INVESTIGATION OF INNER AND OUTER SUBSHELLS VIA TRANSFER REACTIONS

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INVESTIGATION OF INNER AND OUTER

SUBSHELLS VIA TRANSFER REACTIONS

S. Gales

To cite this version:

30URNAL DE PHYSIQUE

Colloque Cf, supplément au n ° 3 , Tome ^-5, mars 198^ page C4-39

I N V E S T I G A T I O N OF INNER A N D OUTER S U B S H E L L S V I A T R A N S F E R R E A C T I O N S

S. Gales

Institut de Physique Nucléaire, B.P. n°l, 91406 Orsay Cedex, France Résumé - Les réactions de transfert de 1 et 2 nucléons à haute énergie inci-dente (100 à 300 MeV environ) ont permis d'étendre considérablement notre connaissance de la fonction de réponse du noyau à une excitation simple. Ces réactions sont particulièrement bien adaptées à l'étude des couches internes et externes de haut moment orbital.

Ces propriétés seront illustrées par quelques exemples significatifs. Sélec-tivité en moment orbital transféré, détermination du spin J des couches in-ternes au moyen de faisceaux de particules polarisées dans le cas du pick up profond d'un nucléon dans les noyaux lourds. Nouvelles approches dans l'étude des distributions de la force à deux particules : premiers résultats

concer-nant la réaction (a,6He) à 218 MeV d'énergie incidente.

On insistera particulièrement sur la mise en évidence récente à haute énergie d'excitation (5 à 15 MeV) d'états à une p a r t i c u l e au m o y e n de r é a c -tion de stripping (a,t) ,(3He,d) et (a,3He). A partir de ces exemples les

résultats expérimentaux seront comparés aux prédictions des modèles nucléaires qui tiennent compte explicitement du couplage entre degrés de liberté indivi-duels et collectifs pour expliquer la fragmentation et l'étalement des forces à une particule.

Abstract - Transfer reactions,investigated a high incident energy (from 100 to 300 MeV),have considerably increased our knowledge of the nuclear response function to a particular simple mode of excitation of the nucleus. These reactions are particularly well suited to the study of high spin inner and outer subshells. The advantages of such approach are illustrated using few characteristic examples.

a) Strong selectivity in angular momentum transfer, determination of the spin J of the inner hole state using polarized proton beam in the case of one nucleon pick-up reaction.

b) New experimental results via the (a,6He) reaction at 218 MeV incident

ener-gy are obtained on the two-nucleon strength distributions in medium-heavy nuclei.

c) First evidence of proton and neutron single-particle strengths at high excitation energy (5 to 15 MeV) in heavy nuclei are reported using the (a,t) (a,3He) and (3He,d) stripping reactions.

The experimental results will be compared to the predictions of nuclear mo-dels which take into account explicitly the coupling between single-particle and collective states in order to explain the observed fragmentation'and spreading of the single-particle strength.

I - INTRODUCTION

The topic of this paper, inner-hole and high-lying states in medium-heavy nuclei, is an example of a simple mode of excitation of the nucleus. In recent years, other modes such as giant resonances, spin-flip excitations, high-spin stretched states have been extensively studied and present a number of commun features with the pre-sent topic.

C4-40 J O U R N A L D E PHYSIQUE

problems o f the e x t r a c t i o n o f t h e 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 damping width, o f the r e a c t i o n model used i n t h e d a t a analysis, a r e very s i m i l a r f o r such h i g h - l y i n g mode o f e x c i t a t i o n s .

The questions I would l i k e t o address here a r e t h e f o l l o w i n g : how are m o d i f i e d t h e bare s i n g l e - p a r t i c l e p r o p e r t i e s as one reaches higher and h i g h e r e x c i t a t i o n energy

i n t h e nucleus ? What are t h e mechanismsresponsible o f t h e fragmentation and then the spreading o f t h e s i n g l e - p a r t i c l e strengths i n n u c l e i ?

Using t h e t r a n s f e r r e a c t i o n approach and some i l l u s t r a t i v e examples, o u r goal i s t o demonstrate t h a t our present knowledge on s i n g l e - p a r t i c l e s t r e n g t h d i s t r i b u t i o n s has been g r e a t l y enhanced d u r i n g t h e past few years. The experimental r e s u l t s span a l a r g e domain o f t h e nuclear mass c h a r t f o r b o t h orotonand neutron p a r t i c l e ( h o l e ) states. On the o t h e r hand t h e t h e o r e t i c a l nuclear models have p o i n t e d o u t t h e key r o l e played by t h e c o u p l i n g between s i n g l e p a r t i c l e motion and surface v i b r a t i o n s i n o r d e r t o reproduce t h e experimental r e s u l t s .

I n t h e f i r s t p a r t on t h i s paper, I s h a l l discuss b r i e f l y t h e r e c e n t r e s u l t s obtained

in

t h e study on one and two nucleon pick-up r e a c t i o n s . I n t h e second p a r t t h e new evidence f o r h i g h - l y i n g p a r t i c l e s t r e n g t h s w i l l be presented. A p r e l i m i n a r y a n a l y s i s o f t h e experimental data i n t h e framework o f t h e distorted-wave Born approximation theory of nuclear r e a c t i o n s i s c a r r i e d o u t i n o r d e r t o e x t r a c t t h e main c h a r a c t e r i s - t i c s ( c e n t r o i d energy, width, s t r e n g t h d i s t r i b u t i o n ) o f such t r a n s i t i o n s . I n t h e case o f proton and neutron s t r i p p i n g reactions, a t h e o r e t i c a l approach o f the under- l y i n g background w i l l be attempted, assuming t h a t t h e main mechanism producing t h e observed background i s due t o t h e break-up o f t h e p r o j e c t i l e .

F i n a l l y t h e r e s u l t s obtained on h i g h - s p i n o u t e r subshells i n l16Sn, 144Sm, 2 0 8 ~ b w i l l be compared t o t h e t h e o r e t i c a l p r e d i c t i o n s o f t h e quasi p a r t i c l e phonon and s i n g l e p a r t i c l e v i b r a t i o n s n u c l e a r models.

I 1

-

ONE AND TWO NUCLEON PICK-UP FROM INNER SHELLS

Perhaps one o f t h e f i r s t example o f observation o f deep-hole s t a t e s u s i n g a pick-up r e a c t i o n , i s the work r e p o r t e d by Sakai and Kubo on t h e 11sSn(3~e,a)'17~n r e a c t i o n /I/. The r e s i d u a l energy spectra i s shown i n f i g . 1 and a c l e a r enhancement o f t h e cross s e c t i o n i s observed around 5.2 MeV e x c i t a t i o n energy i n '17sn. According t o the authors, t h i s e x c i t a t i o n was a t t r i b u t e d t o t h e pick-up o f a neutron from t h e n e x t lower s h e l l , e.g. 1ggI2, 2p subshells as shown i n f i g . 1 .

I N S TOKYO 1972

Fig. 1

-

(left) Residual energy spectra from the ' " ~ n ( ~ ~ e , c c ) '17sn reaction at 81.7MeV An enhancement of cross-section (bump) is clearly seen around 5.2 MeV in l17sn.

(Righk) Schematic picture of the neutron pick-up process to inner-shell for the

Ig, 2p, If subshells in ll'sn.

a r t i c l e s , a d e t a i l e d i n f o r m a t i o n has been r e p o r t e d on t h e s u b j e c t /4,6/. Therefore i n t h e f o l l o w i n g l i n e s o n l y a few examples w i l l be discussed t o emphasize t h e more r e c e n t advances.

