stretched excitations as a means to study the spin

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STRETCHED EXCITATIONS AS A MEANS TOSTUDY THE SPIN MODES OF THE NUCLEUSWITH ELECTROMAGNETIC AND HADRONIC

PROBESR. Lindgren

To cite this version:R. Lindgren. STRETCHED EXCITATIONS AS A MEANS TO STUDY THE SPIN MODES OFTHE NUCLEUS WITH ELECTROMAGNETIC AND HADRONIC PROBES. Journal de PhysiqueColloques, 1984, 45 (C4), pp.C4-433-C4-451. <10.1051/jphyscol:1984433>. <jpa-00224099>

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Colloque C4, suppl6ment a u n03, Tome 45, mars 1984 page C4-433

STRETCHED EXCITATIONS AS A MEANS TO STUDY THE SPIN MODES OF THE

NUCLEUS WITH ELECTROMAGNETIC AND HADRONIC PROBES

R.A. Lindgren

Department of Physics and Astronomy, University of Massachusetts, Amherst MA, U.S.A.

~ & s ~ ~ & - Nous avons 6 tudiC l ' e x c i t a t i o n d e s t r a n s i t i o n s d e moment a n g u l a i r e e n nous s e r v a n t d e sondes &lect romagn&tiques e t hadroniques . L 1 i n t e n s i t 6 spec t roscop ique s e d g d u i t d e s e tudes d e ( e , e l ) , ( p , p l ) , ( IT, IT ' ) e t (p ,n ) des & t a t s a l l o n g e s s6 l ec t ionn6s . Dans nos e tudes il y a d e l l i n t e n s i t & a b s e n t e d e s e x c i t a t i o n s d e moment a n g u l a i r e e l eve . Ce f a i t impl ique que d ' a u t r e s mgcanismes impor t an t s d ' e x t i n c t i o n e x i s t e n t p a r c e que l e mecanisme A - N - ~ ne c o n t r i b u e n i aux e x c i t a t i o n s d e moment a n g u l a i r e &lev6 n i aux t r a n s i t i o n s i s o s c a l a i r e s . Les & t a t s a l l o n g g s s e r v e n t d ' g t a l o n pour v g r i f i e r 3 l a f o i s 1 1 i n t e n s i t 6 t enseu r nuclgon-nucl&on dans l e phgnom&ne d e d i f f u s i o n des p ro tons , e t l ' i n t e n s i t c o r b i t a l e d e moment a n g u l a i r e e n t r e l e p ion e t l e nuclgon dans l e ph6nomene d e d i f f u s i o n des p ions . Les r e s u l t a t s s ' a cco rden t d 'une f acon remarquableavec l e s p r 6 d i c t i o n s d u m o d ~ l e D W I A .

Abs t r ac t - E x c i t a t i o n of s p i n t r a n s i t i o n s u s ing e l ec t romagne t i c and hadronic probes i s d i scussed . Spec t roscop ic s t r e n g t h s a r e deduced from s t u d i e s of ( e , e l ) , ( p , p l ) , (" ,IT') and (p ,n) f o r s e l e c t e d s t a t e s . The miss ing i s o v e c t o r and i s o s c a l a r s t r e n g t h s imply t h e e x i s t e n c e of o t h e r impor tant quenching mechanisms s i n c e t h e A - N - ~ mechanism does n o t c o n t r i b u t e t o h igh s p i n e x c i t a t i o n s o r t o i s o s c a l a r t r a n s i t i o n s . The s t r e t c h e d s t a t e s a r e used a s benchmarks t o t e s t t h e nucleon-nucleon t e n s o r f o r c e i n p ro ton s c a t t e r i n g and t h e pion-nucleon s p i n o r b i t f o r c e i n p ion s c a t t e r i n g . The r e s u l t s a r e i n s t r i k i n g agreement w i t h p r e d i c t i o n s of t h e DWIA model.

INTRODUCTION

I n t h i s s e s s i o n on s p i n e x c i t a t i o n s i n n u c l e i we a r e i n t e r e s t e d i n t h e s t u d y of t h e nuc lea r r e sponse t o nucleon o p e r a t o r s of t h e o~ t ype . It h a s been shown1 t h a t e f f e c t s on t h e s p i n - i s o s p i n o p e r a t o r s due t o p i o n i c o l a r i z a t i o n o f t he nuc lea r medium a r e s t r o n g l y momentum dependent. S t ~ d i e s ~ , ~ . ~ . ~ of M1 and GT resonances have provided impor t an t and fundamental i n fo rma t ion on quenching mechanisms i n t h e s t a t i c l i m i t of q = 0 . S t u d i e s of h igh m u l t i p o l e magnet ic resonances should p rov ide valua- b l e i n fo rma t ion on whether medium e f f e c t s a r e impor tant a t h igh q . Yet , quenching e f f e c t s such a s d e l t a pa r t i c l e -nuc leon h o l e admixtures f o r t h e miss ing GT s t r e n g t h a r e no t expected t o s t r o n g l y couple t o t h e h ighe r m u l t i p o l e magnet ic resonances .6

I n t h i s t a l k i n t h i s s e s s i o n I would l i k e t o p r e s e n t r e s u l t s from a s tudy of t h e h i g h e r magnet ic m u l t i p o l e resonances observed i n ( e , e l ) experiments a t t h e Bates-MIT L inea r Acce le ra to r Center , ( p , p f ) and ( p , n ) experiments a t t h e Ind iana U n i v e r s i t y Cyclot ron, and ( n , ~ ' ) exper iments a t t h e Los Alamos Meson Phys i c s F a c i l i t y t h a t show h igh s p i n " s t r e t ched" s t a t e s a r e a l s o quenched compared t o nuc lea r s t r u c t u r e ca lcu- l a t i o n s by amounts s i m i l a r t o t h a t observed i n Y1 and GT resonances . The absence of a n exp lana t ion of t h e miss ing s t r e n g t h he igh tens t h e i n t e r e s t i n t h e s tudy of s t r e t c h e d e x c i t a t i o n s , p a r t i c u l a r l y i n v iew of t h e i r expected s imp le s t r u c t u r e . For example, on ly one nucleon s p i n m a t r i x element i s expected t o c o n t r i b u t e t o t h e e l ec t romagne t i c and had ron ic c r o s s s e c t i o n , ' no o r b i t a l c u r r e n t c o n t r i b u t i o n s a r e expected i n ( e , e l ) ,7 and two-body meson-exchange c u r r e n t s a r e sma l l and c a l c u l - ab l e .8 Perhaps we have t h e oppor tun i ty h e r e t o s tudy t r a n s i t i o n s where t h e

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C4-434 JOURNAL DE PHYSIQUE

p r i n c i p a l quenching mechanism is most ly due t o conven t iona l nuc l ea r s t r u c t u r e . S ince t h e subnucleonic e f f e c t s a r e expected t o b e weak, a t t e n t i o n can be focussed on t h e nucleon-nucleon c o r r e l a t i o n s and c o r e p o l a r i z a t i o n e f f e c t s . The presence of unexpectedly l a r g e ground s t a t e c o r r e l a t i o n s w i l l have g e n e r a l i m p l i c a t i o n s regard- i n g most nuclear s t r u c t u r e p r o p e r t i e s i n c l u d i n g M l t r a n s i t i o n s . The s t r e t c h e d e x c i t a t i o n s a r e of f u r t h e r i n t e r e s t . Because of t h e i r s i m p l i c i t y they can be used a s benchmarks t o t e s t t h e t e n s o r component V: (q) of t h e nucleon-nucleon f o r c e and t h e s p i n o r b i t component, t:S(q), of t h e pion-nucleon f o r c e i n t h e n ~ c l e u s . ~ And u l t i m a t e l y we c a n u s e t h e had ron ic r e a c t i o n s t o deduce nuc lea r s t r u c t u r e inform- a t i o n on t h e i s o s c a l a r magnetic s t a t e s which is unob ta inab le from ( e , e l ) d a t a a lone . Examples u t i l i z i n g t h e complementary a s p e c t s of e lec t romagnet ic and hadronic r e a c t i o n s w i l l b e shown i l l u s t r a t i n g t h e s e f e a t u r e s . The d i s c u s s i o n w i l l b e i n t h e s p i r i t of m a t e r i a l p re sen ted i n Ee f . 10.

