EXCITATION OF GIANT RESONANCES IN PION INELASTIC SCATTERING

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EXCITATION OF GIANT RESONANCES IN PION INELASTIC SCATTERING

C. Morris, S. Seestrom-Morris, L. Bland

To cite this version:

C. Morris, S. Seestrom-Morris, L. Bland. EXCITATION OF GIANT RESONANCES IN PION INELASTIC SCATTERING. Journal de Physique Colloques, 1984, 45 (C4), pp.C4-327-C4-336.

�10.1051/jphyscol:1984425�. �jpa-00224091�

JOURNAL DE PHYSIQUE

Colloque C4, suppigment au n03, Tome 45, m a r s 1984 page C4-327

EXCITATION OF GIANT RESONANCES IN PION INELASTIC SCATTERING

*+ **++

C.L. Morris*, S.J. Seestrom-Morris and L.C. Bland

: ~ o s AZamos N a t i o n a l L a b o r a t o r y , L o s Alamos, NM 87544, U.S.A.

U n i v e r s i t y o f M i n n e s o t a , M i n n e a p o Z i s , MN 55455, U.S.A.

** + + U n i v e r s i t y o f T e x a s , A u s t i n , TX 7 8 7 1 2 , U.S.A.

U n i v e r s i t y of P e n n s y Z v a n i a , P h i Z a d e l p h i a , PA 1 9 1 0 4 , U.S. A.

RQsum6 - On pr6sente les r6sultats obtenus recemment par diffusion in6lastique de pions

116nergie de la rbsonance, sur la r6gion des r6sonances g6antes des noyaux. Les nouveaux r6sultats incluent l'observation de candidats pour l a r6- sonance dipolaire avec spin-flip dans et ''~i et l'observation

grandes asym6tries des sections efficaces

pour

rbgion du continuum de *Ospb.

A b s t r a c t - ^We p r e s e n t some r e c e n t l y o b t a i n e d d a t a f o r resonance energy i n e l a s t i c p i o n s c a t t e r i n g t o t h e g i a n t resonance r e g i o n of n u c l e i . New r e s u l t s include t h e o b s e r v a t i o n of c a n d i d a t e s f o r spin-dipole resonances i n 1 2 c and Zasi, and t h e o b s e r v a t i o n of l a r g e

c r o s s s e c t i o n asymmetries f o r t h e continuum r e g i o n i n 2Oapb.

I - INTRODUCTION

Both hadronic and e l e c t r o m a g n e t i c probes have been used t o e x c i t e g i a n t resonances i n i n e l a s t i c s c a t t e r i n g . Although t h e s e s t u d i e s have c o n t r i b u t e d much t o our understanding of t h e n u c l e a r response, t h e r e s u l t s have not always been c o n s i s t e n t among t h e d i f f e r e n t probes. Pion i n e l a s t i c s c a t t e r i n g provides a new hadronic probe which, because of i t s unique s p i n - i s o s p i n couplings, may both e x c i t e new modes and provide new i n f o r m a t i o n about p r e v i o u s l y observed resonances t o h e l p r e s o l v e e x i s t i n g d i s c r e p a n c i e s .

Published s t u d i e s of pion i n e l a s t i c s c a t t e r i n g t o t h e giant-resonance r e g i o n s of 40ca[1],

[ 2 ] , 1 2 ~ 131, and 1188, [ 4 ] have shown some i n t e r e s t i n g r e s u l t s . I n t h e t h r e e h e a v i e r n u c l e i t h e g i a n t quadrupole resonance (GQR) was s t r o n g l y e x c i t e d . Although i n a l l t h r e e n u c l e i t h e deduced sum-rule f r a c t i o n was g e n e r a l l y c o n s i s t e n t w i t h t h a t e x t r a c t e d w i t h o t h e r probes, i n 18sn t h e e n e r y-weighted sum-rule f r a c t i o n observed i n

s c a t t e r i n g was twice t h a t observed i n nf s c a t t e r i n g . I n 1 2 ~ l i t t l e o r no quadrupole s t r e n g t h was seen. However, a s t r o n g s i g n a t u r e of t h e g i a n t d i p o l e resonance was observed. I n a d d i t i o n evidence f o r t h e s p i n - f l i p d i p o l e modes expected from t h e g e n e r a l i z e d [5] Goldhaber-Teller model was observed.

