r i b e h i g h e r Q-value r e a c t i o n s ( I Q I a Eiuc/2) and l a r g e a n g l e s c a t t e r i n g one has t o come back t o t h e models and methods d i s c u s s e d i n Machnerls c o n t r i b u t i o n /11/ t o t h i s conference.

I n t h e r e s e n t paper we extend o u r s t u d i e s o f t h e background below g i a n t resonances t o t h e "Zr(p,n) r e a c t i o n a t Einc = 200 MeV /12/. The m o t i v a t i o n f o r t h i s i n v e s t i g a - t i o n was t o determine as a c c u r a t e as p o s s i b l e t h e sum r u l e s t r e n g t h exhausted by t h e famous g i a n t Gamow-Teller (GT) resonance which was r e c e n t l y d i s c o v e r e d i n h i g h e n e r - gy (p,n)-experiments /13-16/ 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 1 it y . The GT- resonance i s t h e s p i n - i s o s p i n (AS=l, AT=l, AL=O) c o l l e c t i v e mode, which was a1 ready p r e d i c t e d by Ikeda, F u j i i and F u j i t a as e a r l y as 1963 /17/. The e x c i t i n g t h i n g about t h e GT-resonances i s t h a t o n l y r o u g h l y 65+5 % of t h e t h e o r e t i c a l l y /17/ expected t o - t a l GT-strength i s found i n t h e s e experiments /18,19/ ( w i t h t h e background s u b t r a c - t i o n as suggested i n r e f . 10). Several a u t h o r s /20,21/ have suggested t h a t t h i s so- c a l l e d quenching p f t h e t o t a l GT-strength i s due t o t h e a d m i x t u r e o f ~ ( 1 2 3 2 ) i s o b a r - nucleon h o l e (AN- ) e x c i t a t i o n s i n t o t h e p r o t o n p a r t i c l e - n e u t r o n h o l e (PN- 1 ) GT- s t a t e . F o r a q u a n t i t a t i v e u n d e r s t a n d i n g o f t h i s A i s o b a r e f f e c t , however, i t i s o f utmost importance t o c a l c u l a t e t h e background i n a most r e l i a b l e way.

R e c e n t l y B e r t s c h and Hamarnoto /22/ have p o i n t e d o u t t h a t a l a r g e f r a c t i o n o f GT- s t r e n g t h (more t h a n 50 % o f t h e m i s s i n g s t r e n g t h ) c o u l d be s h i f t e d i n t o t h e energy r e g i o n above t h e GT-resonance (10 t o 45 MeV e x c i t a t i o n energy r e g i o n ) due t o t h e m i x i n g o f t h e l p l h GT-state w i t h e n e r g e t i c a l l y h i g h - l y i n g two p a r t i c l e - t w o h o l e

(2p-2h) c o n f i g u r a t i o n s and t h a t t h i s s h i f t e d s t r e n g t h would produce a s u b s t a n t i a l p a r t o f t h e continuum background seen i n t h e 200 MeV z e r o degree 9 0 ~ r ( p , n ) - s p e c t r a a t h i g h n e g a t i v e Q-values. I n t h i s paper we t e s t t h i s c o n j e c t u r e o f B e r t s c h and Ha- mamoto /22/ i n very d e t a i l by p e r f o r m i n g a d e t a i l e d a n a l y s i s o f t h e 9 0 ~ r ( p , n ) - s p e c - t r a u s i n g o u r m i c r o s c o p i c background model. I n a d d i t i o n , we a l s o t r y t o determine t h e background below t h e s p i n i s o s p i n g i a n t d i p o l e resonance (hS=l, aT=l, a L = l ) i n o r d e r t o make a statement about t h e s p i n dependence o f t h e quenching /21,23/. The s p i n d i p o l e resonance appears e n e r g e t i c a l l y r o u g h l y 10 MeV above t h e GTR and has a w i d t h o f about 10 MeV /12,16,18/. It has been i n t e r p r e t e d as t h e envelope o f 3 c o l - l e c t i v e s t a t e s w i t h s p i n p a r i t y 0-, 1- and 2- /12,23/. B e f o r e we d i s c u s s t h e r e - s u l t s , however, we s h o r t l y d e s c r i b e t h e background model used i n t h e c a l c u l a t i o n s .