Table I

Fragmentation of the lgg/2, lf5/2 and If712 neutron hole strengths in 1 1 5 ~ ~ a) <Ex> ntj C2S/2j+l MeV 3.6-6.6 lg9/2 0.56 6.6-8.6 lgg/2 0.24 8.6-1 1.6 lggI2 0.14 1 f5/2 0.60 11.6-18.5 lf512 0.35 If712 % 1.00

I 1 .I

-

S e l e c t i v i t y i n angular momentum t r a n s f e r i n one neutron pick-up r e a c t i o n s For a i n n e r h o l e s t a t e l o c a t e d w e l l below t h e Fermi sea, the pure h o l e c o n f i g u r a t i o n ( I h ) w i l l mix through t h e r e s i d u a l i n t e r a c t i o n w i t h t h e dense (lp-2h) s t a t e s leading a spreading o f t h e hole-strength. I n medium-heavy n u c l e i t h i s spreading mechanism yields t o overlapping s t r u c t u r e s corresponding t o c l o s e l y spaced i n n e r - s h e l l s i n t h e r e s i d u a l energy spectra. It i s t h e r e f o r e o f c r u c i a l importance t h a t the s e l e c t i v i t y o f t h e r e a c t i o n process enhances t h e e x c i t a t i o n o f a p a r t i c u l a r subshell n a j w i t h respect t o neighbouring subshells and t o t h e u n d e r l y i n g background.

This s e l e c t i v i t y o f t h e reaction

L e t us p o i n t o u t t h a t t h e numbers quo- t e d i n Table I are s t r o n g l y dependant on t h e assumed background l e v e l (dashed h o r i z o n t a l l i n e i n Fig.2). The i n v e s t i - g a t i o n o f a very l a r g e energy range (up t o about 55 MeV) has been used i n order t o e x t r a p o l a t e t h e background l i n e down t o t h e lower energy region.

a) Ref. 171.

process i s c l e a r l y demonstrated i n t h e spectrum o f Fig.2 where t h e 1g9i2 i n n e r - h o l e s t r e n g t h i n l l S S n i s s t r o n g l y e x c i t e d i n t h e (3He,a) r e a c t i o n a t 283MeV/7/. The l a r g e mismatching suppresses small

a

t r a n s f e r ( a = 1,3) c o n t r i b u t i o n s i n t h e wholerange o f e x c i t a t i o n energy.

The w e l l known c o n c e n t r a t i o n o f lg9/2 s t r e n g t h a t 5.3 MeV do- minates the spectra. I n addition two new bumps a r e c l e a r l y i d e n t i - f i e d a t 7.5 and 15 MeV respec- t i v e l y . The r e s u l t s o f t h e ana- l y s i s i n t h e case o f t h e 1g9/2, l f 5 / 2 and I f 7 / 2 h o l e strengths i n l15Sn are summarized i n Table I . A l a r g e f r a c t i o n o f rn C Z U 6000- 5000 4000- 3000 t h e I f 5 1 2 s t r e n g t h i s l o c a t e d between 8.6-11.6 MeV i n reaso-

Fi .2

-

Residual energy spectra from the nable agreement w i t h t h e pre-

ll'S~~(~He,a) at 283 MeV incident energy. vious r e s u l t s o f Siemssen e t

The angular momentum matching conditions a l . /8/. The main c o n t r i b u t i o n

strongly select the 2 = 4 1g912 inner t o t h e h i g h e r energy bump

hole strength mainly located in the (11.5-18.5 MeV) i s thus expected

C4-42 JOURNAL DE PHYSIQUE

11.2

-

The s p i n J o f t h e i n n e r - h o l e s t a t e and t r a n s f e r r e a c t i o n w i t h p o l a r i z e d beams

I n u s u a l t r a n s f e r r e a c t i o n s t u d i e s o f deep-hole s t a t e s , t h e L v a l u e o f t h e s t a t e has been determined b y a n g u l a r d i s t r i b u t i o n measurements. The s p i n v a l u e J o f t h e h o l e s t a t e

,

however, has been assigned o n l y on t h e b a s i s o f s h e l l model expecta- t i o m a n d / o r on sum-rule a n a l y s i s . I t i s t h e r e f o r e h i g h l y d e s i r a b l e t o measure t h e a n a l y z i n g power Ay(t3) o f t h e t r a n s f e r e d p a r t i c l e u s i n g a p o l a r i z e d i n c i d e n t beam s i n c e s t r o n g J dependance o f t h e a n a l y z i n g power Ay(6) i s expected f r o m DWBA c a l c u l a t i o n s .

S p i n d e t e r m i n a t i o n s o f deeply-bound p r o t o n h o l e s t a t e s have been r e p o r t e d by Wagner e t a1

.

i n t h e s t u d y o f t h e (d,3He) r e a c t i o n on a number o f medium-heavy w e i g t h t a r g e t n u c l e i /5/.

The f i r s t measurement o f t h e s p i n J o f t h e deeply-bound n e u t r o n h o l e s t a t e s i n t h e t i n r e g i o n was performed+at 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 b y t h e MSU-Indiana- Orsay grqup u s i n g t h e 12'sn(p,d) r e a c t i o n a t 90 MeV /9/. I n t h e mean t i m e a s t u d o f t h e ( d , t ) r e a c t i o n a t 40 MeV bombarding energy t o i n n e r - h o l e s t a t e s i n 1117nYSn was a l s o c a r r i e d o u t u s i n g t h e ISN Grenoble c y c l o t r o n

/ l o / .

To demonstrate t h e u s e f u l n e s s o f such s t u d i e s , n o t o n l y t o d e t e r m i n e t h e s p i n J o f t h e s t a t e s b u t a l s o t o u n r a v e l t h e observed d i s t r i b u t i o n s i n t h e case o f o v e r l a p p i n g s u b s h e l l s w i t h d i f f e r e n t n L j quantum numbers, I s h a l l d i s c u s s i n t h e f o l l o w i n g one example. The I f 5 1 2 and n e u t r o n - h o l e s t r e n g t h s i n t h e Z r region.

Deuteron spectrum f r o m t h e ' O ~ r ( p , d ) 8 g ~ r r e a c t i o n i s p r e s e n t e d i n F i g . 3 . Because o f t h e a n g u l a r momentum matching t h e ground s t a t e ( 9 / 2 ) + and t h e 1.46 MeV s t a t e ( 5 / 2 - ) a r e v e r y prominent among t h e l o w - l y i n g l e v e l s . A t e x c i t a t i o n e n e r g i e s above 3.4 MeV, t h e gross s t r u c t u r e s , concluded t o be m a i n l y I f 7 / 2 h o l e s t a t e s /3,11 ,12/,are c l e a r l y seen above a smooth background. The s t r u c t u r e s observed i n t h e p r e s e n t experiment can be separated i n two p a r t s .

One o f them i s t h e bump w i t h s e v e r a l peaks between 3.4 MeV and 7.0 MeV ( l a b e l l e d A i n F i g . 3 ) . Another one i s t h e r e g i o n l y i n g between 7.0 and 21 MeV (B,C,D). T h i s l a t t e r r e g i o n i s s t r u c t u r l e s s e x c e p t f o r t h e s h a r p i s o b a r i c a n a l o g s t a t e s (IAS) o f l o w - l y i n g l e v e l s o f

"Y

( l a b e l e d

T>).

The s p i n - p a r i t y o f 7 / 2 - proposed f o r a l l t h e s e s t r u c t u r e s /3,11,12/ was based on t h e a n g u l a r d i s t r i b u t i o n s and on s p e c t r o s - c o p i c f a c t o r arguments. But o n l y a n a l y - z i n g power measurements c o u l d d e t e r m i n e t h e J v a l u e ( 5 / 2 - o r 7 / 2 - ) s i n c e i n a l l cases t h e a n g u l a r d i s t r i b u t i o n s a r e c h a r a c t e r i z e d by an 2 = 3 t r a n s f e r /3,11,12/.

o ( 6 ) and Ay(6) f o r each area A(3.4- 7.0 MeV) B(7-11.6 MeV), C(11.6-16 MeV) and D(16-21 MeV) were o b t a i n e d by i n - t e g r a t i n g t h e y i e l d above t h e background e x c l u d i n g t h e s h a r p peaks o f t h e IAS around 9 MeV. The f o l l o w i n g arguments f o r J'" assignments a r e based on a com-

Z p a r i s o n w i t h t h e e m p i r i c a l a n a l y z i n g - =I

power, a method which has been success- 5000

f u l l y used i n t h e case o f t h e l g g / 2 h o l e s t a t e i n l19Sn.

