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ISOVECTOR ∆L=1 STRENGTH OBSERVED IN THE(3He, t) REACTION ON SELF CONJUGATE NUCLEIS. van der Werf, S. Brandenburg, A. Drentje, P. Grasdijk, M. Greenfield, M.

Harakeh, W. Segeth, W. Sterrenburg, A. van der Woude

To cite this version:S. van der Werf, S. Brandenburg, A. Drentje, P. Grasdijk, M. Greenfield, et al.. ISOVECTOR ∆L=1STRENGTH OBSERVED IN THE (3He, t) REACTION ON SELF CONJUGATE NUCLEI. Journalde Physique Colloques, 1984, 45 (C4), pp.C4-471-C4-475. �10.1051/jphyscol:1984437�. �jpa-00224103�

JOURNAL DE PHYSIQUE

Colloque C4, supplkment au n03, Tome 45, mars 1984 page C4-471

3 ISOVECTOR AL=l STRENGTH OBSERVED I N THE ( ~ e , t ) REACTION ON SELF

CONJUGATE NUCLEI

S.Y. van d e r Werf, S. Brandenburg, A.G. Dren t j e , P. Grasdi jk , M.B. ree en field*, M.N. Harakeh, W. Segeth, W.A. Sterrenburg** and A. van der Woude

Kernfysisch VersneZZer Insti tuut, Zernikelaan 25, Groningen, The Netherlands

RLsum6 - Nous avons 'etudi'e d e s t r a n s i t i o n s DIi -1 sans e t avec s p i n - f l i p dans l a r e a c t i o n ( 3 ~ e , t ) . On d 6 c r i t un e s s a i pour o b t e n i r l e s fo rces B i j 2 par- t i r des s e c t i o n s e f f i c a c e s pour l e s t r a n s i t i o n s abou t i s san t aux 6 t a t s 2 . Abs t rac t - AZr;l t r a n s i t i o n s both wi th and without s p i n f l i p have been observed v i a t h e ( 3 ~ e , t ) r eac t ion . An a t tempt t o d e r i v e Bij-strengths from r e a c t i o n c r o s s s e c t i o n s f o r t r a n s i t i o n s t o 2- s t a t e s i s described.

AL=l s t r e n g t h has been observed i n h igh energy+(p,f ) r e a c t i o n s and t e n t a t i v e l y i d e n t i f i e d by Gaarde e t a l . [I] wi th t h e fields (o x r )A t-, X=0,1,2. Tabor e t a l . [2] have found s t r u c t u r e s , exc i t ed v i a t h e ( 3 ~ e , t ) r e a c t i o n , t h a t correspond i n shape and l o c a t i o n t o t h e GDR shifte+d over t h e Coulomb ener . These would t h e r e f o r e be t h e response t o t h e f i e l d irt-. l n a s tudy of t h e BC(3He,t)12N r e a c t i o n and t h e subsequent proton-decay we have repor ted (31 on t h e e x i s t e n c e of two iso- vec to r g i a n t resonances wi th 1'=l- and 2- which have been i n t e r p r e t e d a s t h e analogs of t h e GDR and t h e magnetic quadrupole resonance.

The obse rva t ion o f AL=l s t r e n g t h both wi th A S 0 ( A P = ~ - ) and A S 1 (AJ'=o-, 1-,2-) l e a d s t o such i n t e r e s t i n g ques t ions a s whether i t is poss ib le t o map ou t these s t r e n g t h d i s t r i b u t i o n s s e p a r a t e l y and whether t h e s p i n - f l i p s t r e n g t h e x h i b i t s a s i m i l a r c o l l e c t i v i t y a s h a s been observed f o r t h e non-spin-f l ip s t r e n g t h (GDR).

We have s t u d i e d t h e ( 3 ~ e , t ) r e a c t i o n on t h e n u c l e i 1 2 c , 160 , 2 4 * 2 6 ~ g , 2 8 S i and 4 0 ~ a a t i n c i d e n t ene rg ies of 75 and 81 MeV. The experiments have been performed with t h e QMG/2 spectrograph. Proton-decay experiments have been done i n which t h e t r i t o n s were de tec ted a t 8=O0 and t h e protons a t f i v e ang les ranging from 110' t o 150".