I 1

-

THE BACKGROUND MODEL

Our background model

/ l o /

i s chosen such t h a t i t d e s c r i b e s t h e d i s c r e t e and t h e con- t i n u o u s p a r t s o f t h e spectrum as c o n s i s t e n t l y as p o s s i b l e , and t h a t i t a l s o i n c l u d e s s p e c i f i c p r o p e r t i e s o f t h e t a r g e t nucleus l i k e i t s s h e l l s t r u c t u r e , n e u t r o n excess, c o l l e c t i v i t y , etc., i n d e t a i l . The model assumptions a r e as f o l l o w s :

(1) F o r (p,pl ) and (p,n) r e a c t i o n s a t h i g h i n c i d e n t e n e r g i e s ( E a 100 MeV) t h e c r o s s s e c t i o n a t f o r w a r d angles i s dominated by d i r e c t processes as l o n g as t h e e x c i t a t i o n energy i s l e s s t h a n h a l f t h e beam energy. T h i s assumption i s s u p p o r t e d by both ex- periment and t h e o r y . The 0'-cross s e c t i o n s o f t h e 200 MeV (p,n)-data o f Gaarde e t a l . /12/, f o r i n s t a n c e , show a c h a r a c t e r i s t i c f a l l i n g o f f w i t h i n c r e a s i n g e x c i t a t i o n energy. Large c o n t r i b u t i o n s o f m u l t i s t e p processes, however, s h o u l d i n s t e a d l e a d t o a

rise

i n c r o s s s e c t i o n w i t h i n c r e a s i n g e x c i t a t i o n energy due t o t h e g r e a t e r number

o f i n t e r m e d i a t e s t a t e s p o s s i b l e f o r h i g h e r energy losses. C a l c u l a t i o n s o f m u l t i s t e p r e a c t i o n c r o s s s e c t i o n s by Chiang and Hiifner /8/ show t h a t t h e f o r w a r d a n g l e c r o s s s e c t i o n s i n h i g h energy ( p , p l ) r e a c t i o n s a r e l a r g e l y due t o 1 s t e p processes. L a s t b u t not l e a s t , a l s o o u r own model c a l c u l a t i o n s s h o u l d prove o r d i s p r o v e t h i s assump- t i o n .

( 2 ) The e f f e c t i v e p r o j e c t i l e - t a r g e t nucleon i n t e r a c t i o n can be approximated by t h e f r e e N-N t - m a t r i x , i.e. by t h e G 3 Y - i n t e r a c t i o n o f Love and Franey /7/.

( 3 ) The o n l y n u c l e a r s t a t e s c o n t r i b u t i n g t o t h e (p,n)-background a t E a 100 MeV a r e s p i n f l i p (AS-1, a T = l ) s t a t e s . T h i s argument i s based on t h e f a c t t h a t t h e son-part o f t h e G3Y-i n t e r a c t i o n which e x c i t e s s p i n f l i p s t a t e s i s n e a r l y energy independent w h i l e t h e T T - p a r t which e x c i t e s t h e n o n - s p i n - f l i p s t a t e s g e t s s t r o n g l y reduced a t

E a 100 MeV / 7 / .

g e

# e ^cont

&

nuum

pro tons neutrons

Fig. 1

-

Schematic r e p r e s e n t a t i o n o f t h e m i c r o s c o p i c model used f o r t h e background c a l c u l a t i o n s . I n t h e f i g u r e E denotes t h e Fermi energy, Es t h e nucleon s e p a r a t i o n

F .

energy, and Ep t h e i n c i d e n t p r o j e c t i l e energy. F o r t h e e f f e c t i v e p r o j e c t i l e t a r g e t nucleon i n t e r a c t i o n V e f f t h e G3Y-i n t e r a c t i o n o f Love and Franey /7/ i s used.

( 4 ) The f i n a l n u c l e a r s t a t e s a r e assumed t o be o f s i m p l e p r o t o n p a r t i c l e - n e u t r o n h o l e doorway n a t u r e i n c l u d i n g bound, quasibound and continuum s t a t e s (see F i g . 1).

The s i n g l e p a r t i c l e wave f u n c t i o n s o f t h e bound and continuum s t a t e s a r a generated f r o m a Woods-Saxon p o t e n t i a l which i s chosen t o reproduce t h e known e x p e r i m e n t a l s i n g l e p a r t i c l e energies. The p r o t o n p a r t i c l e and n e u t r o n h o l e a r e coupled t o s t a t e s o f s p i n p a r i t y J*. T h i s i s advantageous s i n c e t o 0' cross s e c t i o n s o n l y s t a t e s w i t h low m u l t i p o l a r i t y can c o n t r i b u t e . Furthermore, by t h i s procedure we o b t a i n t h e con- t r i b u t i o n s t o t h e background due t o d i f f e r e n t f i n a l nucleus s p i n s J* s e p a r a t e l y . T h i s g i v e s us t h e p o s s i b i l i t y t o t r e a t t h e n u c l e a r s t r u c t u r e o f s t a t e s w i t h d i f f e r -

C4-16 JOURNAL DE PHYSIQUE

ent J' i n n u c l e a r models o f v a r y i n g s o p h i s t i c a t i o n . F o r example, we may i n c l u d e /22/

n u c l e a r c o l l e c t i v i t y and ~ ( 1 2 3 2 ) - i s o b a r e f f e c t s i n t o t h e n u c l e a r s t r u c t u r e c a l c u l a - t i o n s f o r t h e Gamow-Teller (1')-states w h i l e we use a s i m p l e p a r t i c l e - h o l e model f o r t h e r e s t o f t h e s t a t e s . The l a t t e r form t h e n t h e "background" f o r t h e GT-states. I n a d d i t i o n , we can d i s e n t a n g l e t h e spectrum i n t o t h e v a r i o u s m u l t i p o l a r i t i e s and d i s - cuss 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 each J'.