Fig.3 - Energy spectrum of the

9 0

~ r ( ~ , d ) "2.r reaction at Ep=90 MeV. The major peak above 2.5 MeV are label- led by excitation energies in MeV. The shaded and hatchedareas in the gross structure above 3.4 MeV shows the (~f~/~)-'and (lfgI2)-l state distribu-

tions,respectively. O 25 20 15 10 5 0

I n Fig.4 a r e shown Ay(0) f o r areas A-C and t h e background under area B. The e x p e r i - mental Ay(e) c l e a r l y show t h a t t h e main c o n t r i b u t i o n t o t h e areas B and C i s from t h e same o r b i t and i s d i f f e r e n t f r o m A.

The main c o n t r i b u t i o n t o a r e a A i s concluded t o a r i s e f r o m t h e l f 5 / 2 o r b i t b y com- p a r i s o n w i t h t h e Ay o f t h e known 5/2- s t a t e s a t 1.46 MeV i n " Z r and t h e 0.76 MeV i n 5 7 ~ i as shown i n t h e f i g u r e . Among t h e peaks i n t h i s r e g i o n , t h e 4.1 and 5.2 MeV peaks have a n o n - n e g l i g i b l e c o n t r i b u t i o n of a j =

a t

1 / 2 ( 7 / 2 - ) t r a n s i t i o n s . Areas B and C on t h e o t h e r hand a r e assigned t o correspond m a i n l y t o I f 7 2 n e u t r o n t r a n s f e r s i n c e t h e Ay f o r t h e s e areas matches t h a t f o r t h e known 2.57

he^,

7/2- s t a t e i n 5 7 ~ i as shown i n F i g . 4 .

I n t h i s case t h e a n a l y z i n g power measurements e s t a b l i s h e s c l e a r l y t h e s t r o n g f r a g - m e n t a t i o n of t h e l f 5 / 2 h o l e s t r e n g t h up t o 7 MeV e x c i t a t i o n energy i n " Z r and h e l p t o l o c a t e t h e i n n e r If7,2 h o l e

s t a t e i n t h e r e g i o n B and C. The o v e r l a p p i n g r e g i o n s between t h e l f 5 / 2 and If7l2 h o l e s t r e n g t h s can be determined. t h r o u g h t h e s t u d y o f n e u t r o n p i c k up r e a c t i o n s w i t h a p o l a r i z e d beam.

The s p i n - o r b i t s p l i t t i n g between t h e If5,? and I f 7 / 2 n e u t r o n sub- s h e l l s

i s

o f about 7 MeV i n r e a - sonable agreement w i t h t h e expe- r i m e n t a l v a l u e f o r p r o t o n sub- s h e l l s (5.10 Ref.5).

90 89

Zr(p,d) Zr, E=SOMeV

t

, ,

.

,

.

1

t

.

.

.

.

1

10' 20' 30' LO' 10' 20' 30' LO' Sobcm

F i g . 4 - A n a l y z i n g power f o r areas A,B,C a n d o f t h e background. S o l i d l i n e 2 a r e e m p i r i c a l d i s t r i b u - t i o n s t a k e n from

5 8 ~ 4 ( p

,d) 5 7 ~ i (0.76 ~ e ~ , 5 / 2 - ) f o r a r e a A and 5 8 ~ i ( p , d ) 5 7 ~ i (2.57 MeV 7/2-) f o r areas B and C. The dashed l i n e i s t$e em i r i c a l a n a l y z i n g power f o r 5 / 2 - f r o m g o Z r ( p , d ) s B Z r (1.46 MeV, 5/2-) s t a t e .

11.3 - Two nucleon s t r e n g t h d i s t r i b u t i o n s f r o m ( p , t ) and ( a , 6 ~ e ) r e a c t i o n s Another t y p e o f s i m p l e e x c i t a t i o n mode o f t h e nucleus, i s t h e h i g h - l y i n g two-neu- t r o n h o l e s t a t e s which may be r e l a t e d t o t h e g e n e r a l phenomena o f deep-hole s t a t e s , observed i n one nucleon p i c k - u p r e a c t i o n s . M o s t o f t h e e x i s t i n g d a t a on two-nucleon s t r e n g t h d i s t r i b u t i o n s comes f r o m ( p , t ) r e a c t i o n s c a r r i e d o u t a t r a t h e r l o w i n c i d e n t energy ( < 60 MeV), w i t h s p e c i a l emphasis on l o w - l y i n g , l o w s p i n c o n f i g u - r a t i o n s .

C4-44

JOURNAL

DE PHYSIQUE

A d d i t i o n a l evidence f o r such a conclusion was obtained i n t h e study o f t h e (p,d) r e a c t i o n on two odd t i n isotopes 117'119Sn a t 42 MeV/16/. The r e s u l t i n g spectra from (p,d) and (p,t)

r e a c t i o n s l e a d i n g t o t h e same f i n a l nucleus a r e

.

--

.-- .-.- ~. " , . shown i n Fig.5. A broad 1 8 7 ~ n l p . d ~ 1 1 6 S n

s t r u c t u r e a t about t h e , 8,..

.

16'

j E,: 4 2 MeV

same e x c i t a t i o n energy i s observed i n the two r e a c t i o n s .

I n (p,d) reactions ,these broad peaks can onlycome from t h e c o u p l i n g o f one

h o l e i n t h e i n n e r - s h e l l . .

--.

E"c#raT,w E N M " <W",

( I C J ~ / ~ , 2p) w i t h the h o l e near t h e Fermi sur-

face (d5/2,g7/2) which

i s present i n t h e 117'119~n ground s t a t e (v+d c o n f i g u r a t i o n s )

.

I n (p,t) r e a c t i o n s b o t h v+d and 2d (2 deep holes) c o u l d be excited. The comparison o f spectra o f t h e Fig.5 suggests stron- g l y t h a t the bumps popu- l a t e d i n ( p , t ) s t u d i e s

a r e mostly due t o t h e Fig.5 - Energy spectra f o r t h e 120'118

and 1 1 7 ' 1 1 9 ~ n ( ~ , t) l 1 8 ' l 1 6 s n

v+d c o n f i g u r a t i o n s /16/. ~ n ( ~ , d ) r e a c t i o n s a t ~ ~ ~ ' ~ 42 ~ MeV. ~ ~ n

A l t e r n a t i v e l y , t h e (a,6He) appears as a new and a t t r a c t i v e t o o l t o e x p l o r e t h e two neutron-hole strengths, due t o i t s expected s e l e c t i v i t y towards l a r g e L angular momentum t r a n s f e r a t h i g h i n c i d e n t energy. The h i g h i n c i d e n t e n e r g y o f t h e a -

p , a r t i c l e (218 MeV) and p r o t o n (168 MeV) beams o f t h e Orsay synchrocyclotron are w e l l s u i t e d t o a comparative study o f t h e (a,6He) and (p,t) r e a c t i o n s on medium- heavy t a r g e t s ( " ~ i , ' " ~ r , l I 6 S n , 14"Sm and '08Pb).