Schemat i ca l ly , t h e r e l a t i o n s between t h e weak, s t r o n g , and e l ec t romagne t i c o p e r a t o r s t h a t a r e impor tant i n coupl ing t h e p r o j e c t i l e t o t h e nucleus i n r eg ions of momentum t r a n s 5 e r t h a t f avo r 1' (q=O) and s t r e t c h e d h igh s p i n e x c i t a t i o n s (q22 fm-l) a r e g iven i n Tab le 1.

Table 1. A t a b u l a t i o n of t h e weak, s t r o n g , and e l ec t romagne t i c o p e r a t o r s r e l e v a n t f o r e x c i t a t i o n of u n n a t u r a l p a r i t y s t a t e s of low and high s p i n .

--

Probe 5' = 1+, q=O J' = 4- , 6-, 8-, . . .

The d i f f e r e n t s e n s i t i v i t i e s t o d i f f e r e n t r e g i o n s of q a r i s e s because t h e h ighe r o r d e r s p h e r i c a l Besse l f u n c t i o n j ( q r ) f o r J > l , when fo lded i n w i t h t h e n u c l e a r wave f u n c t i o n and t h e in terac t iog; lsamPles t h e nucleus a t h i g h e r r e g i o n s of q .

Another impor tant o b s e r v a t i o n t h a t d i s t i n g u i s h e s t h e s t r e t c h e d s t a t e s from t h e mag- n e t i c d i p o l e s t a t e s i s t h a t t h e former on ly invo lve t h e nuc lea r s p i n f o r t h e probes i n Table 1, whi l e t h e l a t t e r a l s o inc ludes t h e o r b i t a l momentum i n e l e c t r o n s c a t - t e r i n g . To i l l u s t r a t e t h e d i f f e r e n t s e n s i t i v i t i e s i n ( e , e r ) and ( p , p t ) f o r ex- c i t a t i o n of 1' s t a t e s , F i g . 1 shows a comparison of B(EIl)+ s t r e n g t h ob ta ined from ( e , e l ) w i t h t h e m i r r o r image c r o s s s e c t i o n s ob ta ined from ( p , p l ) t aken a t 8 = 4'

Lab

- 5 0 ~ 1 (e.eS) "

" ~ r (c.eS) '-

' * ~ e (e.e.1 N = a - 1.0- - - r f 0.5- - m

7 8 9 10 11 12 7 8 9 10 11 12 7 8 9 10 11 12

Ex ( MeV 1 Fig . 1 - A comparison of B(Ml)+ s t r e n g t h ob ta ined from ( e e ' ) w i t h mi r ro r image c r o s s s e c t i o n s ob ta ined from ( p , p 1 ) f o r 5 0 ~ i , 5 2 ~ r , and 5 Z ~ e .

f o r s e v e r a l d i f f e r e n t even-even n u c l e i i n t h e f p s h e l l ? ' l l ~ h e d i f f e r e n c e s a r e most s t r i k i n g f o r t h e s t a t e s i n 5 2 ~ r . Although some of t h e s e d i f f e r e n c e s i n e x t r a c t e d s t r e n g t h s a r i s e because of d i f f e r e n t s e n s i t i v i t i e s of t h e s p i n o p e r a t o r t o neu t ron and p ro ton components ( o r i s o s c a l a r and i s o v e c t o r ) , t h e a d d i t i o n a l o r b i t a l compone t f o r proton ex . t a t i o n s i n ( e , e t ) cannot b e neg lec t ed . A most drama t i c comparison 19 is shown f o r "V i n F ig . 2. The s t r u c t u r e near 10 MeV e x c i t a t i o n observed i n ( p , p l )

F ig . 2 - A comparison of ( e , e l ) and

2 2.0 51 ( p , p l ) s p e 5 f y a t low q f o r t h e odd c V ( P . P ' ) A nuc leus . 3 E.: 2 0 0 K . s ~ f 1

Excitat ion Energy (MeV)

a t 3" is no t a t a l l v i s i b l e i n t h e e l e c t r o n s p e c t r a . A p o s s i b l e ex- p l a n a t i o n is t h a t t h e weaker e x c i t a t i o n s i n ( e , e l ) a r i s e s from p o s s i b l e s p i n and o r b i t a l d e s t r u c t i v e i n t e r f e r e n c e . Such a p o s s i b i l i t y becomes i n c r e a s i n g l y more impor tant w i t h i n c r e a s i n g &. The s i n g l e p a r t - i c l e magnet ic d i p o l e m a t r i x element f o r t h e s p i n and o r b i t a l o p e r a t o r s a r e p l o t t e d v e r s u s 9. i n F ig . 3 . At 9. = 4 t h e p ro ton o r b i t a l r ecoup l ing m a t r i x element < ~ + 1 / 2 1 1 R I I 9.+1/2> i s

about 14 nuc lea r magnetons, which i s a s l a r g e a s t h e i s o v e c t o r s p i n - f l i p m a t r i x element between s p i n - o r b i t p a r t n e r s <9.+1/2 1 1 UT 1 I 9.-1/22. Sp in and o r b i t a l d e s t r u c t i v e i n t e r f e r e n c e i s a l s o a p o s s i b l e exp lana t ion why s t r o n g M 1 t r a n s i t i o n s a r e not ob- s e rved i n ( e , e l i n heavy nuc le i13 l i k e " ~ r and z ' ~ F ' ~ . For c lo sed

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I- Z

Fig. 3 - Sing le p a r t i c l e magnetic d ipo le ma t r ix elements f o r s p i n and o r b i t a l

; 20

_I o p e r a t o r s p l o t t e d a s a f u n c t i o n of t h e w o r b i t a l quantum number.

X cr

s h e l l n u c l e i such a r e s u l t imp l i e s t h a t h H

t h e r e would be s i g n i f i c a n t ground s t a t e c o r r e l a t i o n s breaking t h e simple s h e l l 'I model s t r u c t u r e i n o rde r f o r t h i s 0 i& I 0 mechanism t o be impor t an t . Calcu- n l a t i o n s of t h i s t ype should b e performed i n o rde r t o t e s t t h e v a l i d i t y of t h i s 2

I- p o s s i b i l i t y . k!

L 0

Since t h e i n t e r e s t i n t h i s s e s s i o n i s 4

focussed on t h e spin modes of nuc lea r E

e x c i t a t i o n s , we s h a l l avoid d i s c u s s i n g mul t ipo le magnetic t r a n s i t i o n s t h a t knowingly c o n t a i n o r b i t a l c o n t r i b u t i o n s

0 0 1 2 3 4 5 6

t o t h e c r o s s s e c t i o n s , which w i l l e l i m i n a t e t h e ambigu i t i e s d i scussed above.

R

ELECTRON, PROTON, AND PION INELASTIC SCATTERING CROSS SECTIONS TO STATES OF STRETCHED CONFIGURATION

I n e l a s t i c e l e c t r o n , proton, and p ion s c a t t e r i n g c r o s s s e c t i o n s f o r unna tu ra l p a r i t y e x c i t a t i o n s involve t h e magnetic mul t ipo le s of t h e e lec t romagnet ic i n t e r a c t i o n , t h e s p i n dependent c e n t r a l , t e n s o r , and sp in -o rb i t components of t h e nucleon-nucleon i n t e r a c t i o n , and t h e sp in -o rb i t component of t h e pion-nucleon i n t e r a c t i o n and thus depend on t h e i s o s c a l a r and i s o v e c t o r s p i n and o r b i t a l t r a n s i t i o n d e n s i t i e s of t he t a r g e t nucleus . The gene ra l express ions f o r t h e c r o s s s e c t i o n have been given i n Ref. 10 and 14. IIere, we summarize i n p l ane wave Born approximation (PWBA) t h e expres s ions f o r t h e i n e l a s t i c d i f f e r e n t i a l c r o s s s e c t i o n f o r 0+ -t J' " s t r e t ched" e x c i t a t i o n s i n e l e c t r o n , p ro ton , and pion-nucleus s c a t t e r i n g . If is assumed t h a t t he " s t r e t ched" p a r t i c l e - h o l e c o n f i g u r a t i o n is of t h e form ( j a j i L ) ~ , where