( 5 ) The whole background i s assumed t o be a s i m p l e s u p e r p o s i t i o n o f c r o s s s e c t i o n s o f i n e l a s t i c e x c i t a t i o n s t o bound, quasibound and continuum s t a t e s .

( 6 ) The c r o s s s e c t i o n s a r e c a l c u l a t e d i n t h e DWIA-approximation u s i n g t h e f a s t speed DWBA-code FROST-MARS /24/ which i n c l u d e s knock-out exchange a m p l i t u d e s e x a c t l y . The p a r t i c l e - h o l e doorway model discussed i n c l u d e s t h e n u c l e a r continuum e x a c t l y b u t t r e a t s n u c l e a r c o l l e c t i v i t y e x p l i c i t l y o n l y f o r c e r t a i n s e l e c t e d s t a t e s l i k e t h e GTR o r t h e i s o b a r i c analogue 0'-state (IAS). We argue t h a t f o r o u r purpose such a l i m i t - ed i n c l u s i o n o f n u c l e a r c o l l e c t i v i t y i s s u f f i c i e n t . Our argument i s based on t h e work o f Speth e t a l . /25/ who have shown t h a t f o r aS=l, AT=l t r a n s i t i o n s c o l l e c t i v - i t y p l a y s o n l y a r o l e f o r low m u l t i p o l a r i t i e s , i.e. f o r 0-, I+, 1- (AS-1) and, may- be, 2- s t a t e s . T h i s i s s i m p l y an e f f e c t o f t h e f i n i t e range r e s i d u a l p a r t i c l e - h o l e

( p h ) - i n t e r a c t i o n i n t h e aS=l, AT=l channel /25/ which i s s t r o n g l y r e p u l s i v e f o r low s g i n s t a t e s and weak f o r h i g h s p i n s t a t e s (J" > 2-). Therefore s t a t e s w i t h l a r g e J a r e n e a r l y u n a f f e c t e d by t h e r e s i d u a l p h - i n t e r a c t i o n (see a l s o r e f . 23 f o r a de- t a i l e d d i s c u s s i o n ) .

I 1 1

-

RESULTS AND DISCUSSION

I n t h e m i c r o s c o p i c 1 p a r t i c l e - 1 h o l e doorway mod 1 we have c a l c u l a t e d t h e background a t v a r i o u s sca t e r i n g angles f o r t h e r e a c t i o n s 4'Ca(p,n) a t 150 MeV i n c i d e n t energy

/ l o /

and f o r 9'Zr(p,n) a t 200 MeV. F i r s t we shal.1 d i s c u s s t h e background below t h e GT-resonance i n t h e 0'-spectra and a f t e r w a r d s t h e background below t h e g i a n t d i p o l e s p i n - f l i p (aS=l, AT=^, a L = l ) resonance t h e c r o s s s e c t i o n o f which peaks a t 4.5'.

111.1

-

C a l c u l a t i o n s o f t h e Background Below t h e GT-Resonance

I n Fig. 2 we show t h e ~ ~ - s ~ e c t r u m f o r t h e r e a c t i o n 4 8 ~ a ( p , n ) . The e x p e r i m e n t a l data ( t h i c k f u l l l i n e ) have been t a k e n f r o m Anderson e t a l . The c a l c u l a t i o n s f o r t h e con- t i n u o u s spectrum (dot-dashed c u r v e ) reproduce t h e data a t h i g h n e g a t i v e Q-values r e - markably w e l l i n b o t h shape and magnitude. The c a l c u l a t e d spectrum i s t h e i n c o h e r e n t sum o f a l l cross s e c t i o n s w i t h m u l t i p o l a r i t i e s AL=O t h r o u g h AL=3 (J" = 0-,l+,lV, 2+,2-,3+,3-,4-). The c a l c u l a t e d continuum f a l l s o f f s h a r p l y a t Q

-

-20 MeV. T h i s f a l l i n g o f f i s a combined e f f e c t o f t h e Coulomb and t h e c e n t r i f u g a l b a r r i e r which make t h e continuum wave f u n c t i o n o f t h e e x c i t e d p r o t o n I E , t j

>

s m a l l i n t h e n u c l e - a r s u r f a c e r e g i o n , e s p e c i a l l y f o r s m a l l e r e n e r g i e s (E <