Angular d i s t r i b u t i o n s were measured w i t h t h e h i g h - r e s o l u t i o n spectrometer from 2" t o 18". Clean i d e n t i f i c a t i o n o f t h e outgoing t r i t o n s ('He) was achieved. The over- a l l energy r e s o l u t i o n was 220 KeV f o r (a,6He) and 130 KeV f o r ( p , t ) r e a c t i o n s . T y p i c a l spectra obtained on '16Sn t a r g e t

are d i s p l a y e d i n Fig.6. The ll'sn spectrum i s dominated by two s t r u c t u r e s around 3.4 MeV and 8.0 MeV r e s p e c t i v e l y . The

broad s t r u c t u r e around 8 MeV confirms t h e coo

previous r e s u l t s from (p,t) s t u d i e s . How- ever f o r t h e f i r s t time we can p o i n t o u t 500

two components, d i f f e r e n t l y e x c i t e d i n the two r e a c t i o n s (see ~ i g . 6 ) . /18/ The f i r s t component, centered a t 7.4 MeV i s p r e f e r e n t i a l l y e x c i t e d i n t h e ( p , t ) r e a c t i o n

.

The bump as a whole have a w i d t h (FWHM) o f 2.0 i 0.2 MeV. A p r e l i - minary a n a l y s i s o f t h e (a,,6He) r e a c t i o n shows t h a t t h e observed cross-section i s m a i n l y due t o t h e 1 deep-I valence h o l e ~ g g / ~ ) - ' m (2d5/232d3/2)-1] 6+ c o n f i -

1 1 0 8 6 ~ 2 0

gurations. S i m i l a r l y t h e l a r g e enhan- E, (MeV1

~ e m e n t a t 3.4 MeV i s a l s o dominated by F i t g . 6

-

T r i t o n and 6fie energy spectra 6' s t a t e s a r i s i n g mainly from valence- from the (p,t) and ( a , 6 ~ e ) r e a c t i o n s valence

r(

~ g ~ / ~ ) - ' e (2d5/2)-1] c o n f i - on l l 6 s n t a r g e t .

T h e o r e t i c a l i n v e s t i g a t i o n s o f two q u a s i p a r t i c l e s t r e n g t h s i n t h e Sn i s o t o p e s by S o l o v i e v e t a1./17/ a r e i n v e r y good agreement w i t h o u r c o n c l u s i o n s .

F i n a l l y t h e two-deep ( 2 d ) h o l e s t r e n g t h s s h o u l d be around 11.5

-

13.5 MeV i n ll"sn. We d i d n o t f i n d any s i g n i f i c a n t enhancement o f t h e ( p , t ) o r ( a , 6 ~ e ) c r o s s - s e c t i o n s up t o 17 MeV e x c i t a t i o n energy i n ' l 4 S n .

The second s u b j e c t o f i n t e r e s t r e l a t e d t o t h e s t u d y o f t h e ( u , ~ H ~ ) r e a c t i o n i s t h e u n d e r s t a n d i n g o f t h e r e a c t i o n mechanism s i n c e t h e e x i s t i n g d a t a a r e v e r y scarce. Therefore, t h e 2 0 8 ~ b ( a , 6 H e ) 2 0 6 ~ b r e a c t i o n /18/ was chosen due t o t h e r a t h e r p u r e and w e l l spaced two-neutron h o l e components u p t o 4.2 MeV e x c i t a t i o n energy i n 2 0 6 ~ b . T y p i c a l energy spectrum f r o m ( u , ~ H ~ ) r e a c t i o n on 2 0 8 ~ b i s d i s p l a y e d i n Fig.7.

F i g . 7

-

6 ~ e energy spectrum f r o m t h e 2 0 8 ~ b ( a , 6 ~ e ) r e a c t i o n r e c o r d e d a t 0 = 7O l a b a n g l e .

The s e l e c t i v i t y o f t h i s r e a c t i o n a t 218 MeV i s c l e a r l y demonstrated. I n '06Pb t h e f i r s t l o w - l y i n g , l o w - s p i n s t a t e s 0+, 2+, 4 a r e weakly p o p u l a t e d as compared t o t h e Ex = 2.65 MeV, J" = 9- and t h e Ex = 3.25 MeV,

J"

= 6' s t a t e s .

C4-46 JOURNAL DE PHYSIQUE

The r e a c t i o n s t r o n g l y enhances n a t u r a l p a r

J" =

I

( j l = el- 1/21 An a d d i t i o n a l s e l e c t i v i t y i s observed i f

al

= e2. T h i s i s t h e case f o r t h e 6' l e v e l a t 3.25 MeV,the main component i s

J"=

I

(f512)-1 ( f 7 / 2 1 - 1 16'

.

On t h a t b a s i s one may assume t h a t t h e new l e v e l a t 6.1 MeV i s t h e

Jia, = 8' member o f t h e

/

(hg/2)-1

s

( f 7 / 2 ) - 1 8 + m u l t i p l e t p r e d i c t e d around 6.5 MeV /19/. No i n d i c a t i o n o f any enhancement o f cross- s e c t i o n a r i s i n g f r o m t h e p o p u l a t i o n o f 1 deep (Ihll/2) + 1 valence (lf5,2,1h9/2) h o l e s t a t e has been found up t o ' 15 MeV e x c i t a t i o n energy.

Summarizing t h i s new approach we would l i k e t o s t r e s s t h a t t h e ( a , 6 ~ e ) r e a c t i o n a t 218 MeV c o u l d be used as a new and a t t r a c - t i v e s p e c t r o s c o p i c t o o l i n o r d e r t o s t u d y b o t h l o w and h i g h - l y i n g two n e u t r o n - h o l e p a i r s c o u p l e d t o t h e maximum s p i n v a l u e i n medium-heavy n u c l e i . l e v e l s w i t h s p i n and c o n f i g u r a t i o n (j, = a 2 + 1/2)m1

I

Jmax F i g . 8 - T i c a l a n g u l a r d i s t r i b u t i o n s from t h e 2x'Pb(a, 6He) r e a c t i o n a t 218MeV

Dashed l i n e s a r e o n l y i n d i c a t e d t o g u i d e t h e e y e .

111- HIGH-LYING SINGLE-PARTICLE STRENGTHS VIA STRIPPING REACTIONS

A new i m p o r t a n t s t e p has been r e c e n t l y made towards t h e use o f t h e one nucleon t r a n s f e r r e a c t i o n s f o r t h e s t u d y o f h i g h - l y i n g n u c l e a r e x c i t a t i o n s . A new t y p e o f resonance l i k e s t r u c t u r e has been observed i n t h e s t u d y o f p r o t o n s t r i p p i n r e a c - t i o n s ( a , t ) and ('He,d) on a number o f medium-heavy t a r g e t n u c l e i ( ' ' ~ r , l q 6 S n , 14'Sm, 2 0 8 ~ b ) / 2 1 / .

The general b e h a v i o u r o f t h e p a r t i c l e response f u n c t i o n has been r e c e n t l y extended t o t h e n e u t r o n case w i t h t h e h e l p o f t h e (a, 3He) r e a c t i o n s . I n t h e f o l l o w i n g , t h e e m p i r i c a l s y s t e m a t i c s w i l l be p r e s e n t e d and t h e r e s u l t s f r o m t h e d a t a a n a l y s i s com- pared t o t h e p r e d i c t i o n s o f n u c l e a r models. The c l o s e c o n n e c t i o n between h i g h - l y i n g and deeply-bound s t a t e s w i l l be emphasized.

111.1

-

The ( a , t ) and (3He,d) r e a c t i o n t o h i g h - l y i n g p r o t o n s t a t e s i n '"Eu The f i r s t e x p e r i m e n t a l evidence o f h i g h - l y i n g p r o t o n e x c i t a t i o n s i n heavy n u c l e i was o b t a i n e d w h i l e s t u d y i n g t h e ""Sm(a,t) a t 80 MeV, complemented by an i n v e s t i - g a t i o n o f t h e (3He,d) process a t 240 MeV.