J,, = ja + j,, ja = + 112, jb = I, + 112, and ja and jb a r e the%rgest angu la r

momentum found i n t h e l a s t f i l l e d s h e l l and t h e f i r s t open s h e l l , r e s p e c t i v e l y . This c o n f i g u r a t i o n i s unique i n a space excluding lp - lh e x c i t a t i o n s wi th &3blw, s o t h e r e is no mixing w i t h o t h e r lp - lh c o n f i g u r a t i o n s . Of cour se , t h e " s t r e t ched" c o n f i g u r a t i o n s can mix wi th multi-nucleon-multi-hole c o n f i g u r a t i o n s w i t h i n t h e same s h e l l . Such mixing produces phys ica l ground and e x c i t e d s t a t e s t h a t a r e n o t pure c losed s h e l l -ahd p a r t i c l e - h o l e wave f u n c t i o n s , r e s p e c t i v e l y ; however, t h e a d d i t i o n a l components i n t h e wave func t ions w i l l not b e connected by t h e one body s p i n and' o r b i t a l c u r r e n t o p e r a t o r s . The on ly e f f e c t i s then a r e d u c t i o n of t h e t r a n s f t i o n s t r e n g t h wi th t h e c r o s s s e c t i o n s remaining p ropor t iona l t o a s i n g l e p a r t i c l e m a t r i x element corresponding t o t h e s t r e t c h e d conf igu ra t ion . An a d d i t i o n a l s i m p l i f i c a t i o n t h a t a r i s e s i s t h a t t h e o r b i t a l t r a n s i t i o n d e n s i t y and t h e s p i n t r a n s i t i o n d e n s i t y a s s o c i a t e d wi th t h e J+1 orde r Besse l f u n c t i o n vanish a s a r e s u l t of angu la r momentum r e s t r i c t i o n s on t h e s i n g l e p a r t i c l e ma t r ix element.

For i n e l a s t i c magnetic e l e c t r o n s c a t t e r i n g 1 t h e PWBA express ion f o r t h e d i f f e r e n t i a l c r o s s s e c t i o n is

where oM is t h e Mott c r o s s s e c t i o n , n is a r e c o i l f a c t o r , 8 is t h e s c a t t e r i n g a n g l e , q is t h e momentum t r a n s f e r , F~ i s t h e t r a n s v e r s e form f a c t o r , which i s g iven by T

f o r t r a n s i t i o n s t o pure i s o v e c t o r o r i s o s c a l a r s t r e t c h e d s t a t e s where T = 1 o r 0 , r e s p e c t i v e l y and gs and g; a r e t h e i s o v e c t o r and i s o s c a l a r s p i n g - f ac to r s , r e spec t - i v e l y . An e x p l i c i t exp res s ion f o r t h e s p i n t r a n s i t i o n d e n s i t y i n momentum space i s g iven by9

where C = 0 f o r T = 0 , l . F o r harmonic o s c i l l a t o r r a d i a l wave f u n c t i o n s and t h e s t r e t c h z d s t a t e c o n d i t i o n s n = nb = 1, La = R + 1, and J = R + R b , t h e r a d i a l

b o v e r l a p i n eq . (3) is given gv

where b i s t h e o s c i l l a t o r l e n g t h parameter . A u s e f u l a n a l y t i c exp res s ion f o r t h e t r a n s v e r s e e l e c t r o n s c a t t e r i n g form f a c t o r is ob ta ined by s u b s t i t u t i n g eq. ( 3 ) and eq . (4) i n t o eq . (2), o b t a i n i n g

a A 2 2 1 1 ( b ~ ) ~ - ' exp(-b 4 14)

j a j b c j a j b 2 - 7 J'',(J-~, 12 112 I (5) [ ( J - l ) ! ! ( J + l ) ! ! ]

The terms p and p N S a r e c e n t e r of mass and nucleon f i n i t e s i z e c o r r e c t i o n f a c t o r s , cm r e s p e c t i v e l y . The c o e f f i c i e n t s ZJT a r e s p e c t r o s c o p i c ampl i tudes p ropor t iona l t o t h e

one body d e n s i t y ma t r ix elements15

where T . , T f , and T a r e t h e i n i t i a l s t a t e , f i n a l s t a t e , and t r a n s i t i o n i s o s p i n , r e s - p e c t i v e i y .

For i n e l a s t i c p ro ton nucleus s c a t t e r i n g t h e corresponding PWBA expres s ion 10,14,16,17

f o r t h e d i f f e r e n t i a l c r o s s s e c t i o n t o s t r e t c h e d s t a t e s i n t h e s p i r i t of t h e impulse approximat ion i s given by

where %(k ) i s t h e reduced energy (wave number) of t h e i n c i d e n t nucleon, t h e f a c t o r a a r i s e s Yrom t h e decomposit ion of t h e r e l a t i v e nucleon-nucleon momentum -p - - -LS p =nppp -atpt , vT (q ) r e f e r s t o t h e s p i n o r b i t component of t h e e f f e c t i v e nucleon-

nucleon i n t e r a c t i o n , and


a r e t h e l o n g i t u d i n a l and t r a n s v e r s e combinations of t h e c e n t r a l and t e n s o r i n t e r - a c t i o n components. The b a r s on t h e i n t e r a c t i o n components a r e t o i n d i c a t e t h a t they a r e de f ined t o i nc lude , approximate ly , c o n t r i b u t i o n s a s s o c i a t e d wi th knockout exchange.16-'a The component VT i s s o l e l y due t o t e n s o r exchange.16-la To apply t o cha rge exchange, eq . ( 7 ) must b e m u l t i p l i e d by 2 and T is r e s t r i c t e d t o u n i t y .

For i n e l a s t i c pion-nucleus s c a t t e r i n g a t p ion i n c i d e n t e n e r g i e s near t h e (3 ,3) resonance t h e corresponding PWBA ex r e s s i o n f o r t h e d i f f e r e n t i a l c r o s s s e c t i o n t o s t r e t c h e d s t a t e s i s g iven by14,193 2B

where M and K a r e t h e reduced energy and i n c i d e n t wave number of t h e i n c i d e n t p ion, a' is a sTa t i n eq . ( 7 ) and t+S i s t h e i s o v e c t o r ( ~ = 1 ) o r i s o s c a l a r (T=O) sp in - o r b i t c:mponent of t h e e f f e c t i v e pion-nucleon i n t e r a c t i o n . I n t h i s framework pion- nucleus s c a t t e r i n g determines uniquely t h e t r a n s v e r s e s p i n d e n s i t y . I n t h e import- a n t i n c i d e n t energy r e g i o n of t h e ( 3 , 3 ) resonance , t h e pion-nucleon i n t e r a c t i o n is ve ry non-local. This g i v e s r i s e t o c o r r e c t i o n s i n eq . which produce coupl ing t o o r b i t a l c u r r e n t and sp in -cu r r en t t r a n s i t i o n d e n s i t i e s . "413 22 These terms a r e no t expected t o b e impor tant f o r t h e t r a n s i t i o n of s t r e t c h e d c o n f i g u r a t i o n s near t h e peak of t h e angu la r d i s t r i b u t i o n s .

I n t h e c a l c u l a t i o n of t h e i n e l a s t i c p ro ton and pion c r o s s s e c t i o n s t h e c e n t e r of mass and nucleon f i n i t e s i z e c o r r e c t i o n f a c t o r s a r e not inc luded i n t h e s p i n d e n s i t y

P:JT1(q). I n s t e a d t h e c e n t e r of mass c o r r e c t i o n i s made by modifying23 t h e har-

monlc o s c i l l a t o r parameter b by ( A / A - ~ ) ~ / ( ~ and t h e o v e r a l l no rma l i za t ion f a c t o r by

[ (A-1) /A]

I n e l e c t r o n s c a t t e r i n g g y > > g z s o t h i s r e a c t i o n provides mainly in fo rma t ion on t r ans - i t i o n s where psl i s l a r g e . For q = 2 fm-', t h e a rox ima te momentum t r a n s f e r f o r

J J - 1 observing h igh s p l n e x c i t a t i o n s , vl f s dominant ,I4 3"-l8 s o nucleon-nucleus s c a t - t e r i n g is a l s o p r e f e r e n t i a l l y s e n s l t l v e t o i s o v e c t o r s p i n - f l i p s t a t e s of high s p i n . This r e a c t i o n a l s o p rov ides i n fo rma t iop o: i s o s c a l a r h ' gh s p i n s t a t e s because bo th -I7 G~ and 3LS a r e a p p r e c i a b l e a t q 2-2 f m wl th most of vo.coming from knockout ex- cgange.lQ*16-18 For t h e impor t an t i n c i d e n t energy r eg lon corresponding t o t h e (3 ,3 ) resonance , tLS = 2tkS s o pion-nucleus s c a t t e r i n g f a v o r s i s o s c a l a r t r a n s i t i o n s .