PO

B e t ) and a n g u l a r momen- t a t

+

0. As a consequence t h e n u c l e a r t r a n s i t i o n d e R s i t i e s a r e small f o r t h e s e e n e r g i e s and t h e r e f o r e a l s o t h e c r o s s s e c t i o n s . The background j u s t below t h e GT- resonance has t h e n t o be produced f r o m a l l t h e t r a n s i t i o n s which promote a n e u t r o n from t h e 2 s - l d - s h e l l and s h e l l v i a charge exchange i n t o t h e p r o t o n 2 p - l f - s h e l l (see Fig. 1). The c r o s s s e c t i o n s produced by t h e s e s t a t e s a r e shown i n Fig. 2 as d i s c r e t e l i n e s . (Note t h a t t h e c r o s s s e c t i o n s t o t h e GTR and IAS have n o t been p l o t - ted.) Most o f t h i s background c r o s s s e c t i o n i s due t o h L = l (0-,1-,2-) and nL=2 (3') e x c i t a t i o n s . The sum o f a l l c r o s s s e c t i o n s i n t h e Q - i n t e r v a l from 2 t o 15 MeV amounts t o 5.4 mb f r o m which 2.5 mb a r e due t o 0-, 1.4 mb due t o 2-, and 1.0 mb due

E=160 MeV 1'. T=3

ec.m.=0'

talc. background

---. exp. background

l+,~=&

subtracted AL=1

\

_._.-' ^-.-.-.

___.-.

/

A '.

E=160 MeV

~ , . m = O O

AL,=l

Fig. 2

-

Zero degree s p e c t r a f o r t h e r e a c t i o n s 4 8 ~ a ( p , n ) and 4 0 ~ a ( p , n ) , The d a t a ( t h i c k f u l l l i n e ) a r e t a k e n f r o m r e f s . 26 and 12 (see t e x t ) . The d i s c r e t e l i n 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 due t o bound and quasibound s t a t e s . The arrow l a b e l l e d w i t h a L = l i n d i c a t e s t h e l o c a t i o n where t h e a L = l resonance (0-,1-,2-) would occur i f n u c l e a r c o l l e c t i v i t y were i n c l u d e d f o r t h e s e s t a t e s . The t h e o r e t i c a l c r o s s s e c t i o n s due t o t h e GTR and IAS a r e p l o t t e d . The o p t i c a l parameters f o r t h e c r o s s s e c t i o n c a l c u l a t i o n s have been t a k e n from r e f . 39.

t o 3' e x c i t a t i o n s . Note t h a t most o f t h e A i = l (0-,1-,2-) s t r e n g t h i s s h i f t e d i n t o t h e energy r e g i o n around Q = -22 MeV (as i n d i c a t e d i n t h e f i g u r e ) when t h e r e s i d u a l p h - i n t e r a c t i o n i s s w i t c h e d on. We emphasize t h a t t h e r e e x i s t s a sum r u l e f o r AL=l charge exchange modes /14/. T h i s sum r u l e t e l l s us t h a t when we c o n s i d e r a r e s i d u a l p h - i n t e r a c t i o n t h e s t r e n g t h i s o n l y r e d i s t r i b u t e d , i .e. t h e s t r e n g t h i s moved from t h e low t o t h e h i g h e x c i t a t i o n energy region. T h e r e f o r e t h e 5 mb c a l c u l a t e d i n our u n p e r t u r b e d ph-doorway model r e p r e s e n t an upper l i m i t f o r t h e background below t h e GTR i n 4 8 ~ a . I n t h e e x p e r i m e n t a l a n a l y s i s , however, a background o f r o u g h l y 17 mb i s s u b t r a c t e d (see F i g . 2a). Our c a l c u l a t i o n s show t h a t a t l e a s t 12 mb o f t h i s back- ground a r e a c t u a l l y GT-strength. By a d d i n g t h i s c r o s s s e c t i o n o f 12 mb t o t h a t o f t h e

I+,

T=3, 11 MeV s t a t e t h e GT-cross s e c t i o n a t 0' i s changed f r o m 48 t o 60 mb which makes an e f f e c t o f 25 %.

The r e s u l t s p r e s e n t e d above have been c o n f i r m e d i n t h e meantime by Rapaport /19/ and by Anderson e t a l . 1291. Both groups /19,29/ a r e u s i n g q u i t e d i f f e r e n t methods t h a n o u r s t o determine t h e background. Anderson e t a l . /29/, f o r i n s t a n c e , f i r s t s u b t r a c t a quasi f r e e s c a t t e r i n g c r o s s s e c t i o n f r o m t h e ~ ~ - ( ~ , n ) - s ~ e c t r u m . Then t h e y p e r f o r m a m u l t i p o l e decomposition o f t h e r e m a i n i n g background and f i n d t h a t most o f t h i s cross s e c t i o n has an AL=O a n g u l a r d i s t r i b u t i o n l i k e t h e GTR. They a l s o conclude t h a t 13 mb of t h e e x p e r i m e n t a l l y s u b t r a c t e d background below t h e GTR i n 4 8 ~ a (p,n) i s a c t u a l l y GT-st rength.