The ( a , t ) experiment was performed w i t h a - p a r t i c l e beams d e l i v e r e d by t h e Grenoble c y c l o t r o n . Outgoing t r i t o n s were d e t e c t e d by a gaz d e l a y - l i n e c o u n t e r backed by two p l a s t i c s c i n t i l l a t o r s i n t h e f o c a l p l a n e o f t h e QD s p e c t r o m e t e r . B o t h h i g h (50 keV) and l o w (230 KeV) energy r e s o l u t i o n s p e c t r a were r e c o r d e d u s i n g t h i n (0.5 mg/cm2) and t h i c k ( 6 mg/cm2) t a r g e t up t o 22 MeV e x c i t a t i o n energy. Angular d i s t r i b u t i o n s were measured f r o m 1'75

t o 18" ( l a b o r a t o r y a n g l e ) i n 3 " s t e p . The l b 5 E u energy spectrum f r o m t h e ( a , t ) r e a c t i o n i s p r e - sented i n F i g . 9a. A t l o w e x c i t a t i o n energy, one 5

observed a s e l e c t i v e p o p u l a t i o n o f t h e I h l l / 2

2

s t a t e due t o t h e known s e l e c t i v i t y o f t h i s r e a c t i o n f o r l a r g e

a

values ( h e r e

a

= 5,6J. B e f o r e t h i s s t u d y no i n f o r m a t i o n was a v a i l a b l e f o r p r o t o n s t a t e s above 2.5 MeV.

A t h i g h e x c i t a t i o n energy (Ex

>

4 MeV), two broad bumps a r e s t r o n g l y e x c i t e d above a subs- t a n t i a l background. T h e i r s p a c i n g i n energy, t h e i r r e s p e c t i v e w i d t h , and i n p a r t i c u l a r t h e f a c t t h a t t h e second bump ( B ) appears as a s h o u l d e r o f t h e main s t r u c t u r e (A) r e c a l l t h e s i m i l a r f e a t u r e s observed i n t h e s t u d y o f d e e p l y bound l g and 2p h o l e s t a t e s i n t i n i s o t o p e s /2-4, % ~ ~ , 1 0 - 1 2 / . ~ r o u n d 14MeV a s h a r p peak c o r r e s p o n d i n g t o t h e Ihll/2 and li 13/2 IAS i s observed f o r t h e f i r s t t i m e .

I n o r d e r t o g a i n f u r t h e r i n s i g t h i n t h e s t u d y o f t h i s phenomena, t h e same range o f e x c i t a - t i o n energy i n 1 4 5 ~was i n v e s t i g a t e d by ~

means o f t h e r e a c t i o n 1 4 4 ~ m ( 3 ~ e , d ) 1 4 5 ~ ~ a t 240 MeV u s i n g t h e 3He beam f r o m t h e Orsay

s y n c h r o c y c l o t r o n and a l a r g e magnetic spec- E x (MeV) \; "'EU t r o m e t e r . The emerging deuterons were d e t e c -

t e d by two m u l t i w i r e p r o p o r t i o n a l chambers backed by two p l a s t i c s c i n t i l l a t o r s . The r e s u l t i n g energy spectrum i s d i s p l a y e d i n

F i g . 9b. The broad s t r u c t u r e s A and B a r e F i g . g a , b - ~ r i t o n ( d e u t e r o n ) e n e r g y

a l s o observed i n t h e p r e s e n t e d spectrum, s p e c t r a from t h e reactions 14'sm(a,t) t h e i r p o s i t i o n s and w i d t h s b e i n g c o n s i s t e n t (upper p a r t ) a n d 1 4 4 ~ m ( 3 ~ e , d ) . The

w i t h t h e ( a , t ) r e s u l t s . T h e i r r e l a t i v e dashed l i n e shows t h e background l i n e

y i e l d s i n t h e two s p e c t r a a r e q u i t e d i f f e - s h a p e from t h e PWBU model. The s o l i d

r e n t due t o t h e d i f f e r e n t s e l e c t i v i t y i n c u r v e show t h e r e s u l t of t h e f i t t i n g

C4-48 JOURNAL

DE

PHYSIQUE

One p l a u s i b l e e x p l a n a t i o n f o r these peaks i s t h a t t h e y a r i s e f r o m p r o t o n s t a t e s i n t h e n e x t major s h e l l c o n s i s t i n g o f c l o s e l y spaced h i g h - s p i n o r b i t a l s , e _ g . 2 f 7 / 2

,

l h g / 2 and l i l 3 / 2

.

I n o t h e r words we a r e i n v e s t i g a t i n g " o u t e r s u b s h e l l s

.

I n o r d e r t o t e s t t h i s assumption a d e t a i l e d a n a l y s i s o f t h e data has been c a r r i e d out. 11 I. 1.1

-

Tee_

b a c k s r o u n d l i n e s h a p e and b r e a ' r : ~ p - o f t h e p r o j e c t i l e

The e x t r a c t i o n o f t h e centroTd e n e r g i e s , w i d t h s and d i f f e r e n t i a l c r o s s - s e c t i o n s of t h e "peaks" A and B i m p l i e s an assumption on t h e background l i n e shape. Since t h e s p e c t r a l shapes o f a and 3He p a r t i c l e break-up processes a t i n c i d e n t energy r a n g i n g f r o m 20 t o 40 MeV/nucleon a r e w e l l e x p l a i n e d by a s i m p l e p l a n e wave break-up mode? /22,23/, (PWBU ) , s i m i l a r c a l c u l a t i o n s i n c l u d i n g c o r r e c t i o n s due t o t h e Coulomb f o r c e were c a r r i e d o u t i n o r d e r t o have a c o n s i s t e n t d e s c r i p t i o n o f t h e background. The t h e o r e t i c a l p r e d i c t i o n s were normalized t o t h e d a t a a t f o r w a r d angles

( e

<

6 " ) and a t h i q h e x c i t a t i o n energy (Ex

>

20 MeV). The r e s u l t s a r e shown as dashed l i n e s i n F i g s 9 a and 9b.

This s i m p l e model was n o t a b l e t o reproduce t h e l i n e shape o f t h e continuum c r o s s - s e c t i o n i n t h e case o f t h e (a,t) r e a c t i o n a t 80 MeV on heavy n u c l e i , whereas f o r t h e t3He,d) r e a c t i o n t h e p r e d i c t i o n s a r e i n good agreement w i t h t h e experimental data.

111.1.2

-

Data r e d u c t i o n and

_...

DWBA a n a l y s i s

The f a i l u r e o f t h i s s i m p l e PWBU model i n t h e case o f t h e ( a , t ) r e a c t i o n l e a d u s t o u s e t h e s o - c a l l e d " e m p i r i c a l background l i n e shape". I n F i g . 9a t h e s o l i d l i n e , w h i c h smoothly connectsthe s t r u c t u r e l e s s p a r t o f t h e spectrum t o t h e minima o f cross s e c t i o n s n e a r 3.5 MeV,representsthat assumption ( r e g i o n

C).

The r e m a i n i n g p a r t o f t h e c r o s s - s e c t i o n was f i t t e d by two Gaussian peaks h a v i n g d i f f e r e n t w i d t h s . The r e s u l t s o f t h i s f i t t i n g procedure i s shown i n F i g . 9 a (Gaussian peaksA and B)

.

Fig. 10 - Experimental Fig.11 - Angular distributions from the reactlon

data and theoretical 14*~m(a,t) to high-lying proton states. Solid and

DWBA curves from the dashed lines are DWBA calculations for the indica-

lWsm(a,t) 14'~u reac- ted Ilva1ues.Centroidenergies of the b u m p a r e given.

tion t o l o w l y i n g states. The dot-dashed curve correspond to the prediction

of the PWBU model.