STRETCHED TRANSITIONS VIA ELECTRON SCATTERING

The h igh s p i n s t r e t c h e d magnetic t r a n s i t i o n s a r e r e a d i l y observed i n e l e c t r o n s c a t - t e r i n g a t h igh q-2 fm-' and a t a backward a n g l e 8>140° where non-magnetic t r a n s - i t i o n s a r e r e t a r d e d . I n l i g h t p s h e l l n u c l e i s t r e t c h e d 114 (d5/2p3/2! t r a n s i t i o n s have been observed i n a l l s t l e n u c l e i from 12c through ''0. The distribution of M4 s t rength24y25,8 ,26,27 i n "C, 13c, 14c, and 1 4 ~ a s observed i n e l e c t r o n s c a t - t e r i n g a t 0 = 180° is shown i n Fig . 4 . The decomposit ion of t h e d i s t r i b u t i o n of s t r e n g t h i n terms of s p i n and i s o s p i n i s impor tant t o s tudy because it provides i n fo rma t ion on t h e s p i n and i s o s p i n dependent p a r t s of t h e e f f e c t i v e i n t e r a c t i o n i n n u c l e i by p rov id ing well-def i n f g s y s t e m a t i c s t h a t should b e reproduced by any r e a l i s t i c model. The nucleus C illustrates t h e f e a t u r e t h a t on ly one s t r o n g i s o v e c t o r s t r e t c h e d t r a n s i t i o n i s o b ~ e r v e d * ~ * ~ ~ i n n u c l e i whose ground s t a t e s have ze ro i s o s p i n and zero angu la r momentum. T h i s a l s o t r u e f o r M4 t r a n s i t i o n s 2 9 7 3 0 i n 160 and M6 t r a s i t i o n s 3 1 ~ 3 2 ~ 3 3 i n 2 4 ~ g and i . A second imbor t an t f e a t u r e i l l u s t r a t e d 8 by i s t h a t i n neu t ron excess n u c l e i w i t h ground s t a t e i s o s p i n To, t h e s t r e n g t h i s fragmented i n t o s e v e r a l 4- s t a t e s w i th i s o s p i n To and one s t r o n g 4-

4 -

2

F i g . 4 - E l e c t r o n s p e c t r a from t a r g e t s -1 12713'14C and 14iY a t q v 2 fm and 8 = 180" i l l u s t r a t i n g p r e f e r e n t i a l e x c i t a t i o n of M4 t r a n s i t i o n s .

I 2 c ( e , e 4 ) E o = 196.5 MeV I

- 8 = 180"

-

-

I I

cn I- = 2 - 3 0 0 -

W

- I3c ( e , e 4 ) Eo = 1 9 9 . 5 M e V 8 = 180" M 4

I

M 4 1


s t a t e w i t h T + 1. A s i m i l a r d i s t r i b u t i o n of M6 and M8 s t r e n g t h h a s been ob- served34>35 ?n 2 6 ~ g and 5 4 ~ e i n t h e s e n s e t h a t one To + 1 s t a t e is observed and s e v e a 1 To s t a t e s a r e observed. The ~ i l l e n e r - ~ u r a t h 3 6 1Mw s h e l l model c a l c u l a t i o n on l E C and t h e L,awson35,37 ( f 7 1 2 e ? 2 ) 6 - and (g912f j j2 ) s h e l l model c a l c u l a t i o n s f o r 2 6 ~ g and 5 4 ~ e , r e s p e c t i v e l y , a r e I n rough agreement w i th t hese obse rva t ions t h a t only one To + 1 l e v e l should be observed. Th i s aupea r s t o be t h e .IK = 4-, T=2 l e v e l a t 24.3 MeV i n 14c, t h e J~ = 6-, T=2 l e v e l a t 18 .1 EleV i n 2614g, and t h e J' = 8-, T=2 l e v e l a t 13.26 MeV i n 5 4 ~ e .

A t h i r d f e a t u r e i n which 1 4 ~ s e r v e s a s t h e on ly example 2 6 7 2 7 s o f a r i s t h a t f o r ground s t a t e s w i th z e r o i s o s p i n and s p i n 1, t h e i sovec to r M4 s t r e n g t h is fragmented i n t o t h e expected 3-, 4-, and 5- s t a t e s . And i n 13c where we have ne h e r zero angu la r momentum nor ze ro i s o s p i n i n t h e ground s t a t e t h e L*4 s t r eng th iS appears t o fragment i n t o J = 712, 912 and T = 112, 3 /2 s t a t e s which poses a s t r o n g e r theo- r e t i c a l cha l l enge .

Because t h e s e s t r e t c h e d l e v e l s a r e l o c a t e d i n t h e continuum, and d i f f i c u l t t o un- r a v e l from unresolved neighbor ing l e v e l s , some c a r e must b e t aken i n i d e n t i f y i n g m u l t i p o l a r i t i e s and deducing s t r e n g t h s . There i s always t h e p o s s i b i l i t y t h a ~ more than one l e v e l is be ing observed. I n a d d i t i o n , many o f t h e l e v e l s a r e unbound t o e i t h e r p ro ton o r neu t ron emiss ion and, t h e r e f o r e , continuum wave funct ions38 .in a r e a l i s t i c f i n i t e p o t e n t i a l w e l l such a s t h e Wood-Saxon form (WSWF) should b e con- s i d e r e d . With excep t ion of t e s t i n g t h e s e n s i t i v i t y of t h e c r o s s s e c t i o n t o Wood- Saxon r a d i a l shapes f o r r e l a t e d examples, t h e q u e s t i o n of r e a l i s t i c w e l l s is ignored h e r e . I n s t e a d , t h e r e s u l t s of a sys t ema t i c s tudy of most of t h e s t r o n g i s o v e c t o r l e v e l s observed i n ( e , e l ) based on the u s e of harmonic o s c i l l a t o r r a d i a l wave f u n c t i o n s (HOWF) is p re sen ted . With t h i s assumpt ion t h e form f a c t o r f o r t h e 1 H w s t r e t c h e d p a r t i c l e - h o l e c o n f i g u r a t i o n s has t h e s imp le q dependence, i n d i c a t e d i n eq. ( 5 ) ,

which peaks a t q = =/b. Th i s s i m p l i c i t y i s a n impor tant a s s e t i n t h e i d e n t i f i - c a t i o n of t h e m u l t i p o l a r i t y . The squa re of t h e t r a n s v e r s e form f a c t o r F$ i s shown v e r s u s qeff f o r s e v e r a l t r a n s i t i o n s i n v a r i o u s n u c l e i i n F i g . 5 . D i s t o r t i o n e f f e c t s due t o t h e e l ec t ron -nuc leus coulomb a t t r a c t i o n a r e t aken i n t o account by c o r r e c t i n g t h e momentum t r a n s f e r u s ing t h e r e l a t i o n

The cu rves through t h e d a t a p o i n t s i n Fig . 5 were determined by a l e a s t squa re f i t of t h e form f a c t o r c a l c u l a t e d assuming t h e extreme s i n g l e p a r t i c l e - h o l e (ESPHM) model. The o s c i l l a t o r parameter , b , and a no rma l i za t ion f a c t o r ,

were used a s f i t t i n g parameters . The r e s u l t i n g v a l u e s of b and t h e normal iz ing f a c t o r S2 a r e summarized f o r s e v e r a l i s o v e c t o r t r a n s i i o n s i n Table 2. The v a l u e s ob ta ined f o r b a r e c l o s e t o t h a t expected from t h e AlT6 r u l e . It is no s u r p r i s e t h a t t h e f a c t o r s S2(ESpHM) a r e c o n s i s t e n t l y much l e s s t han one. These f a c t o r s a r e i n t e n t e d t o s e r v e a s a u n i t i n which t o conven ien t ly compare deduced s p e c t r o s c o p i c s t r e n g t h s . S~(ESPHM) = 1 corresponds t o t h e maximum i s o v e c t o r s t r e n g t h expected i n a s i n g l e l e v e l i n t h e ESPHM. For example i n 160 t h e M4 (d5/2P3/2) s t r e n g t h i n t h e 18.98 MeV l e v e l i s S2(~spHM) = 0.41 o r 41% of t h e ESPHM p r e d i c t i o n .