C4-18 J O U R N A L DE _PHYSIQUE

l l l ~ l l l ~ l l l ~ l l l ~ l l l ~

- -

- ⁹⁰

Z r ( p n ) 9 0 ~ b -

- -

E=200 MeV

-

- _{0 = 0}

0

- -

-

- -

- -

- -

- - -

- -

_I \

- f

I , I . ~ ~ ~ ~ I ~ ~ ~ I ~ ~ , ~

i ^{'.--A / \}

.

/

--

-

^{/ '---cz-}

I 1

I

^I

-

Fig. 3

-

Zero degree spectrum f o r t h e r e a c t i o n " ~ r ( ~ , n ) . The data ( t h i c k f u l l l i n e ) a r e t a k e n f r o m r e f . 12. The d i s c r e t e l i n 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 due t o bound and quasibound s t a t e s . The t h e o r e t i c a l c r o s s s e c t i o n s due t o t h e GTR and IAS a r e

not

p l o t t e d . The o p t i c a l parameters f o r t h e c r o s s s e c t i o n c a l c u l a t i o n s have been t a k e n f r o m r e f . 39.

I n F i g . 3 we show t h e 0'-spectrum of t h e r e a c t i o n "zr(p,n). The e x p e r i m e n t a l d a t a ( f u l l c u r v e ) have been t a k e n f r o m r e f . 12. The dashed c u r v e r e p r e s e n t s t h e c a l c u - l a t e d continuous background. Again we sum a1 1 c r o s s s e c t i o n s w i t h m u l t i p o l a r i t i e s aL=O t h r o u g h AL=3 (J* = 0-,1-,lt,2-,2+,3-,3+,4-) and i n c l u d e t h e r e f o r e a t l e a s t a1 1 3 o - l p l h - e x c i t a t i o n s i n t h e c a l c u l a t i o n s . There e x i s t s one d i f f e r e n c e between t h e c a l c u l a t i o n s f o r 4 8 ~ a ( p , n ) and ' O ~ r ( ~ , n ) , namely t h e l a t t e r i n c l u d e s a l s o a s p i n o r b i t p o t e n t i a l f o r t h e continuum wave f u n c t i o n o f t h e e x c i t e d p r o t o n w h i l e t h e s p i n - o r b i t p o t e n t i a l was n e g l e c t e d i n 4 8 ~ a ( p , n )

/lo/.

It i s a c t u a l l y t h e s p i n - o r b i t p o t e n t i a l which i s r e s p o n s i b l e f o r t h e resonance t y p e s t r u c t u r e s i n t h e c a l c u l a t e d continuous background around Q-values Q = -25 and Q = -31 MeV. Both bumps a r e essen- t i a l l y due t o (aL=2) J* = lf,2+,3' e x c i t a t i o n s and f o r m t h e b u i l d i n g " b l o c k s " f o r t h e A L = 2 resonance. The s p i n - o r b i t p o t e n t i a l VSO s p l i t s t h e s t r e n g t h which i s essen- t i a l l y degenerate when VSO = 0. It s h o u l d be mentioned t h a t t h e bumps would be ap- p r e c i a b l y smeared out i f we would a l s o i n c l u d e a s p r e a d i n g w i d t h i n t h e c a l c u l a - t i o n s .

Ther i s a n o t h e r @ p o r t a n t d i f f e r e n c e between t h e r e s u l t s f o r t h e c o n t i n u o u s s p e c t r a i n 4'Ca(p,n) and Zr(p,n). While t h e back round c a l c u l a t i o n s reproduce t h e e x p e r i - mental d a t a a t h i g h n e g a t i v e Q-values f o r j8Cajp,n) t h e y f a i 1 t o do so f o r 9 0 ~ r ( p , n ) and u n d e r e s t i m a t e h e r e t h e data by a f a c t o r o f about 2. The " m i s s i n g " c r o s s s e c t i o n i n t h e c a l c u l a t e d spectrum around Q = -28 MeV i s n o t r e a l l y m i s s i n g s i n c e most o f t h e c r o s s s e c t i o n due t o 0-, 1-, and 2- s t a t e s which appear i n our model a t lower

F i g . 4

-

S t r e n g t h d i s t r i b u t i o n o f t h e a L = l (0-,1-,2-) charge exchange resonance i n 9 0 ~ r as d e t e r m i n e d by an R P A - c a l c u l a t i o n o f B e r t s c h , Cha and Toki /30/.