The parameters used i n t h e DWBA a n a l y s i s were s u c c e s s f u l l y t e s t e d on known low l y i n g s t a t e s /21/. Moreover, s i n c e t h e observed gross s t r u c t u r e s a r e l o c a t e d w e l l above t h e p r o t o n t h r e s h o l d , unbound form f a c t o r s u s i n g Gamow f u n c t i o n s /20/ were

employed i n t h e a n a l y s i s . T y p i c a l experimental angular d i s t r i b u t i o n s and t h e o r e t i c a l DWBA curves f o r both well-known l o w - l y i n g s t a t e s (2d5/2, l g 7 / 2 and Ihll,2 l e v e l s i n

" " 5 ~ )

and t h e h i g h - l y i n g "peaks" A and B are shown i n ~ i g s . 1 0 and l l , ~ ~ s p e c t i v e l y .

A v e r y oood agreement i s found between t h e data and DWBA c a l c u l a t i o n s i f one assumes an a = 5 t r a n s f e r f o r t h e bump A and an

a

= 6 t r a n s f e r f o r t h e bump B.For complete- ness one should mention t h a t an

a

= 3 t r a n s f e r does n o t reproduce t h e t r e n d o f t h e experimental data b u t a 20% m i x i n g o f a = 3 i n t h e bump A w i l l n o t change s i g n i f i c a n t l y t h e q u a l i t y o f the f i t . As regard t o t h e deduced strengths,the results o f t h e DWBA a n a l y s i s i n d i c a t e s t h a t t h e f u l l

a

= 5 l h g 2 p r o t o n s t r e n g t h i s found i n t h e bump A w i t h a p o s s i b l e 20% admixture o f

a

= 3, s t r e n g t h and t h a t t h e

a

= 6 l i l)/2 proton s t r e n g t h i s concentrated i n r e g i o n f!7/2Final l y the angular d i s t r i b u t i o n s obtained f o r t h e background (see F i g . 11) agree reasonably w e l l w i t h the p r e d i c t i o n o f t h e PWBU model.

111.2

-

Empirical systematics o f h i g h - l y i n g p r o t o n s t a t e s Under t h e same experimental c o n d i t i o n s t h e

(a,t) r e a c t i o n a t 80 MeV has been s t u d i e d on

"

'08Pb and l16Sn t a r g e t . The r e s i d u a l energy s e c t r a o f t h e t h r e e f i n a l n u c l e i ll'sb,

_t

I 5Eu and '08Bi are displayed i n Fig. 12.

We would l i k e t o p o i n t o u t t h e s i m i l a r i t y o f 7~

the e m p i r i c a l background 1 in e shapes which r e i n f o r c e s our assumption, namely t h e main p a r t o f t h e cross-section found i n t h e under- l y i n g continuum comes from t h e break-up o f

t h e a - p a r t i c l e . Weak dependance o f t h e back-

'

ground y i e l d versus t h e atomic number A i s one o f the c h a r a c t e r i s t i c s o f t h e break-up process. O f p a r t i c u l a r importance i s t h e c a l c u l a t i o n o f t h e continuum i n t h e case o f t h e *08pb(a,t) r e a c t i o n by R.Shyam e t a l . The

-

double d i f f e r e n t i a l cross-section d20 / d ~ d E

2

70

i s c a l c u l a t e d i n t h e framework o f t h e DWBA p l6

approach f o r p r o j e c t i l e break-up and takes

*

i n t o account e l a s t i c and i n e l a s t i c r e a c t i o n s

::

o f t h e break-up fragments. The deduced curve

i s p l o t t e d i n absolute value w i t h no addi- t i o n a l normalization. The shape o f t h e u n d e r l y i n g continuum i s w e l l reproduced by t h e r e a c t i o n model whereas t h e absolute values a r e o f f by 40 t o 50%. Both o p t i c a l model

parameters and zero-range approximation may E

.

BOMeV

account e a s i l y f o r t h e missing cross-sections, Turning now t o t h e h i g h - l y i n g s t r e n g t h d i s - t r i b u t i o n s the a n a l y s i s o f t h e bump A i n l17Sb shows t h a t most o f t h e proton s t r e n g t h l o c a t e d i n t h e o u t e r h i g h - s p i n subshelrs, e.g. lhgI2 and li13/ (Z>82) i s found i n t h a t energy region. ?he buvp i s l o c a t e d around 10.8 MeV w i t h a w i d t h o f 5.5.MeV. I n the case o f '09Bi a very d e t a i l e d ana- l y s i s has been c a r r i e d out. The r e s u l t s

can be summarized as f o l l o w s :, Fig.12 -Residual energ spectra from

the (a,t) reaction on Y16Sn,144Sm and

C4-50

JOURNAL

DE

PHYSIQUE

I n a d d i t i o n t o t h e well-know l o w - l y i n g and r a t h e r pure s i n g l e p a r t i c l e s t a t e s ( l h 9 / 2 , 2f7,2, l i 1 3 / 2 ) a number o f 9. = 6 t r a n s i t i o n s a r e found between 2 t o 6 MeV e x c i t a t i o n energy i n '09Bi.

They may correspond t o t h e f r a g m e n t a t i o n o f t h e li13/2 p r o t o n s t r e n g t h . However s i - g n i f i c a n t f r a g m e n t s o f t h e 2 = 7 Ij151p s t r e n g t h a r e a l s o found i n t h a t energy range.

I n t h e r e g i o n l a b e l l e d A i n F i g . 12 we found a s m a l l f r a c t i o n o f t h e

a

= 6 _lillI2 and

a =

4 2g9/2 p r o t o n . I n r e g i o n B most o f t h e s i n g l e p a r t i c l e s t r e n g t h f r o m t h e h i g h - s p ~ n o u t e r s u b s h e l i s l i l l / 2 and 1 j 1 5 / 2 i s c o n c e n t r a t e d .

The above m e n t i o n e d c o n c l u s i o n s a r e c o n f i r m e d

ty

t h e (3He,d) s t u d y o f t h e same t a r g e t n u c l e i as i t i s shown i n F i g . 13.

The s t r u c t u r e s observed i n t h e ( a , t ) s t u d y a r e c l e a r l y c o n f i r - med b y t h e (3He,d) experiments. Again i t i s w o r t h p o i n t i n g o u t t h a t t h e PWBU model reproduces f a i r l y w e l l t h e s l o p e and shape o f t h e u n d e r l y i n g continuum f o r a l l t h e i n v e s t i g a t e d t a r g e t nu-

c l e i . The c h a r a c t e r i s t i c s o f t h e h ~ h - l y i n g f r o t o n s t a t e s in117sb

Eu and 'Bi, c e n t r o F d energy s p r e a d i n g , w i d t h and s p e c t r o - s c o p i c s t r e n g t h a r e p r e s e n t e d i n T a b l e 11.

These q u a n t i t i e s b e i n g deduced f r o m t h e d a t a r e d u c t i o n and t h e a n a l y s i s , we can compare now o u r r e s u l t s t o t h e p r e d i c t i o n s o f n u c l e a r models

.

i n s

E x c ~ l a t ~ o n energy

Eig.13 - Residual energ spectra from the (3He d) reaction at 240 MeV on "Zr, '20~n, ''91n and "'pb target nuclei. The dashed line is the prediction of the PWBU model for the underlying background.

Table I1

-

Summary of the results from the analysis of the ( a t) and (3He d) reactions to high-lying proton states in '17sb, 1 4 5 ~ ~ and ' o ' B ~ .

C Z S 0.9 0.97 0.75

,

0.19 0.94 0.15 % I .O Nucleus/Bump 'l7sb A '"EU A B 2 O g B i A B

*

From the (3He,d) spectra.

111.3

-

Comparison with nuclear models

During t h e recent y e a r s , t h e l a r g e amount of experimental d a t a on inner-hole stren$hs i n medium-heavy nuclei lead t o a s i m i l a r growth of t h e o r e t i c a l papers on t h e f r a g - mentation and damping of nuclear e x c i t a t i o n /25,28/.