Ln f ig . 1 ( top) a spectrum from l * ~ ( ~ H e , t ) l ~ ~ i s shown. The most s t r i k i n g f e a t u r e s a r e t h e two g i a n t bumps a t Ex=4.2 MeV and 7.0 MeV. The dashed l i n e under t h e spectrum r e p r e s e n t s t h e shape of t h e photo-nuclear spectrum on 12c [ 4 ] , which i s e s s e n t i a l l y t h e GDR s t r e n g t h d i s t r i b u t i o n , s h i f t e d over 15.1 MeV. The h i g h e s t bump i n t h e ( 3 ~ e , t ) spectrum corresponds t o t h i s GDR no t only i n l o c a t i o n but a l s o i n shape. The lowest bump (Ex=4.2 MeV) h a s been ass igned 1'=2-. Its analog h a s been observed i n i n e l a s t i c e l e c t r o n s c a t t e r i n g [5] and i d e n t i f i e d wi th a g i a n t magnetic quadrupole resonance. This i n t e r p r e t 3 t i o n is+con%istent wi th 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 AL=1 o p e r a t o r s i r t and (a x r ) t A=0,1,2 from TDA c a l c u l a t i o n s by Glllet-Vinh Mau [6] and s h e l l model c a l c b ~ t ' i o n s by Kurath and Mi l l ene r [ 7 ] ( f ig .1) . Our assignments r e ly a l s o on a DWBA a n a l y s i s of t r i t o n angular d i s t r i b u t i o n s and t r i ton-proton angu la r c o r r e l a t i o n s . We used t h e program DWBA82 of Raynal 181. Form f a c t o r s were generated from t h e TDA wave f u n c t i o n s of Gillet-Vinh Mau and from those of Clark-El l io t t [91. I n o r d e r t o g e t a handle on t h e microscopic s t r u c t u r e of t h e wave func t ions we a r e fo rced t o l i m i t ourselves t o a d i r e c t r e a c t i o n mechanism only. We have adopted t h e . e f f e c t i v e p r o j e c t i l e - nucleon i n t e r a c t i o n of Schaeffer [ l o ] which i s of t h e 2-Yukawa type and h a s a

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1984437

JOURNAL D E PHYSIQUE

XVI 2676

600 - 8, '0" E3He= 81 MeV

0

200 -

4F ::; s~:-~llp

Gallet-

I Vlnh Mau -

J 3 U

L=1 S=O Kurath-

non spm-flip Mlllensr

Ex (MeV)

c e n t r a l and a t ensor component. Two s t e p s mechanisms have been shown t o be important i n ( 3 ~ e , t ) but they have l i t t l e i n f l u e n c e on t h e shape of t h e angu la r d i s t r i b u t i o n s . Their e f f e c t i s t h e r e f o r e mainly r e f l e c t e d i n a renor- ma l i za t ion of t h e e f f e c t i v e i n t e r - a c t i o n . A c l a s s of s t a t e s h a s been s e l e c t e d which have p a r t i c u l a r l y s imple wave func t ions . Among those a r e t h e lowest members o f each nega t ive p a r i t y family i n 1 6 ~ , Q: -4$; , t h e 2- s t a t e a t 0.772 MeV i n Sc and t h e 0' T=l s t a t e a t Ex=0.23 MeV i n 26~1. The t r a n s i - t i o n s t o t h e s e s t a t e s span a wide range of m u l t i p o l a r i t i e s . Surp r i s ing ly a l l but one normal izat ion f a c t o r N = J u ~ ~ / u ~ ~ ~ ~ needed t o f i t t h e d a t a a r e found t o l i e i n a small range N=2.1 - 2.4. The 3- (0.722 MeV) s t a t e i s t h e excep t ion wi th e 6 . 1 . Fig. 2 shows t h e angu la r d i s t r i b u t i o n s f o r t h e 0- - 4; s t a t e s e x c i t e d i n t h e 1 6 ~ ( 3 ~ e , t )46F reac t ion . Fig. 3 ( top) shows a 1 6 0 ( 3 ~ e , t ) 1 6 ~ spectrum with t h e Coulomb-shifted (y ,n) spectrum4) a s a dashed l i n e . St rength d i s t r i b u t i o n s from TDA c a l c u l a t i o n s a r e given i n t h e lower sec t ions . Again t h e shape of t h e GDR i s found back i n t h e ( 3 ~ e , t ) spectrum. On t h e b a s i s of t h e i r angu la r d i s t r i - but ions and t r i ton -p ro ton angular c o r r e l a t i o n s t h r e e s t a t e s i n 16F have been i d e n t i f i e d a s 1==2-: t h e known 0.424 MeV s t a t e , a s t a t e a t Ex=5.858 MeV and t h e l a r g e bump a t 7.4 MeV.