Zr A L = l STRENGTH 1 -

e x c i t a t i o n e n e r g i e s ( t h e d i s c r e t e l i n e s i n F i g . 3) would be s h i f t e d t o t h i s energy r e g i o n i f we would i n c l u d e n u c l e a r c o l l e c t i v i t y i n o u r c a l c u l a t i o n s . To d e m o n s t r a t e t h i s we show i n F i g . 4 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 0-, 1- and 2- s t a t e s i n 'Ozr o b t a i n e d i n an RPA c a l c u l a t i o n by B e r t s c h , Cha and Toki /30/. I n t h e s e RPA c a l - c u l a t i o n s a l l t h e 0- and most o f t h e l- s t r e n g t h i s moved t o t h e energy r e g i o n around Q = -28 MeV w h i l e t h e 2- s t r e n g t h i s d i s t r i b u t e d o v e r a somewhat w i d e r energy range. The sum o f 0-, 1-, and 2- cross s e c t i o n s i n F i g . 3 amounts roughly t o

-

14 mb, f r o m w h i c h 6.6 mb a r e due t o 0-, 1.4 mb due t o 1-, and

-

⁶ mb due t o 2- t r a n s i t i o n s (see T a b l e 1). U s i n g t h e r e s u l t s o f B e r t s c h e t a l . /30/ d i s p l a y e d i n F i g . 4 we f i n d a maximum o f about 7.4 mb A L = l c r o s s s e c t i o n d i r e c t l y below t h e GT- resonance. T h i s means t h a t a l s o i n ' O ~ r ( ~ , n ) we have p r a c t i c a l l y no background below t h e GT-resonance, i.e., a l l t h e c r o s s s e c t i o n i n t h e Q - v a l u e range -12>0>-20 i s GT- s t r e n g t h . A r e a l problem, however, i s t h a t t h e c a l c u l a t e d c o n t i n u o u s spectrum under- e s t i m a t e s t h e e x p e r i m e n t a l d a t a i n t h e Q - v a l u e range -32>Q>-50. One c o u l d argue t h a t t h i s " m i s s i n g " c r o s s s e c t i o n m i g h t be produced by nL=4 e x c i t a t i o n s n o t i n c l u d e d i n o u r c a l c u l a t i o n s . We have checked t h i s p o i n t by c a l c u l a t i n g c r o s s s e c t i o n s f o r t r a n - s i t i o n s w i t h t h e l a r g e s t B(M4)-values. These t r a n s i t i o n s have e i t h e r s p i n p a r i t y J' = 4' o r 5'. We found t h a t t h e s e s t a t e s make a n e g l i g i b l e c o n t r i b u t i o n t o t h e c r o s s s e c t i o n a t f o r w a r d a n g l e s as one w o u l d e x p e c t f r o m t h e nL=4 shape of t h e i r an- g u l a r d i s t r i b u t i o n s . Furthermore, i f t h e m i s s i n g c r o s s s e c t i o n would be due t o nL=4 t r a n s i t i o n s t h e d i s c r e p a n c y between e x p e r i m e n t a l and c a l c u l a t e d c r o s s s e c t i o n s h o u l d i n c r e a s e w i t h a n g l e s i n c e c r o s s s e c t i o n s o f aL=4 shape g i v e t h e b i g g e s t c o n t r i b u t i o n a t l a r g e r s c a t t e r i n g angles. T h i s b e h a v i o u r , however, i s n o t seen i n t h e s p e c t r a . There i s a c t u a l l y j u s t t h e o p p o s i t e tendency i n t h a t t h e d i f f e r e n c e between measured and c a l c u l a t e d c r o s s s e c t i o n becomes s m a l l e r w i t h i n c r e a s i n g s c a t t e r i n g a n g l e , as can be seen f r o m Figs. 5 and 6. We t h e r e f o r e conclude t h a t t h i s " m i s s i n g " c r o s s sec- t i o n a t l a r g e Q-values and f o r w a r d a n g l e s can o n l y be produced by a n o t h e r mechanism.

b

- I

An e x p l a n a t i o n c o n s i s t e n t w i t h t h e s u g g e s t i o n s o f B e r t s c h and Hamamoto /22/ (see

- -

a l s o r e f s . 31,32,33) i s t h a t t h i s c r o s s s e c t i o n n o t d e s c r i b e d by t h e background c a l -

+ 2-

-5 w

m 2-

I-

2- 0- -

-

V)

2- -

I- 1- 1-

I I I I 1 I

C4-20 JOURNAL DE PHYSIQUE

Table 1

-

Sum o f cross s e c t i o n s o f a l l l f i w n L = l t r a n s i t i o n s w i t h s p i n - p a r i t i e s 'J = 0-, I-, and 2- o b t a i n e d f o r d i f f e r e n t s c a t t e r i n g angles o. Column 4 shows t h e sum o f 0-, 1- and 2- c r o s s s e c t i o n s w h i l e column 5 shows t h e cross s e c t i o n o b t a i n e d by sub- t r a c t i n g t h e c a l c u l a t e d continuous cross s e c t i o n from t h e e x p e r i m e n t a l one i n t h e Q- value range -20>Q>-50 MeV.

E=200 MeV

r+2- 0-+I-+ 2-

Fig. 5

-

Same as Fig. 3 b u t f o r oc.,,. = 4.5'.