To t e s t t h e s e n s i t i v i t y of t h e e x t r a t e d S2 t o shapes of t h e r a d i a l wave f u n c t ' o n s , ca l cu$g t ions o f 5 i h e form f a c t o r s were performed u s i n g bound s t a t e WSWF. For 14C, 1 4 ~ , S i , and Fe, S~(ESPHM) was found t o be 0.51, 0.61, 0.37, and 0.57 f o r t h e c o r r e s onding t r a n s i t i n s l i s t e d i n Table2. To t e s t t h e qeff approximat ion i n n u c l e i 160, 2'Mg, 28~ i , and 5zFe, DWBA c a l c u l a t i o n s , u s i n g t h e code HEIMAG, 43 modif ied t o u se HOWF, were performed by f i t t i n g t h e c r o s s s e c t i o n s i n s t e a d of t h e form f a c t o r s . The no rma l i za t ion f a c t o r s were t h e same a s t h o s e deduced i n PWBA f i t s t o w i t h i n 3 % , but t h e s i z e parameter b was s y s t e m a t i c a l l y l a r g e r by 2-4%.

Fig . 5 - The squa re of t h e t r a n s v e r s e 2

f a c t o r FT(q) is shown v e r s u s qe f o r s e v e r a l s t r e t c h e d t r a n s i t i o n s o i d i f f e r e n t m u l t i p o l a r i t y i n v a r i o u s n u c l e i .

There is ample evidence t h a t t h e ground s t a t e o r b i t s a r e n o t f u l l y occupied a s assumed i n ESPHM. The column l a b e l e d S'(THY) c o n t a i n s t h e r e s u l t s w i t h Z ~ ( T H Y ) deduced from v a r i o u s t h e o r e t i c a l models t h a t t a k e i n t o account c o r e p o l a r i z a t i o n e f f e c t s and c o r r e l a t i o n s i n t h e ground s t a t e . For example, M i l l e er-Kurath wave functionii6(MKtJf) a r e used t o c a l c u l a t e t h e M4 s t r e n g t h i n "c, "C, '*N, and "0. I n 12c, C , and 1 4 ~ t h e complete p s h e l l space is used t o c a l c u l a t e t h e ground s t a t e wave f u n c t i o n . The space is f u r t h e r enlarged t o a l l ow one nucleon i n t h e sd- s h e l l t o c a l c u l a t e t h e odd p a r i t y s t a t e s . Some p r o v i s i o n i s a l s o made t o a l l ow f g r 2$w e x c i t a t i o n s from t h e I s t o l p s h e l l , b u t n o t from t h e l p t o t h e 2 s ld s h e l l . The r e s u l t s 8 of t h i s c a l c u l a t i o n f o r t h e t h r e e s t r o n g 4- s t a t e s i n 14c a r e shown i n Table 3.

S i g n i f i c a n t improvement i s ob ta ined f o r t h e T= l s t a t e s a t 11.7 and 17 .3 MeV us ing t h e MKWF. S t i l l , however, t h e c a l c u l a t e d s t r e n g t h i s about 40% too l a r g e . Very l i t t l e improvement is ob ta ined f o r t h e T=2 s t a t e a t 24.3 MeV. When two-body meson- exchange c u r r e n t s a r e i nc luded i n t h e c a l c u l a t i o n of t h e M4 form f a c t o r , t h e ca lcu- l a t e d c r o s s s e c t i o n i n c r e a s e s by about 15% and, t h e r e f o r e , i n c l u s i o n of MEC in - c r e a s e s t h e subsequent d isagreement between experiment and theo ry by about 15%. The i n a b i l i t y t o f i t t h e M4 s t r e n g t h s c l e a r l y i n d i c a t e s a more r e a l i s t i c t r ea tmen t of t h e e x c i t e d s t a c e and ground s t a t e is r e q u i r e d , f o r example, a l lowing f o r 3Hw

c o n f i g u r a t i o n admixtures i n t h e e x c i t e d s t a t e a s w e l l a s 2p-4h ground s t a t e admix- t u r e s . I n 160 where b e t t e r agreement is ob ta ined , multi-particle-multi-h~le con-


Table 2. Deduced spec t roscop ic s t r e n g t h S2 from ( e , e l ) f o r s t r e t c h e d s t a t e s w i th s t r o n g i s o v e c t o r components.

b s S2 Ref . Z 2

Nucleus Ex .TT, T CONF

(ESPHM) " (THY) (ESPHM) (MeV)

tHarmonic o s c i l l a t o r parameter b and no rma l i za t ion ~ 2 were determined by a l e a s t squa re f i t of t h e DWBA c a l c u l a t e d c r o s s s e c t i o n t o t h e d a t a . The c e n t e r of mass and f i n i t e s i z e e f f e c t s have been inc luded i n t h e form f a c t o r du r ing t h e f i t t i n g procedu e .

2 t t S 2 = Z'(EXP)/Z2(ESPHM) where Z (ESPHM) is de f ined i n eqs . (3) and ( 6 ) . For pure

proton o r neut ron c o n f i g u r a t i o n s , z2=1.

Table 3. A comparison of t h e deduced i s o v e c t o r (d ) M4 s t r e n g t h w i t h t h e p r e d i c t i o n s of t h e ESPEM and a t r ~ n c a t e d ~ ~ ~ ~ ? ~ ~ m o d e l u s ing MKWF.

-- -- -- -

Ex J* , T S2 (ESPW4) S (MIZWF)

wi thou t w i th MEC wi thou t w i t h MEC (MeV)

24 f i g u r a t i o n s a r e a l lowed both i n t h e 8f;ound s t a t e and t h e e x c i t e d s t a t e . 3 6 I n Mg and 2 8 ~ i open s h e l l RPA c a l c u l a t i o n s p r e d i c t t o o much M6 s t r e n g t h by a f a c t o r of two. Again t h e ground s t a t e i s t r e a t e d r e a l i s t i c a l l y a l l owing f o r l d 5 / 2 . 2 ~ ~ / ~ . ld312 admixtures wh i l e t h e e x c i t e d s t a t e only a l l o w s f o r one nucleon i n t h e f712 o r b i t . Recent s h e l l model c a l c u l a t i o n s by Amusa and ~ a w s o n ~ ~ which u s e a space of

I I I !

- 8 = 160" - E~ = 221.46 MeV -

- BATES

E x ( M e V )

Fig . 6 - E l e c t r o n s p e c t r a from t a r g e t s of 5 4 9 5 6 ~ e and 58'60~i i l l u s t r a t i n g pref eren- t i a l e x c i t a t i o n of M 8 t r a n s i t i o n s .

c4-444 JOURNAL DE PHYSIQUE

t h e type (d5/2~1/2)11 f712 y i e l d s s i m i l a r quenching f a c t o r s . I n t h e extreme deformed l i m i t of t h e c o l l e c t i v e model, t h e M6 s t r e n g t h is fragmented over seven r o t a t i o n a l bands from K=O t o K=6. Each K#O r o t a t i o n a l band would g e t 2/13 of t h e extreme s i n g l e p t i c l e - h o l e model p r e d i c t i o n s . Although t h i s deformed l i m i t is u n r e a l i s t i c f o r "Si, i t does suggest a mechanism f o r producing f ragrnenta t ion.46,47 More r e a l i s t i c f ragmentat ion has been p red ic t ed by ~ m e r ~ ~ ~ by in t roduc ing C o r i o l i s coupl ing between bands b u t p r e d i c t s too much s t r e n g t h i n a s i n g l e s t a t e f o r r e a l i s - t i c deformat ions .