One common f e a t u r e of these s t u d i e s was the l i m i t e d forward a n g u l a r range of t h e d a t a . Recently, t h e EPICS channel and s p e c t r o m e t e r 161 a t LAMPF have bCen modified t o allow d a t a t o be taken a t f a r forward a n g l e s . I n t h e p r e s e n t t a l k we d e s c r i b e t h e s e m o d i f i c a t i o n s and p r e s e n t some new d a t a o b t a i n e d w i t h t h i s system.

I1 - SMALL ANGLE MODIFICATIONS

Small-angle measurements of pion i n e l a s t i c s c a t t e r i n g a r e d i f f i c u l t because of high counting r a t e s and l a r g e muon backgrounds a r i s i n g from i n - f l i g h t decays of both beam and e l a s t i c a l l y s c a t t e r e d pions. S e v e r a l m o d i f i c a t i o n s t o t h e s t a n d a r d EPICS system were made t o allow forward-angle d a t a t o be obtained. These m o d i f i c a t i o n s a r e shown i n t h e schematic drawings of the pion channel and s p e c t r o m e t e r (Fig. 1) and a r e d i s c u s s e d below.

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1984425

C4-328 JOURNAL DE PHYSIQUE

The p r o t o n f l u x through t h e EPICS channel i s approximately 10 times l a r g e r t h e the p i o n f l u x . A t a n g l e s l a r g e r t h a n 20° t h e s e p r o t o n s cause no problems i n normal d a t a t a k i n g . Forward of t h i s a n g l e t h e l a r g e energy-loss s i g n a l s produced by e l a s t i c a l l y s c a t t e r e d p r o t o n s i n the f r o n t spectrometer chambers cause r e d u c t i o n i n e f f i c i e n c y due t o space-charge e f f e c t s . I n o r d e r t o remove t h e s e protons from t h e i n c i d e n t

SEWRATOR

SCATTERING

- - - _ _

-

..

PRODUCTION SCATTERING

TARGET EM0 l ^TARCET

B M 0 4

Fig. 1 - L e f t ) Schematic view of the EPICS pion channel and Right) t h e EPICS spectrometer.

beam, a 250mg/cm2 a b s o r b e r was placed i n t h e channel a t t h e f o c u s between t h e l a s t two channel d i p o l e magnets, BM03 and BM04 ( s e e Fig. 1) The magnetic f i e l d i n BM04 was a d j u s t e d t o compensate f o r energy l o s s of t h e p i o n s i n passing through t h e absorber. Protons s u f f e r e d a much l a r g e r energy l o s s i n t h e a b s o r b e r and were b e n t o u t of t h e beam by BM04. Measurements made w i t h and w i t h o u t t h e absorber i n t h e beam showed t h a t t h e only d e t e c t a b l e e f f e c t of the a b s o r b e r on t h e pion beam was d e g r a d a t i o n of t h e energy r e s o l u t i o n from 150 keV (FWHM) t o 200 keV (FWHM).

Remaining problems were due t o muon backgrounds. Counting r a t e s w i t h the f u l l channel acceptance (--2x10~ n+/sec) were t o o l a r g e t o handle. The channel acceptance was reduced i n momentum from f1.0% t o between +0.15% and ?0.07%, with t h e s m a l l e r acceptance used a t t h e most forward s p e c t r o m e t e r a n g l e s , u s i n g t h e c o l l i m a t o r FJ04.

This r e s u l t e d i n a reduced v e r t i c a l beam s p o t s i z e of between 6 and 3 cm. To f i r s t o r d e r , t h e beam s p o t i s imaged on t h e f r o n t chambers ((21-4) w i t h a m a g n i f i c a t i o n of minus one. A l e a d c o l l i m a t o r w i t h an o ~ e n i n g of 5.1 cm was placed i n f r o n t of Cl-4 i n o r d e r t o reduce the acceptance f o r muons (which r e s u l t i n a l a r g e r image than s c a t t e r e d p i o n s ) r e l a t i v e t o t h a t f o r pions. The l o c a t i o n of t h i s c o l l i m a t o r is shown i n F i g u r e 1.