1

ai (0-,1-,2-) [mb/sr]

i

16.2 6 3 48 21

1

^a i ^(2-) i

[ mbl 6 28 21 12

c u l a t i o n s i s a c t u a l l y GT-strength which was s h i f t e d t o t h i s h i g h e x c i t a t i o n energy r e g i o n due t o t h e m i x i n g o f t h e " l o w - l y i n g " l p - l h GT-state w i t h h i g h - l y i n g 2p-2h c o n f i g u r a t i o n s . Corresponding t o o u r c a l c u l a t i o n s t h e amount o f GT-strength l o c a t e d i n t h e energy range -2O<Q<-50 c o u l d be as l a r g e as 25 mb. T h i s c o n c l u s i o n i s a l s o i n agreement w i t h e s t i m a t e s o f Scholten, B e r t s c h and Toki /34/ who used a more phenome- n o l o g i c a l model f o r t h e c a l c u l a t i o n o f t h e background i n t h e spectrum-

- oeXP-aCalC [mb/sr]

-20>Q(p ,n)> -50 MeV 40

52 38 20 a ( 1 )

i [mbl 1.4 23 17 6.3 o

o0

4.5O 9.5O 12.8'

1

⁰ ( 0 i

[mbl 8.8 12 10 2.7

Fig. 6

-

Same as Fig. 3 b u t f o r Ocam. = 9.5'.

One m i g h t ask why t h e 2p-2h p o l a r i z a t i o n e f f e c t seems t o be more i m p o r t a n t f o r ' O Z ~ t h a n f o r 4 8 ~ a . T h i s i s p r o b a b l y due t o a s i m p l e s h e l l s t r u c t u r e e f f e c t . F o r example, t h e g i a n t MI-resonance observed i n i n e l a s t i c e l e c t r o n 1351 and i n e l a s t i c p r o t o n 1361 s c a t t e r i n g experiments i s v e r y sharp i n 4 8 ~ a b u t r a t h e r broad i n 9 0 ~ r 1 3 6 1 i n d i c a t - i n g a d i f f e r e n t degree o f c o u p l i n g o f t h e M1-states w i t h 2p-2h s t a t e s i n b o t h nu- c l e i . The damping mechanism o f t h e GT-state due t o 2p-2h s t a t e s i s much more e f f i - c i e n t i n heavy t h a n i n l i g h t n u c l e i due t o t h e l a r g e r d e n s i t y o f 2p-2h s t a t e s i n heavy n u c l e i .

111.2

-

C a l c u l a t i o n o f t h e Background Below t h e G i a n t D i p o l e ( A L = ~ ) Resonance I n Figs. 5 and 6 we show ' ' ~ r ( ~ , n ) s p e c t r a f o r a n g l e s o f 4.5' and 9.5', r e s p e c t i v e - l y . The d a t a ( f u l l l i n e ) have been t a k e n from r e f . 12 and t h e d o t t e d l i n e s r e p r e s e n t t h e c a l c u l a t e d c o n t i n u o u s spectrum. The peaks a t Q-values of Q = -24 and Q = -32 MeV a r e a g a i n due t o t h e (aL=2) J' = 1+,2+,3+ resonance. As i s seen froin t h e f i g u r e s t h e ( A L = ~ ) J' = 0-,1-,2- resonance g i v e s a l a r g e c o n t r i b u t i o n t o t h e c r o s s s e c t i o n

( d i s c r e t e l i n e s i n t h e f i g u r e s ) . The summed c r o s s s e c t i o n o f a l l l4w Om, I-, and 2- e x c i t a t i o n s amounts t o 63 mb a t t h e s c a t t e r i n g a n g l e o f 4.5' and t o 48 mb a t 9.5'

(see Table 1). Most o f t h e A L = ~ s t r e n g t h w i l l be s h i f t e d i n t o t h e energy r e g i o n around Q = -26 MeV when t h e r e s i d u a l p h - i n t e r a c t i o n i s s w i t c h e d on (see Fig. 4). As one can see f r o m Figs. 5 and 6 we have now, however, a b i g p r o b l e m s i n c e we have much more ( A L = ~ ) c r o s s s e c t i o n t o d i s t r i b u t e t h a n t h e e x p e r i m e n t a l d a t a p e r m i t . T h i s

i s e s p e c i a l l y s t r i k i n g f o r t h e 9.S0 spectrum. I f we s u b t r a c t i n t h e Q - v a l u e range

C4-22 JOURNAL DE PHYSIQUE

f r o m 20 t o 50 MeV t h e c a l c u l a t e d c o n t i n u o u s c r o s s s e c t i o n from t h e e x p e r i m e n t a l one we o b t a i n r o u g h l y

-

31 mb. The c a l c u l a t e d AL=l cross s e c t i o n , on t h e o t h e r hand, amounts t o 48 mb which i s by a f a c t o r o f