I n t h e f p s h e l l t h e f ragmentat ion of s t r e t c h e d M8 s t r e n g t h i s being s t u d i e d a s a f u n c t i o n of proton and neu t ron number. E l e c t r o n s c a t t e r i n g measurements have been taken on 5 4 ~ e , 5 6 ~ e , 58~i , 6 0 ~ i , a t Bates and a l s o on 5 2 ~ r a t NIKHEF.~' A comparison of s p e c t r a a r e shown i n Fig. 6 i n d i c a t i n g t h e s t r i k i n g s e l e c t i v i w i th whi h t h e 8- l e v e l s a r e e x c i t e d . Form f a c t o r s 5 p e been e x t r a c t e d f o r 5 4 ~ e , "Ni , and 6 S N i , and a n a l y s i s is still i n p rogres s on Fe. Two c h a r a c t e r i s t i c f e a t u r e s of t h e d a t a a r e : (1) t h e t o t a l M8 s t r e n g t h i s about 113 of t h e ESPHM p r e d i c t i o n f o r each nucleus and (2) t h e M8 s t r e n g t h i s s p l i t i n t o two groups wi th i s o s p i n To and To + 1. This fea- t u r e is p a r t i c u l a r l y emphasized f o r 5 6 ~ e and 6 0 ~ i where t h e r e is a c l e a r energy gap AE = Vo(To + l ) /A , which is c o n s i s t e n t w i th an asymmetry energy5' of Vo = 109210 MeV, which is c l o s e t o t h e s imple Lane model va lue of 100 MeV. Among t h e s e n u c l e i , t h e s t r o n g e s t M8 t r a n s i t i o n occur s f o r t h e Ex = 13.26 MeV T=2 s t a t e i n 5 4 ~ e , which g ives s~(EsPHM) = 0.51. Ca lcu la t ions by ~ e t s c h 4 8 which inc lude conf igu ra t ions of t h e type (gg/2p3/2f j j2)8- us ing t h e modified s u r f a c e d e l t a i n t e r a c t i o n (MSDI) y i e l d S ~ ( T H Y ) = 0.72 f o r t h e same t r a n s i t i o n . However t h e comparison between experiment and theory i s s t i l l poor f o r t h e T=l s t a t e s i n 5 2 ~ e a s is shown i n Fig . 7 . Even when t h e 2p-4h c o n f i g u r a t i o n s a r e included, on ly two T=l 8- s t a t e s a r e p red ic t ed and a r e much too s t rong . Only those c a l c u l a t e 8- s t a t e s t h a t o n t a i n more than 1% of the M8 s t r e n g t h a r e shown i n Fig . 7. I n 58Ni calculation^^^ us ing MSDI i n a s h e l l model space con ta in ing p a r t i c l e - h o l e c o n f i g u r a t i o n s of t h e type rgg12 t n d r2ggJ2f7 j2 , where r s t a n d s f o r one of the o r b i t s 2p 2 2p112, and l f 5 / 2 y i e l d S (THY) = 0.31 f o r t h e s t r o n g e s t T-2 M8 t r a n s i t i o n i n Resu l t s f o r To + To M8 t r a n s i t i o n s i n 5 8 ~ i a r e a l s o p red ic t ed t o be too l a r g e by f a c t o r s of two t o th ree . Yore sophis- t i c a t e d c a l c u l a t i o n s a r e r equ i red s i n c e e x i s t i n g r e s u l t s p r e d i c t f a r t oo much s t r e n g t h .

I n 2 0 8 ~ b where one might expect t h e s h e l l model assumpt ions t o be most adequate , measurements of the { e , e ' ) c r o s s s e c t i o n s t o t h e JT = 12-, Ex = 6.43 and 7.02 MeV s t a t e s and t o t h e JT = 14-, Ex = 6.74 MeV s t a t e a r e about h a l f t h e v a l u e s p red ic t ed by t h e ESPHM a s shown i n Table 2. I n deducing t h e s t r e n g t h , t i s assumed t h a t t h e f s t r u c t u r e of each l e v e l i s given by t h e v j 15/2i1?j$2, ~ i ~ ~ / ~ h i ~ / ~ , and ~ j ~ ~ / ~ i i 3 / ~

40 - I - I- =

5 4 ~ e ( e .a') - EXP (8 - ) I

il --- lp-3h MSDI METSCH !l .-.-. lp-3h

!I I I

LAWSON

METSCH

F i g . 7 - Comparison of exper imenta l and t h e o r e t i c a l H8 s t r e n g t h i n 5 4 ~ e f o r v a r i o u s models.

8 10 12 14 16

E x ( M e V )

conf igu ra t ions . This assumption is confirmed by r e c e n t c o r e p o l a r i z a t i o n and p a r t i c l e - v i b r a t i o n c a l c u l a t i o n s . The c o r e p o l a r i z a t i o n c a l c u l a t i o n s by Hammamoto e t a1.51 which inc lude a sum of lp-lh,lHw, 2Mw, 3%w, e t c . , con£ i g u r a t i o n s a l s o p r e d i c t t h e c o r r e c t s t r e n g t h . However, t h e c a l c u l a t i o n s employ a zero range d e l t a f o r c e (Vo = 170 ~ e v - f r n ~ ) , which is known t o be too s t r o n g a t l a r g e a i n c o m ~ a r i s o n t o r e a l i s t i c e f f e c t i v e i n t e r a c t i o n s . Recent c o r e p o l a r i z a t i o n c a l ~ u l a t i o n s > ~ in- c lud ing t h e e f f e c t s of meson and rho exchange of t h e 12- and 14- e l e c t r o n s c a t t e r i n g form f a c t o r s by Suzuki p r e d i c t too much s t r e n g t h by f a c t o r s of two and do not f i t t h e shape of t h e form f a c t o r . On t h e o t h e r hand p a r t i c l e - v i b r a t i o n coupl ing ca l cu - l a t i o n s by Krewald and ~ ~ e t h 5 ~ show a 50% reduc t ion i n M12 and M14 s t r e n g t h t o the E = 6.43, 7.02, and 6.74 MeV l e v e l s i n agreement w i t h experiment. However, t h e m?ssing s t r e n g t h i n t h e s e s t a t e s appears a s a d d i t i o n a l M12 and M14 s t r e n g t h i n a group of s t a t e s a t 8.0-9.0 MeV e x c i t a t i n , which have not been i d e n t i f i e d exper i - menta l ly . C lea r ly , t h e s i t u a t i o n i n "'Pb needs f u r t h e r exper imenta l and t h e o r e t i c a l e f f o r t . It does appear, however, t h a t t h e b e s t agreement between theory and experiment obta ined t o d a t e f o r t h e s e h igh s p i n s t a t e s occur s f o r '08pb.

For most of t h e To + 1 e x c i t a t i o n s i n Table 2 t h e r e i s improved agreement between theory and experiment when t h e model space is enlarged t o i n c l u d e more r e a l i s t i c ground s t a t e wave func t ions . Using t h e ESPHM, t h e average s2 = 0.38 and f o r t h e more r e a l i s t i c t h e o r i e s s2 = 0.66 wi th HOWF. Ex t rac t ed s t r e n g t h s a r e 15% t o 20% h ighe r i n l i g h t n u c l e i when WSWF a r e employed and about 15% lower when MEC c o r r e c t i o n s a r e in- c luded. I f bo th e f f e c t s were s imul taneously included, t h e r e s u l t s would be i n e f f e c t s i m i l a r t o those i n Table 2. Somewhat l a r g e r , spec t roscop ic s t r e n g t h s have been observed f o r t h e r e l a t e d s t r e t c h e d OMw e x c i t a t i o n s observed i n (p,n) charge exchange experiments .54 The spec t roscop ic s t r e n g t h s from Table 2 a r e , however, i n c o n t r a s t w i th t h e much l a r g e r s i n g l e p a r t i c l e s t r e n g t h s e x t r a c t e d f o r t h e l a r e s t ( s t r e t c h e d ) c o n t r i b u t i n g mul t ipo le i n e l a s t i c magnetic e l e c t r o n s c a t - ter ings ' on odd A t a r g e t s w i th ground s t a t e s p i n s j = ka + . The d i f f e r e n c e i n t h e i n e l a s t i c and e l a s t i c magnetic s t r e n g t h s sugges?s t h a t ground s t a t e and exc i t ed s t a t e c o r r e l a t i o n s a r e very important , s i n c e t h e i n t e r f e r i n g backward going ampli- t ude i n RPA c a l c u l a t i o n s f o r i n e l a s t i c t r a n s i t i o n s would not b e p resen t i n e l a s t i c s c a t t e r i n g . 5 5 For t h e To s t r e t c h e d magnetic e x c i t a t i o n s i n non-self-conjugate n u c l e i , t h e s i t u a t i o n appears more complex. For example, t h e r e i s even g r e a t e r f r agmen ta t ion and l e s s s t r e n g t h found exper imenta l ly r e d i c t e d b c u r r e n t theory ( s e e Refs . 8 , 14, 35, and 36) r ega rd ing 14c. ''K: 94Fe, and 5 S % N i w i th t h e except ion of 2 0 8 ~ b . Subnucleonic mechanisms l i k e particle-nucleon h o l e admixtures i n t h e wave f u n ~ t i o n s , ~ which have been proposed t o e x p l a i n t h e quenching of t h e Gamow-Teller s t r e n g t h i n n u c l e i , do not seem t o be a l i k e l y exp lana t ion f o r t h e quenching of h i g h s p i n s t a t e s . There i s always t h e p o s s i b i l i t y t h a t t h e r e a r e many more weak t r a n s i t i o n s t h a t cannot b e d i sce rned from t h e background. Although t h i s may be t r u e , s t i l l c u r r e n t theory i s f a r from p r e d i c t i n g such l a r g e amounts of f ragmentat ion.