A s c i n t i l l a t o r ( S l ) 3.8 cm h i g h by 3 mm t h i c k was placed i n the c e n t e r of the c o l l i m a t o r opening t o e l i m i n a t e e v e n t s corresponding t o s l i t - e d g e s c a t t e r i n g from t h e hardware t r i g g e r and t o provide a s t a r t s i g n a l f o r measuring time of f l i g h t (TOF) through t h e s p e c t r o m e t e r d i p o l e magnets. A s t h e s e TOF s i g n a l s were n o t c o r r e c t e d f o r path-length v a r i a t i o n s , only about 80% of muon e v e n t s could be r e j e c t e d from t h e hardware t r i g g e r u s i n g S1 without b i a s i n g t h e acceptance f o r pions. Path-length c o r r e c t i o n s were made t o t h e TOF on an event-by-event b a s i s i n t h e software. The r e s u l t i n g time r e s o l u t i o n of 700 ps (FWHM) enabled c l e a n s e p a r a t i o n of pions and muons, a s shown i n t h e TOF s p e c t r a p r e s e n t e d i n Fig. 2.

At the most forward a n g l e s the muon r e j e c t i o n provided by TOF was i n s u f f i c i e n t t o

d e f i n e a t r i g g e r c l e a n enough t o o b t a i n i n e l a s t i c d a t a . Another l e v e l of muon

r e j e c t i o n was provided by p l a c i n g a carbon wedge backed by a s c i n t i l l a t o r i n t h e

s p e c t r o m e t e r f o c a l p l a n e , a s shown i n Fig. 1. The t h i c k n e s s of t h e wedge was s e t t o

b e - c l o s e t o t h e pion range a s a f u n c t i o n of f o c a l plane p o s i t i o n ( c r u d e l y

corresponding t o momentum). Pions w e n both ranged out and absorbed by n u c l e a r

i n t e r a c t i o n s , whereas muons passed through t h e absorber and were d e t e c t e d by Sb.

The e f f e c t i v e n e s s of t h i s technique i s demonstrated i n Fig. 2, where TOF s p e c t r a a r e s e p a r a t e l y presented f o r e v e n t s accepted and r e j e c t e d by S4. E f f i c i e n c y scans of t h e muon r e j e c t e r made by observing a n e l a s t i c l i n e w i t h the s p e c t r o m e t e r magnet f i x e d and channel magnets v a r i e d showed approximately 96% of a l l muons were r e j e c t e l while only 2% of pions were r e j e c t e d by t h i s method.

Fig. 2 - ^{Time of} f l i g h t spectrum f o r a ) p i o n s , b ) muons a s determined by t h e focal-plane muon r e j e c t e r .

I n a d d i t i o n t o t h e methods l i s t e d above each e v e n t was liequired t o have a t r a j e c t o r y which p r o j e c t e d back t o t h e t a r g e t , and t o have a n g l s e n t e r i n g t h e spectrometer which were c o n s i s t e n t w i t h those e x i t i n g t h e spectromet 2 r w i t h i n f 1 0 mrad u s i n g t h e known o p t i c s . This requirement was e s p e c i a l l y u s e f u l f o r r e j e c t i n g e v e n t s i n which pions decayed between t h e f r o n t and r e a r chambers.

A t forward a n g l e s t h e hardware t r i g g e r r e q u i r e d t h e TOF through t h e spectrometer t o be i n the range expected f o r p i o n s , and r e q u i r e d t h e absence of a s i g n a l from t h e f o c a l p l a n e muon r e j e c t e r . I n a d d i t i o n , a f i r s t o r d e r hardware c a l c u l a t i o n of momentum l o s s , u s i n g c o a r s e p o s i t i o n information from hhe d r i f t chambers, was used t o r e j e c t 99 o u t of e v e r y 100 e l a s t i c s c a t t e r i n g e v e n t s from t h e hardware t r i g g e r . A t l a r g e r a n g l e s the t r i g g e r requirements were relaxed and t h e corresponding c u t s were made i n t h e software. The t y p i c a l f r a c t i o n of e v J n t s which were p i o n s v a r i e d from s e v e r a l p e r c e n t a t 8' t o n e a r l y 1.0 a t 20°. More t h a n 96% of t h e muon e v e n t s were e l i m i n a t e d from t h e hardware t r i g g e r by t h e requPrements l i s t e d above. The remaining muons were e l i m i n a t e d by s o f t w a r e c u t s .

A missing-mass spectrum o b t a i n e d a t 8' f o r 162 MeV pion i n e l a s t i c s c a t t e r i n g from

i s shown i n Figure 3. This spectrum h a s been c o r r e c t e d f o r focal-plane

e f f i c i e n c y , and h a s been c o r r e c t e d f o r t h e r e j e c t e d e l a s t i c e v e n t s .

JOURNAL DE PHYSIQUE

Q - VALUE (MeV)

Fig. 3 - Missing mass spectrum f o r 162 MeV

s c a t t e r i n g from 1 2 c a t 8' l a b o r a t o r y angle.