-

1.5 l a r g e r t h a n t h e e s t i m a t e d cross sec- t i o n above. T h i s happens a l t h o u g h we have i m p l i c i t l y assumed a l r e a d y t h a t t h e a L = l s t r e n g t h i s d i s t r i b u t e d over t h e whole Q-value range f r o m -20 t o -50 MeV. The l a t t e r amounts t o t h e assumption t h a t h i g h - l y i n g 2p-2h c o n f i g u r a t i o n s /22/ c o u p l e t o t h e AL=l resonance i n a s i m i l a r way as t o t h e GT-resonance and spread o u t t h e a L = l s t r e n g t h o v e r a wide energy range. I n s p i t e o f t h i s assumption we s t i l l need a quenching o f about 50 % i n o r d e r t o r e c o n c i l e t h e t h e o r e t i c a l and e x p e r i m e n t a l c r o s s s e c t i o n s . P a r t o f t h i s quenching i s c e r t a i n l y due t o ground s t a t e c o r r e l a t i o n s n o t i n c l u d e d i n our c a l c u l a t i o n s . Ground s t a t e c o r r e l a t i o n s w i l l reduce b o t h t h e A L = ~ cross s e c t i o n and * t h e c a l c u l a t e d c o n t i n u o u s c r o s s s e c t i o n b e i n g t h e r e f o r e an e f f e c t i v e agent t o d i m i n i s h t h e s u r p l u s c r o s s s e c t i o n mentioned above. I f we assume a r e d u c t i o n o f

-

²⁵ % f o r b o t h t h e background and t h e A L = l c r o s s s e c t i o n s t h e n t h e e x p e r i m e n t a l and c a l c u l a t e d c r o s s s e c t i o n s would j u s t agree. It may, however, a l s o w e l l be t h a t t h i s i s an o v e r e s t i m a t e and t h a t an a d d i t i o n a l quenching due t o admix- t u r e s o f ~ ( 1 2 3 2 ) i sobar-nucleon h o l e c o n f i g u r a t i o n s i n t o t h e AL=l resonance i s need- ed t o d e s c r i b e t h e d a t a as has been r e p e a t e d l y p o i n t e d o u t i n t h e a n a l y s i s o f 2- s t a t e s measured i n 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 experiments /37/.

SUMMARY

We have p r e s e n t e d m i c r o s c o p i c backgro d c a l c u l a t i o n s f o r ( p , n ) - r e a c t i o n s a t i n t e r - mediate e n e r g i e s which reproduce t h e "Ca (p,n) continuum a t

oO,

b u t which u n d e r e s t i

-

mate t h e z e r o degree 9 0 ~ r ( p , n ) continuum a t h i g h v a l u e s by a f a c t o r o f about 2. We show t h a t t h i s m i s s i n g c r o s s s e c t i o n i n case o f "ir(p,n) i s most p r o b a b l y due t o Gamow-Teller s t r e n g t h which has been s h i f t e d t o t h e h i g h e x c i t a t i o n energy r e g i o n by m i x i n g o f t h e " l o w - l y i n g " l p - l h Gamow-Teller s t a t e w i t h h i g h - l y i n g 2p-2h c o n f i g u r a - t i o n s . The amount o f GT-strength s h i f t e d t o t h e energy r e g i o n -22>Q>-50 MeV i n 9 0 ~ r ( p , n ) c o u l d be as much as

-

25 mb. Then

-

⁸⁰ % o f GT-strength i s seen i n t h e

(p,n) experiments. We a l s o show t h a t t h e r e i s e s s e n t i a l l y no background j u s t below t h e GT-resonance. T h i s statement h o l d s f o r b o t h r e a c t i o n s , 4 8 ~ a (p ,n) and ' O ~ r ( ~ , n ) . We have a l s o c a l c u l a t e d t h e background below t h e g i a n t d i p o l e (AL=l, a S = l ) r e s o - nance. We f i n d t h a t a l s o t h e A L = l s t r e n g t h s u f f e r s from t h e c o u p l i n g t o 2p-2h s t a t e s and has t o be spreadout over a wide energy range up t o 50 MeV e x c i t a t i o n energy.

Even t h e n t h e t h e o r e t i c a l A L = l c r o s s s e c t i o n a t angles o f 4.5' and 9.5' i s much l a r g e r t h a n t h e c r o s s s e c t i o n which i s o b t a i n e d by s u b t r a c t i n g t h e c a l c u l a t e d m i c r o - s c o p i c background f r o m t h e e x p e r i m e n t a l c r o s s s e c t i o n . We have t o i n t r o d u c e a quenching o f t h e n L = l s t r e n g t h by about 50 % w h i c h may be p a r t l y due t o ground s t a t e c o r r e l a t i o n s n o t c o n s i d e r e d i n o u r c a l c u l a t i o n s and p a r t l y due t o t h e a d m i x t u r e o f A i s o b a r - n u c l e o n h o l e s t a t e s i n t o t h e A L = l g i a n t d i p o l e s t a t e .

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