Two t h e o r e t i c a l approachs were r a t h e r successful i n reproducing t h e empirical sys- tematics of t h e inner-hole s t r e n g t h d i s t r i b u t i o n s .

The Dubna group 1251 using t h e quasi particle-phonon nuclear model has i n v e s t i g a t e d t h e fragmentation mechanism. The n e c e s s i t y of taking i n t o account t h e "quasi- p a r t i c l e plus two phonons" components and of c a l c u l a t i n g with a l a r g e phonon basis has been shown. On t h e o t h e r hand, a t h e o r e t i c a l model t h a t has found a considerable success i s based on a damping mechanism i n which t h e simple e x c i t a t i o n mix w i t h t h e s u r f a c e v i b r a t i o n s . A s e l f c o n s i s t e n t mixing between s i n g l e p a r t i c l e motion ( c a l c u l a t e d with t h e Hartree-Fock Hami l t o n i a n )

,

and vi b r a t i o n s f r o m RPA c a l c u l a t i o n s coulb be achieved /26,28/ and the r e s u l t i n g s t r e n g t h functions are compared t o t h e empirical systematics. In t h e case of high-lying p a r t i c l e s s i n c e no data was a v a i - l a b l e , no c a l c u l a t i o n s were reported u n t i l now. Soon a f t e r t h e publication of our f i r s t r e s u l t s , p r e d i c t i o n s o f proton s t r e n g t h functions became a v a i l a b l e .

In Fig. 14 a r e presented t h e t h e o r e t i c a l s t r e n g t h f u n c t i o n s ( u n i t of s t r e n g t h per u n i t energy i n t e r v a l ) f o r t h e high-lying 2f7/2, lhg/2 and l i 1 3 / 2 o u t e r s u b s h e l l s i n 1 4 ' E u c a l c u l a t e d within t h e framework

of t h e quasi particle-phonon model /29/. The r e s u l t s of t h e c a l c u l a t i o n a r e compared t o t h e experimental values (deduced from

t h e a n a l y s i s of (ol,t) and (3He,d) reactions). 5-p protons states ~n l L 5 ~ u

In t h e f i g u r e i s a l s o indicated t h e l e v e l

-The0

scheme of proton q u a s i - p a r t i c l e s t a t e c a l - (qp-phononsl

culated i n a WoodsSaxon p o t e n t i a l . The t h e o r e t i c a l s t r e n g t h functions d i f f e r noticeably from each o t h e r . However t h e values of t h e second moment of t h e t h r e e d i s t r i butions a r e c l o s e .

The agreement w i t h experiment i s q u i t e good f o r t h e i13/2 subshell whereas t h e damping of t h e 2f7/2 and lhg/2 s t r e n g t h s i s r a t h e r l a r g e compared t o t h e e x p e r i - mental ones.0ne may n o t i c e a l s o a energy d i f f e r e n c e of about 1.0 MeV between t h e centroTd e n e r g i e s of t h e t h e o r e t i c a l and experimental s t r e n g t h d i s t r i b u t i o n s . Such desagreement may be explained by t h e procedure used i n t h e data a n a l y s i s

(Gaussian shapes) and/or by a l e s s accu- 3 5 7 9 1 1

r a t e determination of t h e experimental E,(M~V)

s t r e n g t h s i n t h e overlapping regions.

Fig. 14 - Comparison between theoreti-

cal / 2 9 / and experimental proton strength distributions for high-lying subshells in '"Eu.

In Fig. 15, s i m i l a r comparison i s made i n t h e case of t h e o u t e r l i l l / 2 and 1j15/2 s u b s h e l l s i n '09Bi. Here again a q u a l i t a t i v e agreement i s achieved.

JOURNAL

DE

PHYSIQUE

209

5-p protons states In 8 1 LOW-LYING s-p STATES I" 2 0 9 ~ 1

- Theo[HF+RPA)

,

- - - E x p

9

Fig. 15 same as Fig.14 for the case of the li11/2 and ljI5/2 proton strengths in 'OgBi.

Fig.16 - Comparison between theoretical/30/ and experimental strengths for the low-lying single particle states in 2 0 9 ~ i .

The t h e o r e t i c a l p r e d i c t i o n s a r e made f o r both t h e low-lying and high-lying proton s u b s h e l l s , giving an a d d i t i o n a l i n t e r e s t t o such approach s i n c e t h e whole.single par- t i c l e proton spectrum can be compared t o t h e experimental r e s u l t s .

In Fig. 16 t h e t h e o r e t i c a l p r e d i c t i o n s f o r t h e s t r e n g t h d i s t r i b u t i o n s of t h e low-lying lhg/2

,

2f7/2 and lil-312 s u b s h e l l s a r e compared t o t h e experi- mental r e s u l t s . I t i s worth pointing out t h a t t h e r e i s no f r e e parameter i n such c a l - c u l a t i o n s , t h e s i n g l e p a r t i c l e s t a t e s being generated from t h e H.F. p o t e n t i a l using S I I I f o r c e . The agreement i s r a t h e r s a t i s f a c t o r y both f o r t h e p o s i t i o n and t h e

s t r e n g t h located i n t h e main fragment of t h e low-lying lhg12, Zf7/2 and l i 1 3 / 2 pro- t o n c t a t ~ q i n 209Ri.

Turning now t o t h e high-lying l i l l 1 2 HIGH-LYING 5-p STATES in 2 0 9 ~ ~ and lj15/2 s t r e n g t h d i s t r i b u t i o n s

t h e comparison between t h e predicted

EXP 1 I 1 1 , ~ s p e c t r a l f u n c t i o n s and t h e experimental

- Theo ( H F + R P A ) ones i s displayed in Fig. 17.

A

n

The damping of t h e s e high-lying subshells i s not reproduced bv t h e c a l c u l a t i o n s .

hec concentration

of the high-lying proton

n s t r e n a t h i s c o r r e c t l v oredicted a s well

. "

D L 8 _{a s t h ; observed strong' overlap of t h e}

b.5 8 5 12 5

-,Ex

(MeV) two s t r e n g t h d i s t r i b u t i o n s . The theore- t i c a l s t r e n g t h functions have much more s t r u c t u r e than experiment, a general f e a t u r e already noted i n t h e case of inner-hole s t r e n g t h distributions/26,28/. Surface v i b r a t i o n s mixing can account f o r 40-60% of t h e observed damping but t h e mixing with s t a t e s of higher com-

o e p l e x i t y i s not taken i n t o account i n

L 5 8 5 1 2 5 *€,(MeV) such c a l c u l a t i o n s .

111.4

-

A new excitation

-

The high-lying neutron p a r t i c l e s t a t e s

The empirical systematics on the s i n g l e - p a r t i c l e response function include now, the inner-hole (both proton and .neutron), and the proton p a r t i c l e s t a t e s . To be complete an experimental investigation of the neutron p a r t i c l e s t a t e s i s therefore highly desirable. Most of the existing data on neutron p a r t i c l e strength functions come from e a r l i e r (d,p) studies carried out a t ratherlow bombarding energies or from neutron s c a t t e r i n g experiments.

Following the t r a n s f e r reaction approach, which has been q u i t e successful in probing high-lying proton strength d i s t r i b u t i o n s , we report here ofi the f i r s t stud of quasi- bound or unbound high-spin neutron s t a t e s using the (.,'He) on 90Zr,"6'11a'120Sn and 20BPb t a r g e t nuclei a t 183 MeV incident energy.

The experimental method i s very s i m i l a r t o the one already described i n sect. 111.1. The (a,3He) process has been chosen due t o i t s

known s e l e c t i v i t y in angular momentum t r a n s f e r f o r large Q values. In Fig. 18are displayed the residual ener y s e c t r a from (a,3He) reaction

₉

on 90Zr

,

OSn and '08Pb targets.