111 - LOW LYING COLLECTIVE STATES

A t i n c i d e n t pion e n e r g i e s between 100 and 300 MeV t h e A resonance dominates t h e pion-nucleon i n t e r a c t i o n . I n t h e static-DWIA mode?; where i n t e r m e d i a t e

propagation is ignored, t h e r e l a t i v e s t r e n g t h s of t h e c e n t r a l , spin-dependent, and isospin-dependent p a r t s of t h e f o r c e a r e f i x e d with r e s p e c t t o each o t h e r by t h e quantum numbers of t h e A. The s t r o n g e s t p a r t of t h e f o r c e is t h e s p i n - i s o s p i n independent p a r t . Consequently c o l l e c t i v e s t a t e s a r e s t r o n g l y e x c i t e d i n pion i n e l a s t i c s c a t t e r i n g .

A comparison of DWIA c a l c u l a t i o n s using e m p i r i c a l l y determined form f a c t o r s from 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 i n g e n e r a l g i v e s e x c e l l e n t agreement w i t h pion i n e l a s t i c s c a t t e r i n g t o s u c h c o l l e c t i v e s t a t e s [7-101. Cross s e c t i o n s and c a l c u l a t i o n s of resonance energy ( i n c i d e n t pion energy of 180 MeV) pion s c a t t e r i n g I111 from t h e ground s t a t e and 2f member of t h e r o t a t i o n a l band i n 1 5 2 ~ m a r e p r e s e n t e d a s an example i n Figure 4. The DWIA (dashed l i n e ) and coupled-channel-impulse approximation (CCIA s o l i d l i n e ) c a l c u l a t i o n s shown i n t h e f i g u r e have used c o l l e c t i v e - m o d e l form f a c t o r s determined from e l a s t i c and 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 . A d e p a r t u r e from t h e s t a t i c model i s an energy s h i f t of -28 MeV used i n e v a l u a t i n g t h e T - m a t r i x elements from pion-nucleon phase s h i f t s . This phenomenology has been shown t o improve f i t s t o e l a s t i c s c a t t e r i n g 1121. The q u a l i t y of agreement between t h e c a l c u l a t i o n s and t h e d a t a i n t h i s c a s e is t y p i c a l of t h a t o b t a i n e d i n o t h e r n u c l e i f o r s t r o n g l y e x c i t e d c o l l e c t i v e s t a t e s .

Some e x c e p t i o n s t o t h i s g e n e r a l l y good agreement have been observed. I n a

comparison of DWIA c a l c u l a t i o n s w i t h d a t a f o r low l y i n g s t a t e s i n 12C and 4 0 ~ a , [ 7 ]

small-angle c r o s s s e c t i o n s f o r t h e 2f (4.44 MeV) s t a t e were observed t o be

underestimated by n e a r l y a f a c t o r of two w h i l e t h o s e f o r t h e 0; s t a t e were

overestimated by a s i m i l a r f a c t o r . The r e s u l t s of a more d e t a i l e d s t u d y of pion

i n e l a s t i c s c a t t e r i n g from I 2 c a t forward a n g l e s a t 162 MeV i n c i d e n t pion energy

along w i t h some c a l c u l a t i o n s a r e p r e s e n t e d i n Figure 5. The e x p l a n a t i o n of t h e

d i s c r e p a n c i e s between static-DWIA c a l c u l a t i o n s ( s o l i d l i n e ) and t h e d a t a r e s t s i n

two d i f f e r e n t higher-order processes. The enhancement of t h e 2; c r o s s s e c t i o n s a t

forward a n g l e s a r i s e s from s p i n - f l u x t e n s o r coupling terms t h a t appear i n t h e

isobar-hole model. These have been e v a l u a t e d i n a dynamic-DWIA c a l c u l a t i o n by Lenz,

Fig. 4 - Data and c a l c u l a t i o n s f o r e l a s t i c and i n e l a s t i c s c a t t e r i n g of 180 MeV pions from lS2Sm. The c a l c u l a t i o n s a r e d e s c r i b e d i n t h e t e x t .

Thies and Horikawa [ I 3 1 (dashed l i n e ) . These e x t r a censor p i e c e s of t h e i n t e r a c t i o n do n o t a f f e c t t r a n s i t i o n s w i t h A j < 1, and s o do n o t e x p l a i n t h e forward-angle c r o s s s e c t i o n s f o r t h e 0; s t a t e , a s can be seen by comparing t h e dynamic-DWIA and static-DWIA c a l c u l a t i o n s f o r t h i s s t a t e .