HIGH SPIN STRETCHED STATES AS BENCHMARKS: COMPARISON WITH HADRONIC PROBES

Although t h e s e pure s p i n t r a n s f e r , s t r e t c h e d t r a n s i t i o n s a r e not y e t complete ly understood i n terms of c u r r e n t nuclear s t r u c t u r e models, t hey a r e s t i l l very u s e f u l a s "benchmarks" i n t e s t i n g d i r e c t , one s t e p i n e l a s t i c s c a t t e r i n g models f o r hadronic r e a c t i o n s such a s ( p , p ' ) , ( p , n ) , and ( n - , r ) . The reason f o r t h i s is t h a t w i t h i n t h e s p i r i t of t h e DWIA model, t h e same s p i n t r a n s i t i o n d e n s i t y appea r s i n the t r a n s i t i o n ampl i tude f o r a l l of t h e s e r e a c t i o n s a s was d i sp layed i n eq . ( 2 ) , eq. ( 7 ) , and eq. (10) . D i s t o r t i o n e f f e c t s a r e taken i n t o account through t h e use of DWBA in s t ead of PWBA and t h e exchange ampl i tudes f o r t h e nucleon-nucleus r e a c t i o n s a r e included e x a c t l y through t h e use of t h e code DWBA70. The comparisons of i n t e r e s t h e r e provide informat ion on t h e i sovec to r t enso r p a r t of t h e e f f e c t i v e nucleon-nucleon i n t e r - a c t i o n and t h e sp in -o rb i t component of t h e e f f e c t i v e pion-nucleon i n t e r a c t i o n . TO i l l u s t r a t e t h e former , t h e modulus of v : (~) , ~ k ~ ( ~ ) and f o r 140 MeV protons a s deduced from the f r e e nucleon-nucleon ampl i tudes i n Ref. 16 is shown i n F ig . 8. An important f e a t u r e of t h e i n t e r a c t i o n of Ref. 1 6 i s t h a t t he r a d i a l dependence i s given a s sums of Yukawa terms wi th t h e long range p a r t s of t h e c e n t r a l and t enso r


+ F i g . 8 - Modulus of the isovector 140 MeV Love- Franey t-matrix i n momentum space.

lsovector - 1 ?:/--.. ' 1 components matched t o OPEP. Clearly, 3;'f(q) is I

is dominant i n the range of q where the e lec t ron s c a t t e r i n g form f a c t o r s displayed i n Fig. 5 peak. This shows very nicely t h a t the comparison of ( e , e l ) and (p ,p l ) f o r isovector s t re tched s t a t e t r a n s i t i o n s provides inform- a t i o n on the st-cengrh and q dependence of the isovector tensor i n t e r a c t i o n i n the approximate range q = 1-2.5 fm-l. For p ic tu res of the pion- nucleon spin-orbi t i n t e r a c t i o n a t the (3,3) resonance, the reader i s re fe r red t o Refs. 14.

10 I ,v , 1 1 9 . a n d 2 2 .

0 I 2 3

q ( f m - ' 1 The d i f f e r e n t i a l cross sec t ion f o r t h e 4 - , ~ = 1 and t h e , T=l isovector s t re tched s t a t e s i n 160 and "Si, r espec t ive ly , have been measured using the ( e , e l ) , ( p , p l ) , (p ,n) , and (n ,n l ) reac t ions . The da ta and ca lcu la t

Fig. 9 - A plot of t h e ( e , e l ) 33 ( p , p t ) 6 1 ( ~ , n ) , ~ ~ and ( n , n r ) 2 b , 6 2 -9 measured and calculated cross sec t ions f o r t h e (f7,2d;+2)6- t r a n s i t i o n i n 28si.

f o r t h e 6-, T = l s t a t e i n 2 8 ~ i a r e shown a s a funct ion of q i n Fig. 9 . The t r a n s i t i o n densi ty o s c i l l a t o r parameter b and normalization s2, corresponding to f i t t i n g the cross sec t ion t o the peak i n Fig. 10 a r e summarized i n Table 4 together with several other t r a n s i t i o n s . The

value of s2 from the (p,n) and (p ,p ' ) reac t ion is about 15% lower than the values of s2 from ( n , n 7 ) and ( e , e l ) . Additional r e s u l t s f o r t h e 6-,T=1 l e v e l i n 2 8 ~ i observed i n ( 3 , ~ ' ) a t E = 333 and 500 MeV give S = 0.25 aRd 0.29 .68 This indi- c a t e s t h e energy dependence of t h e isovector tensor i n t e r a c t i o n a s given by the Love-Franey nucleon-nucleon t matrix i s approximately cor rec t i n the q r e ion sampled i n these comp- a r i s o n ~ . ~ ~ . ~ ' This is not the case f o r other e f f e c t i v e i n t e r a c t i o n s a s discussed by ~ m e r ~ . ~ ~ Similar sys- tematics a r e obtained f o r the 4 - , T=l s t a t e i n 160 i n Table 4 with s l i g h t l y more s c a t t e r than i n 28~ i . Using t h e Love-Franey nucleon-nucleon I 2 3 t-matrix16 f o r 2 8 ~ i and 54Fe and t h a t of Re$. 70 f o r 160 and 2 4 ~ g , q ( f m - I )

S ~ ( ~ , ~ ' ) / S A ~ , ~ ' ) averages 0.84. Near t h e peak of the form fac tor

Tab le 4 . A comparison of s2 deduced from hadronic probes t o s2 from ( e , e 7 ) f o r s t r o n g i s o v e c t o r s t r e t c h e d s t a t e s .

-

Targe t Probe J', T CONF s2 bt Ref . 2 S ( x , x l )

tt

( x , x l ) Ex

(M~v) (ESPHM) 2 s ( e , e t )

-1 '08Pb ( p , 6.43 12-,22 (j1512i1312) 0.80 2.30 67 0 .67i0 .05

t t h e e n t e r of mass c o r r e c t i o n f a c t o r h a s been inc luded i n t h e f i n a l de t e rmina t ion of S' and b .