F i r s t l e t me comment on the strong s e l e c t i v i t y of t h i s process f o r high-spi

n

single-particle s t a t e s . The f i r s t low-lying neutron s t a t e s in 2 0 9 ~ b have a large spectroscopic strength (0.8 t o 0.6) but in the displayed 208Pb(a,3He) '09Pb spectrum, one can see t h a t the 1j15/2 (Q=7) s t a t e has a cross section 10 times larger than the one of the 29912 ( Q = 4 ) ground- s t a t e . The fragmentation of the

I

j15/2 subshell has been a long outstanding problem in nuclear structure. Here f o r the f i r s t time the frag- mented components a r e c l e a r l y seen in t h e energy range 3-6 MeV.

A t

higher excitation energy, the observed spec-

t r u m

i s dominated by a wide "bump" centered around 10.7 MeV in *09pb. I t may be already assumed t h a t t h i s large enhancement of cross- sections a r i s e from neutron stripping t o high- spin outer subshells. To assess such assump- t i o n s , HF calculations of the s i n g l e - p a r t i c l e neutron spectrum in 2 0 9 ~ b were carried out/31/ and the resulting level scheme i s displayed

i n

the l e f t part of Fig.19. I t appears that a t about 10 MeV above the 2g9/2 g.s. high-spin subsheTls namely, the 2h11/2, I k 7

2

and lj13/2 a r e p r e d ~ c t e d by the calcu~a41ons.

In the r i g h t part of t h e same figure a r e pre- sented the extracted angular distributions of the well known low-lying 29 12, l i and 1 j1512 neutron s t a t e s t o g e t # e r wi

~!I''~DUBA

predictions f o r the indicated

n

a j quantum numbers. The agreement i s q u i t e good. There- f o r e the experimental angular d i s t r i b u t i o n f o r the bump located a t 10.7 MeV i n 2 0 9 ~ b has been extracted from the data assuming f o r the background l i n e shape, t h e dashed l i n e

displayed i n Fig. 18. This l i n e shape i s F i g . 18

-

Residual energy spectra the r e s u l t of a BWBU calculation as discus- from the _on ( a 3He)reaction a t 183MeV

9 0 ~ r , 12'sn and 2 0 8 ~ b t a r g e t s . sed previously i n s e c t . III.1.1.DWBA c a l - _{The dashed l i n e i s the pred'iction} culations assuming

a

_lj13/2

_or

_a

_2h11/2

_{of the CWBU model f o r the back-}

C4-54 JOURNAL DE PHYSIQUE

Fig.19 - a) sin le particle level scheme for neu-

tron states in "'Pb (see text).

b) Experimental angular distributions and DWBA

theoretical curves from the 2 0 8 ~ b ( a , 3 ~ e ) 2 0 9 ~ b at

183 MeV to the lg9/2, l i l l / 2 and l j 1 5 / 2 low-lying

states.

c o n f i r m i n g o u r assumption t h a t t h e observed enhancement i s due t o n e u t r o n s t r i p p i n g t o h i g h - s p i n o u t e r s u b s h e l l s . To conclude t h i s f i r s t r e p o r t on h i g h - l y i n g n e u t r o n s t a t e s , I would

-

L 10 l i k e t o emphasize t h e s i m i l a r i t i e s w h i c h we observed f o r such h i g h - l y i n g s t a t e s i n n e u t r o n p i c k - u p

c) Same as b ) for the bump located at 10.7 MeV in

' ' ' ~ b . o r s t r i p p i n g experiments. As i t has been p o i n t e d o u t i n n e u t r o n p i c k - u p s t u d i e s on t h e t i n i s o - topes, t h e 1g9/2 i n n e r - h o l e s t a t e (N

<

50) appears as a sharp peak l o -

w i t h a w i d t h o f l e s s t h a n 1 MeV around 5 MeV e x c i t a t i o n energy. Moreover a s h o u l d e r a t h i g h e x c i - t a t i o n energy i s always observed

and c o r r e s p o n d s t o t h e damping o f _{5 -} t h e 2p, I f 5 1 2 i n n e r s u b s h e l l s .

I n n e u t r o n s t r i p p i n g experiment, one may d e s c r i b e t h e observed 1 2 0 ~ n ( a , 3 ~ e ) 1 2 1 ~ n energy spedrum (see F i g . 18) w i t h a l m o s t e x a c t l y

I V

-

CONCLUSIONS

The e m p i r i c a l knowledge on s i n g l e - p a r t i c l e s t r e n g t h f u n c t i o n s inmedium-heavy n u c l e i has been g r e a t l y enhanced by t h e o b s e r v a t i o n o f new h i g h - l y i n g modes i n b o t h p r o t o n and n e u t r o n s t r i p p i n g experiments. I n t h i s case t h e break-up o f t h e p r o j e c t i l e o f f e r s a n a t u r a l e x p l a n a t i o n o f t h e u n d e r l y i n g background. A t h i g h i n c i d e n t energy

( E x 40 MeV/nucleon) a s i m p l e p l a n e wave break-up model may be used t o d e t e r m i n e t h e shape and a n g u l a r dependance o f t h e observed background. Under such c o n d i t i o n s t h e e x t r a c t i o n from t h e e x p e r i m e n t a l d a t a o f t h e s t r e n g t h d i s t r i b u t i o n s i s more r e l i a b l e . However a s y s t e m a t i c i n v e s t i g a t i o n o f t h i s phenomenon i s needed i n o r d e r t o e s t a - b l i s h f i r m l y t h e method proposed here.

HFcal

(Sm)

neutrons

-

1 , 1 , 1 , 1 , 1 , , , ~ , , , ,. , . ,.. . . ., . . , , ,, ,,. , , 3 d 3 / 2 0 L 8 12 16 20

eCm(deg)

, . . . ., , ,, , ..,, ., , - _{L S 1 / 2}

From t h e e x p e r i m e n t a l s i d e , one forsees t h e n e c e s s i t y o f e x c l u s i v e experiments,such as Y o r p a r t i c l e decay o f h i g h - l y i n g s t a t e s , i n o r d e r t o a v o i d background s u b s t r a c - t i o n problems and t o g a i n i n s i g h t on t h e d e t a i l o f t h e damping mechanisms.

Acknowledgments

Much o f t h e work r e p o r t e d h e r e has been done i n c o l l a b o r a t i o n w i t h a number o f p h y s i c i s t s f r o m v a r i o u s l a b o r a t o r i e s and i n s t i t u t i o n s .

I would l i k e t o thankmy colleaguesfrom0rsay:Drs E. G e r l i c , J . G u i l l o t , H. Langevin- J o l i o t , S. F o r t i e r , J.M. Maison, E. Hourani, J.P. S c h a p i r a and F. Azayes.

Drs. G. P e r r i n , G. Duhamel, P. M a r t i n and V. Comparat f r o m Grenoble,

Dr. C.P. Massolo f r o m U n i v e r s i t y o f La P l a t a who t a k e s a m a j o r p a r t i n t h e a n a l y s i s o f t h e s t r i p p i n g r e a c t i o n s w h i l e she was a t Orsay, P r o f e s s o r G.M. Crawley f r o m M i c h i g a n S t a t e U n i v e r s i t y , Dr. D.Friese1 f r o m IUCF (USA) and Dr. B . Z w i e g l i n s k i f r o m I n s t i t u t e o f N u c l e a r Research a t Warsaw (Poland).

I would l i k e t o acknowledge Pr0f.V.G. S o l o v i e v , Drs. Ch.Stoyanov, A.I. Vdovin f o r communications o f t h e i r r e s u l t s p r i o r t o p u b 1 i c a t i o n and Dr. N. Van G i a i f o r t h e s u p p l y of h i s r e c e n t s i n g l e - p a r t i c l e v i b r a t i o n s c o u p l i n g c a l c u l a t i o n s .

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