This discrepancy has been removed by Sparrow and Gerace [14] by c a l c u l a t i n g two-step c o n t r i b u t i o n s through t h e 2f s t a t e . These have been e v a l u a t e d i n t h e coupled channel impulse approximation (CCIA), shown a s t h e dot-dash l i n e i n t h e f i g u r e . The form f a c t o r s used i n t h e s e c a l c u l a t i o n s have been f i t t o a v a i l a b l e e l e c t r o m a g n e t i c o b s e r v a b l e s and, a s can be s e e n , g i v e a good d e s c r i p t i o n of t h e d a t a .

I V - SPIN-FLIP DIPOLE STATES

Resonance-energy pion i n e l a s t i c s c a t t e r i n g can a l s o e x c i t e s t a t e s which involve AS

0 and/or AT

0. One example of such an e x c i t a t i o n which involves AS

0, AT

1 is t h e g i a n t d i p o l e resonance (GDR). I f t h e Goldhaber-Teller model of t h i s resonance is extended t o include s p i n degrees of freedom, and i f spin-dependent n u c l e a r f o r c e s a r e i g n o r e d , t h e n t h e r e ought t o be s t a t e s w i t h AS

1 ( w i t h Jv

0-,

1- and 2-1 degenerate i n energy with t h e GDR. The T

0 members of t h i 6 m u l t i p l e t correspond t o d i p o l e e x c i t a t i o n s w i t h spin-up p a r t i c l e s o s c i l l a t i n g a g a i n s t spin-down p a r t i c l e s r a t h e r t h a n neutrons o s c i l l a t i n g a g a i n s t p r o t o n s a s i s t h e case f o r t h e GDR. Strong evidence f o r c o n s i d e r a b l e 2- s t r e n g t h w i t h T = 0 and 1 i n t h e r e g i o n of t h e GDR i n

has a l r e a d y been observed i n pion i n e l a s t i c s c a t t e r i n g [3].

The evidence f o r 1- s p i n - f l i p s t r e n g t h was much weaker because t h e d a t a d i d not go t o small enough a n g l e s .

Both DWIA and e i k o n a l model c a l c u l a t i o n s p r e d i c t a n g u l a r d i s t r i b u t i o n s f o r a J"

1-; AS

1 e x c i t a t i o n t o f o l l o w [ J ~ ( ~ R ) ] ~ a t forward a n g l e s . This is u n l i k t h e a n g u l a r d i s t r i b u t i o n expected f o r t h e GDR, which i s expected t o f o l l o w [Jl(qR)] 8

and t o go t o z e r o a t oO, ^but i s the same a s t h a t expected f o r a 0+ e x c i t a t i o n . The

p r e v i o u s l y d e s c r i b e d small-angle m o d i f i c a t i o n s have been used t o measure i n e l a s t i c

s c a t t e r i n g from 1 2 ~ , 2881 and kOca t o s e a r c h f o r s t a t e s w i t h t h i s p r e d i c t e d forward

a n g l e behavior [ I S ] .

JOURNAL DE PHYSIQUE

Fig. 5 - Angular d i s t r i b u t i o n s measured f o r 162 MeV 1 2 ~ ( r + , r + ' ) 1 2 ~ a l o n g w i t h s t a t i c DWIA ( s o l i d ) , dynamic DWIA ( d a s h e d ) , and CCIA (dot-dashed) c a l c u l a t i o n s .

S p e c t r a f o r both 1 2 c and 2 8 ~ i a r e p r e s e n t e d i n F i g u r e 6. I n both n u c l e i s t r o n g l y forward-peaked a n g u l a r d i s t r i b u t i o n s were observed f o r s t a t e s o r groups of s t a t e s l o c a t e d a t e x c i t a t i o n e n e r g i e s of 20.0 and 17.6 MeV r e s p e c t i v e l y . The a n g u l a r d i s t r i b u t i o n s f o r b o t h s t a t e s a r e c o n s i s t e n t w i t h t h a t expected f o r t h e e x c i t a t i o n of a

o r spin-f l i p d i p o l e s t a t e .