2 tt e r r o r s on r a t i o s on ly inc lude u n c e r t a i n t i e s i n S ( e , e r ) .

f o r t h e s e pu re i s o v e c t o r t ~ a n s i t i o n s we a r e on ly s e n s i t i v e t o t h e t e n s o r f o r c e . These r e s u l t s could imply t h a t t h e f r e e nucleon-nucleon t e n s o r f o r c e is too s t r o n g s i n c e t h e e x t r a c t e d s t r e n g t h ob ta ined from ( p , p l ) is 16% weaker t h a n t h a t from ( e , e l ) . However, a word of c a u t i o n concerns t h e c o r r e c t i o n t o t h e one body s p i n d e n s i t y e x t r a c t e d from ( e , e l ) d a t a f p e t o . two body meson exchange cu r r en t s . ' Meson- exchange c u r r e n t c a l c u l a t i o n s 8 f o r C us ing Millener-Kurath and ESPHM wave f u n c t i o n s

2 show t h a t t h e meson exchange c u r r e n t c o n t r i b u t i o n h a s t h e e f f e c t of reducing S ( e , e ' ) by about 15%. From t h i s , one might conclude t h a t t h e spec t roscop ic f a c t o r s2 deduced from ( e , e 7 ) should b e reduced b e f o r e comparing wi th s2 deduced from hadron s c a t t e r i n g . Th i s would b r i n g the e l e c t r o n r e s u l t s i n b e t t e r agreement w i th t h e Love-Franey pa rame t r i za t ion of t h e t e n s o r force .16 I n e l a s t i c p ro ton s c a t t e r i n g s t u d i e s t o s t r e t c h e d 6- s t a t e s i n 2 6 ~ g a r e a l s o i n progress .69 The o v e r a l l g e n e r a l cons i s t ency i n r e s u l t s f o r ( e , e l ) , ( p , p l ) , and ( . r r , . i r l ) d i scussed so f a r i s q u i t e s t r i k i n g and i s s u p p o r t i v e of t h e DWIA d e s c r i p t i o n of t h e had ron ic s c a t t e r i n g p roces s . Th i s g i v e s u s a good measure of t h e s t r e n g t h of t h e t e n s o r and sp in -o rb i t components of nucleon- and pion-nucleon i n t e r a c t i o n s i n t h e r ange of q near t h e peak c r o s s s e c t i o n i n a nuc l ea r medium.

The r e s u l t s f o r t h e two 12- s t a t e s i n 2 0 8 ~ b a r e n o t c o n s i s t e n t . One of t h e s e l e v e l s

is p r ? g r i l y a n i13L2hi$/2 p ro ton c o n f i g u r a t i o n and t h e o t h e r is p r imar i ly a ji511i13j2 neu t ron c o n f i g u r a t i o n . Only t h e f i r s t i s s t r e t c h e d and s i n c e t h e r e a r e two eve s , t h i s i s no t a c l e a n example of t h e unique s t r e t c h e d e x c i t a t i o n s which


have been t h e primary t o p i c of d i s c u s s i o n he re . I t was shown i n Ref. 68 t h a t a c o n s i s t e n t exp lana t ion of t h e ( e , e 1 ) and ( p , p l ) d a t a f o r t h e s e 12- l e v e l s could not be achieved by cons ide r ing c o n f i g u r a t i o n mixing between t h e two l e v e l s a l o n e . A p o s s i b l e problem i s t h a t t h e p ro ton c r o s s s e c t i o n f o r tbg86.43 MeV neu t ron 12- l e v e l may c o n t a i n a c o n t r i b u t i o n from a n r e so lved 13- l e v e l . For pur e u t r o n ex- c i t a t i o n s l i k e t h e ( g g / 2 f j i 2 ) 8 - i n "Ca and t h e ( j i 5 2 i i3 /2)14- i n "'Pb, t h e i so - s c a l a r s p i n - o r b i t and t e n s o r c o n t r i b u t e a s w e l l a s t h e l s o v e c t o r t e n s o r component of t h e f o r c e . It would b e h i g h l y d e s i r a b l e t o de termine t h e i s o s c a l a r s p i n d e n s i t y from a n independent experiment i n o r d e r t o i s o l a t e t h e e f f ts of t h e f o r c e . Al- though agreement between t h e ( e , e l ) and ( p , p l ) r e s u l t f o r "Ca i n d i c a t e s t h a t t h e d i f f i c u l t y may n o t b e i n t h e u n c e r t a i n t i e s i n t h e f o r c e . S i n c e 2 0 8 ~ b i s such a n impor tant s h e l l model nuc l eus , i t is e s s e n t i a l t h a t i t be examined more c a r e f u l l y and complete ly w i t h r ega rd t o t h e h igh s p i n s t a ~ e s . ~ :

Ther a r e some d i f f i c u l e s i n f i t t i n g t h e ( p , p l ) and (p ,n ) a t h ighe r q f o r t h e 6- i n "Si and t h e 4 - i n 160. The p o s s i b l e appearance of a second maximum i n 160(p,p ') and (p ,n) sugges t s e v e r a l p o s s i b i l i t i e s . The t e n s o r component g e t s r a p i d l y weaker a t h igh q and t h e i s o v e c t o r s p i n - o r b i t i n t e r a c t i o n which is no t a s w e l l determined begins t o dominate. E f f e c t s due t o t h e shapes of r a d i a l wave f u n c t i o n s and t h e nuc lea r medium may a l s o be impor tant h e r e . The l o c a l nucleon-nucleon t m a t r i x ex- c ludes medium e f f e c t s such a s P a u l i b lock ing , c o n s i d e r a t i o n of t h e Fermi motion o f t a r g e t nucleons , and t h e in fo rma t ion on t h e o f f - s h e l l n a t u r e of t h e nucleon-nucleus i n t e r a c t i o n . Ca re fu l s t u d i e s of t h e energy dependence of t h e t -matr ix and o t h e r e f f e c t i v e i n t e r a c t i o n s which i-nclude medium e f f e c t s r e l a t e d t o s p i n obse rvab le s a r e r e q u i r e d and a r e underway46,61y72 and may become more impor tant a t h ighe r q.

CONCLUSIONS

From a comparison of ( e , e ' ) , ( p , p l ) , and (p ,n) e x c i t a t i o n s of 1' s t a t e s a t low q , i t is ev iden t t h a t t h e r e a r e s i g n i f i c a n t s p i n and o r b i t a l i n t e r f e r e n c e e f f e c t s , which, presumably, could be used t o d e r i v e nuc lea r o r b i t a l c u r r e n t i n fo rma t ion a s w e l l a s s p i n . On t h e o t h e r hand, e x c i t a t i o n s of s t r e t c h e d s t a t e s v i a e l ec t romagne t i c and hadronic probes e x c l u s i v e l y provide in fo rma t ion on t h e nuc lea r s p i n c u r r e n t s . Comparison t o s t a t e of t h e a r t s t r u c t u r e c a l c u l a t i o n s i n d i c a t e t h a t t h e r e is s i g - n i f i c a n t quenching of t h e i s o v e c t o r s p i n - f l i p s t r e n g t h t o h i g h s p i n s t r e t c h e d s t a t e s (38 t o 66%). The absence of subnucleonic quenching mechanisms sugges t s t h a t t h e mi s s ing s t r e n g t h may b e found i n conven t iona l nuc l ea r c o n f i g u r a t i o n mixing c a l c u l a t i o n s t h a t more r e a l i s t i c a l l y t r e a t nuc l ea r c o r r e l a t i o n s , p o l a r i z a t i o n , and nuc lea r deformat ion e f f e c t s . S ince s i m i l a r i s o v e c t o r s p e c t r o s c o p i c s t r e n g t h s a r e a l s o ob ta ined from p ro ton and pion s c a t t e r i n g , t h e miss ing s t r e n g t h is u n r e l a t e d t o any s p e c i f i c probe o r wnether t h e i n t e r a c t i o n i s s t r o n g o r e l ec t romagne t i c . Af t e r approximate ly c o r r e c t i n g t h e e l e c t r o n d a t a f o r two-body meson-exchange c u r r e n t s , agreement between ( e , e T ) and ( p , p l ) f o r s e l e c t e d i s o v e c t o r s t r e t c h e d s t a t e s is w i t h i n a few per c e n t u s ing t h e Love-Franey p a r a m e t r i z a t i o n of t h e t enso r

f o r c e . Th i s p a r t i c u l a r form is ve ry c l o s e t o t h a t p r e d i c t e d us ing a p p r o p r i a t e mix- t u r e s of one p ion exchange and rho exchange microscopic fo rces .73 Con t inua t ion o f t h e complimentary s t u d i e s extending t h e n u c l e a r a r e n a t o i n c o r p o r a t e t h e i s o s c a l a r magnetic obse rvab le s should a l l o w f o r a broader i n t e r p r e t a t i o n of quenching pheno- mena and a more fundamental p i c t u r e of n u c l e a r behavior.

ACKNOWLEDGMENTS

The a u t h o r exp res ses h i s g r a t i t u d e t o R . L . Huffman, M.A. Plum, C . Olmer, J. Mi l l ene r , and F. Pe t rov ich f o r t h e u s e of unpublished in fo rma t ion i n t h i s paper . The a u t h o r is pleased t o acknowledge Mrs. Dor i s Atkins f o r h e r e f f i c i e n t t yp ing of t h e manu- s c r i p t .

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stretched excitations as a means to study the spin

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