The f r a c t i o n s of t h e monopole, energy-weighted sum r u l e r e q u i r e d t o reproduce t h e observed c r o s s s e c t i o n s , u s i n g a breathing-mode form f a c t o r i n t h e DWIA, i s 15% i n 1 2 c and 25% i n

These a r e much l a r g e r t h a n observed i n t h i s e x c i t a t i o n e n e r g y r e g i o n i n (He3 ,He3') [16]. Although no monopole s t r e n g t h was observed i n any n u c l e u s l i g h t e r than 6 4 ~ n i n e a r l i e r O0

[ I 7 1 a more r e c e n t experiment [ I 8 1 r e p o r t s s i g n i f i c a n t monopole s t r e n g t h i n 28Si a t a s i m i l a r e x c i t a t i o n e n e r g y - A l t e r n a t i v e l y , m i c r o s c o p i c c a l c u l a t i o n s of t h e c r o s s s e c t i o n s t o a doorway s t a t e which c o n t a i n s a l l of t h e s p i n - f l i p d i p o l e s t r e n g t h expected i n a ltlw s h e l l - m o d e l s p a c e a l s o reproduce t h e observed a n g u l a r d i s t r i b u t i o n s . The observed c r o s s s e c t i o n s i n d i c a t e 62% of t h i s (non-energy weighted) sum r u l e i s exhausted i n 1 2 c and 84% i n 28Si i f t h e s e s t a t e s a r e assumed t o be i s o s c a l a r . N e i t h e r t h e s p i n - f l i p d i p o l e n o r t h e monopole c a l c u l a t i o n g i v e s a good a c c o u n t of t h e energy dependence of t h e s e c r o s s s e c t i o n s .

I n o r d e r f o r t h e s e s t a t e s t o be i d e n t i f i e d a s T

s p i n - f l i p components of t h e GDR,

t h e p o s s i b i l i t y of a monopole assignment needs t o be r u l e d o u t u s i n g measurements

made w i t h o t h e r probes. S p i n - f l i p p r o b a b i l i t y measurements i n ( p , p ' ) might be v e r y

u s e f u l t o h e l p s o r t out t h i s puzzle. S y s t e m a t i c s a l s o need t o be e s t a b l i s h e d i n

o t h e r n u c l e i .

Fig. 6 - L e f t ) ~ ~ c ( w + , T + ' ) ~ ~ c a t 8O(lab) and TT=164 MeV. R i g h t ) Same f o r 2 8 ~ i .

V - "ISOSCALAR" GIANT RESONANCES I N 2 0 8 ~ b

We have a l s o u s e d t h e small-angle m o d i f i c a t i o n s t o s t u d y p i o n i n e l a s t i c s c a t t e r i n g a t a n i n c i d e n t energy of 162 MeV f o r t h e g i a n t resonance r e g i o n i n 2 0 8 ~ b . P r e v i o u s work i n medium-mass n u c l e i ( d i s c u s s e d e a r l i e r ) h a s shown t h a t i s o s c a l a r resonances a r e s t r o n g l y e x c i t e d w i t h good s i g n a l - t o - n o i s e r a t i o s . The s p e c t r a o b t a i n e d (Fig.

7) show t h a t t h i s is a l s o t h e c a s e f o r *08pb. The d a t a have been analyzed as a sum of Gaussian peaks superimposed on a background which v a r i e s slowly both i n a n g l e and i n e x c i t a t i o n energy. Peaks were observed a t e x c i t a t i o n e n e r g i e s of 10.5, 13.5, 17.7, and 22.0 MeV. These correspond t o t h e p r e v i o u s l y observed g i a n t quadrupole

Fig. 7 - Normalized s p e c t r a f o r 162 MeV p i o n i n e l a s t i c s c a t t e r i n g t o t h e g i a n t

resonance r e g i o n i n 208pb.

C4-334 JOURNAL DE PHYSIQUE

(GQR), g i a n t monopole (GMR), h i g h energy o c t u p o l e (HEOR), and a sum of t h e i s o s c a l a r g i a n t d i p o l e (ISGDR) and t h e i s o v e c t o r g i a n t quadrupole (IVGQR) resonances. The c r o s s s e c t i o n a n g u l a r d i s t r i b u t i o n s o b t a i n e d f o r both n+ and n- s c a t t e r i n g t o t h e GQR a r e p r e s e n t e d i n Figure 8.

One s t r i k i n g f e a t u r e of t h e d a t a i s t h e d i f f e r e n c e i n c r o s s s e c t i o n s measured f o r r + and n- f o r both t h e g i a n t resonances and t h e continuum. This can be r e a d i l y observed i n t h e f i g u r e . This d i f f e r e n c e s u g g e s t s t h a t t h e r o l e s played by n e u t r o n s and p r o t o n s i n t h e s u r f a c e r e g i o n ( t h e r e g i o n probed by pion i n e l a s t i c s c a t t e r i n g ) a r e very d i f f e r e n t .

A s e m i - q u a n t i t a t i v e understanding of these c r o s s s e c t i o n r a t i o s , R

o(n')/o(n+), can be obtained from t h e plane-wave Born approximation. Since t h e i s o s c a l a r pion-nucleon i n t e r a c t i o n i s twice a s s t r o n g a s t h e i s o v e c t o r i n t e r a c t i o n a t e n e r g i e s n e a r t h e resonance ( n e a r 180 MeV i n c i d e n t pion e n e r g i e s ) o(nf +

^and

o(n- + n ) a r e 9 times l a r g e r t h a n o(n+ + n) and o(n- + ^p). Applying t h i s t o pion-nucleus s c a t t e r i n g g i v e s :

Fig. 8-- Cross s e c t i o n a n g u l a r d i s t r i b u t i o n f o r t h e GQR i n Pb. Curves ( d e s c r i b e d i n t h e t e x t ) a r e t h e r e s u l t of a DWIA c a l c u l a t i o n .

where F (F) and Fn(?) a r e r e s p e c t i v e l y t h e p r o t o n and n e u t r o n t r a n s i t i o n d e n s i t i e s a t t h e s t r o n g a b s o r p t i o n r a d i u s P i. For a n i s o s c a l a r e x c i t a t i o n R i s expected t o be u n i t y . For a hydrodynamical model e x c i t a t i o n ( e q u a l amplitude o s c i l l a t i o n s of both t h e n e u t r o n s and t h e p r o t o n s ) R i s expected t o be approximately N / Z . The observed v a l u e of R

3.0 f o r t h e GQR i s not expected from e i t h e r of t h e above models.

1 n . o r d e r t o o b t a i n a more q u a n t i t a t i v e understanding of t h e i m p l i c a t i o n s of t h e d a t a

we have performed DWIA c a l c u l a t i o n s using c o l l e c t i v e - m o d e l f o m f a c t o r s . I n t h e s e

c a l c u l a t i o n s the neutron deformation parameter, BXn, and t h e p r o t o n deformation

parameter, BAp, were s e p a r a t e l y s c a l e d t o o b t a i n f i t s t o t h e measured

a n g u l a r

d i s t r i b u t i o n s . These were t h e n used t o o b t a i n t h e f r a c t i o n s of the i s o s c a l a r and t h e i s o v e c t o r energy-weighted sum r u l e exhausted by t h e GQR. The r e s u l t of such a c a l c u l a t i o n u s i n g t h e same r a d i a l shape f o r both t h e n e u t r o n and proton form f a c t o r s i s shown i n Figure 8. The f r a c t i o n of t h e E2 i s o s c a l a r sum r u l e , SIS, n e c e s s a r y t o e x p l a i n t h e d a t a w i t h t h i s model i s 71%, i n good agreement w i t h o t h e r hadronic [19-211 measurements. However 23% of t h e E2 i s o v e c t o r sum r u l e , SIV, is r e q u i r e d t o e x p l a i n both t h e

and n- c r o s s s e c t i o n s . From t h e hydrodynamical model SIV

[ ( N - Z ) / ( N + Z ) ] * S ~ ~ o r 3% i s expected.

There a r e two s o l u t i o n s t o Eq. 1 ) f o r SIS and SIV. The second s o l u t i o n l e a d s t o a predominantly i s o v e c t o r s t a t e w i t h SIV

330% and SIS

5%. This s o l u t i o n is i n c o n s i s t e n t with a l l o t h e r measurements.

Another method of determining both t h e i s o s c a l a r and i s o v e c t o r s t r e n g t h f o r a t r a n s i t i o n i s t h e comparison of probes w i t h d i f f e r e n t s e n s i t i v i t i e s t o t h e i s o s c a l a r and i s o v e c t o r p i e c e s of t h e form f a c t o r . Such a comparison is provided by (a,@') and ( e , e ' ) . U n f o r t u n a t e l y t h e r e is s i g n i f i c a n t disagreement about t h e amount of s t r e n g t h observed i n ( e , e ' ) [22-251. Although P i t t h a n e t a l . [23] have r e p o r t e d observing a l a r g e f r a c t i o n of the i s o s c a l a r E2 sum r u l e n e a r 10.5 MeV, more r e c e n t h i g h - r e s o l u t i o n s t u d i e s 1251 i n d i c a t e very l i t t l e E2 s t r e n g t h i n t h i s region. The above a n a l y s i s can be p r e s e n t e d i n terms of a n e u t r o n and a p r o t o n ( e l e c t r o m a g n e t i c ) sum r u l e . We f i n d t h a t although 72% of the neutron sum r u l e is exhausted by t h i s s t a t e only 8.4% of t h e proton sum r u l e i s exhausted. Thus t h e r e s u l t s of t h i s a n a l y s i s a r e c o n s i s t e n t w i t h both o t h e r hadronic measurements and w i t h t h e r e c e n t high r e s o l u t i o n ( e , e ' ) measurements but n o t w i t h t h e e a r l i e r ( e , e ' ) measurements.

W e have examined t h e s e n s i t i v i t y of t h e s e r e s u l t s t o d i f f e r e n c e s between t h e ground-state neutron and p r o t o n r a d i i and t o d i f f e r e n c e s between t h e neutron and p r o t o n r a d i i used i n o b t a i n i n g t h e form f a c t o r s ( l e a v i n g t h e ground-state d e n s i t i e s unchanged). This a n a l y s i s should i n d i c a t e whether n e u t r o n t a i l s on t h e form f a c t o r s can e x p l a i n the l a r g e value of R. Radius changes of 0.3 fm changes l e a d t o only s m a l l d i f f e r e n c e s i n SIS and

The c r o s s - s e c t i o n r a t i o s could a l s o be e x p l a i n e d by enhancing t h e i s o v e c t o r

i n t e r a c t i o n , V1 w i t h r e s p e c t t o t h e i s o s c a l a r p a r t of t h e i n t e r a c t i o n , Vo. The hydrodynamical model would e x p l a i n t h e d a t a i f V1/V was 1.26 r a t h e r t h a n 0.5 a s expected from t h e pion-nucleon i n t e r a c t i o n . Altgough H i r a t a , Lenz and Theis 1261 p r e d i c t enhancements of 25% i n V1 w i t h r e s p e c t t o Vo (V1/VO = 0.63) t h i s i s much s m a l l e r t h a n needed t o e x p l a i n t h e p r e s e n t d a t a .

The a n a l y s i s presented above i n d i c a t e s t h a t e i t h e r the GQR i n 2 0 8 ~ b i s a g i a n t n e u t r o n resonance o r we do n o t understand t h e pion-nucleus i n t e r a c t i o n . A n a n a l y s i s of t h e HEOR i n d i c a t e s t h a t it is a l s o predominantly a neutron s t a t e . I f t h e s e a r e neutron s t a t e s , where is the missing proton s t r e n g t h ? Since the background i n the e n t i r e continuum r e g i o n a p p e a r s t o be n- enhanced, t h i s missing proton s t r e n g t h must l i e e i t h e r h i g h e r i n energy, o r must be quenched. I f indeed i t i s a g i a n t neutron resonance t h i s idea can be f u r t h e r s u b s t a n t i a t e d by measuring t h e decay from t h e analog of t h i s neutron g i a n t resonance i n 2 0 8 ~ i u s i n g t h e ( p , p ' ) r e a c t i o n . This experiment[27] was done f o r lower-lying s t a t e s and provides examples f o r t h e neutron parentage of t h e s e s t a t e s i n 2 0 9 ~ b .

V I - ^SUMMARY

Some new d a t a f o r pion i n e l a s t i c s c a t t e r i n g from t h e giant-resonance r e g i o n of n u c l e i h a s been presented. New e x p e r i m e n t a l techniques have enabled measurements t o be made a t small angles. The d a t a i n d i c a t e t h a t pions provide a probe which i s u s e f u l f o r l o c a t i n g s p i n - f l i p modes a s w e l l a s f o r measuring new p r o p e r t i e s of p r e v i o u s l y observed g i a n t resonances.

The a u t h o r s would l i k e t o thank o u r c o l l a b o r a t o r s from t h e U n i v e r s i t y of

Pennsylvania, t h e U n i v e r s i t y of Texas, and Los Alamos N a t i o n a l Laboratory f o r

permission t o p r e s e n t new d a t a p r i o r t o p u b l i c a t i o n . This work has been supported

i n p a r t by t h e US Department of Energy and t h e N a t i o n a l Science Foundation.

JOURNAL DE PHYSIQUE

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