Fig. 1. Top: ectrum of t h e 1 2 ~ ( 3 ~ e , t ) 1 2 ~ react ion. TheT2C(y ,n) s p e c t r a . s h i f t e d over 15.1 MeV i s shown a s a dashed l i n e . The lower s e c t i o n s show AIFI s t r e n g t h dis- t r i b u t i o n s c a l c u l a t e d from model wave func t ions discussed i n t h e t e x t .

The connection between c ross s e c t i o n and M2- ( o r B. .-) s t r e n g t h i s made by observing t h a t : 1 J

i ) c a l c u l a t e d c r o s s s e c t i o n s ( eva lua ted a t a common Q-value) a r e w i t h i n 20% propor t iona l t o c a l c u l a t e d AL=l, AS.1 s t r e n g t h f o r 0- and 2- s t a t e s . This i s shown i n fig.4 (bottom) f o r t h e lp-lh wave f u n c t i o n s o f Gillet-Vinh Mau.

i i ) t h e normal izat ion cons tan t I+ oex /a A needed t o f i t angu la r d i s t r i b u t i o n s of s t a t e s wi th w e l l known waie P u n 8 f o n s was found almost constant. Among t h o s e s t a t e s were two 1==2- s t a t e s .

It may be conjectured t h a t 2- s t a t e s a r e e x c i t e d i n t h e ( 3 ~ e , t ) r e a c t i o n wi th c ross s e c t i o n s n e a r l y p ropor t iona l t o t h e i r B. --strengths. The e f f e c t of t h e Q- va lue must be t aken out.

1 3

I n t h e case of 6~ a c a l i b r a t i o n i s a t hand. The Bi j -s t rength f o r t h e t r a n s i t i o n s t o t h e 0.424 MeV s t a t e i s deduced from t h e f t -va lue of t h e f i r s t unique forbidden $-decay of 16N (g.s.) which is t h e i s o b a r i c m i r r o r of t h e 16F (0.424;2-) s t a t e , t o l 6 0 (g - s . ) .

160 ( 3 ~ e , t ) 1 6 ~

E3He=81 M e V

Ex-0192 MeV

E20.722 MeV

E;6372 MeV

Fig. 2. Angular d i s t r i b u t i o n s from t h e 6 0 ( i ~ e , t216 F r e a c t i o n l ead ing t o t h e O1 - 4 s t a t e s i n 16F. The

1 s o l i d curves a r e f i t s wi th t h e Schaef f e r fo rce . The c o n t r i b u t i o n s of t h e 7 , 07- and TT- p a r t s of t h e f o r c e a r e i n d i c a t e d sepa ra te ly .

Fig. 3. Top: Spectrum from t h e 1 6 0 ( 3 ~ e , t ) 1 6 ~ r e a c t i o n (wi th t h e Coulomb s h i f t e d (y ,n) spectrum a s a dashed l i n e ) . The lower s e c t i o n s show A>1 s t r e n g t h d i s t r i b u t i o n s from model wave funct ions .

E3He=81 M e V O=Oo I :

1 mn spin-flip

Gillet-Vinh Mau

15 io 5 6 Ex (MeV)

4

2

0

4-

2

0

4

2

The deduced va lue i s I< f 1 l ( a x rYl)2t-l 1 i>12 = 1.67 fm2. By using t h i s c a l i b r a t i o n , va lues of 0.42 fm2 and 3.48 fm2 a r e deduced f o r t h e s t a t e s a t 5.858 MeV and 7.4 MeV. This i s i n good agreement wi th TDA c a l c u l a t i o n s i f t hese s t a t e s a r e i d e n t i f i e d wi th t h e 2 and 2 model s t a t e s . The combined

3 s t r e n g t h on t h e s e t h r e e s t a t e s corresponds t o about 6b% of t h e sumrule.

We conclude t h a t t h e ( 3 ~ e , t ) r e a c t i o n may be a p o t e n t i a l "Bij-metert' which can be uqed + t o q u a n t i t a t i v e l y l o c a t e AL=l, A S 1 s t r e n g t h a s s o c i a t e d wi th t h e opera to r (a x r )* t-, very much i n t h e same way a s t h e (p,n) r e a c t i o n has been used t o measure Gamow-Teller s t r eng ths .

0 I

-

-

spin-flip - ----- 2- ..... . 0- _

-

L r

f ! : I

r I I

non spin-flip -

-

I I

Clark-Elllott -

I I

C4-474 JOURNAL DE PHYSIQUE

Fig. 5. Spectrum from t h e 2 4 M g ( 3 ~ e , t ) 2 4 ~ 1 reac t ion com-

with t h e Coulomb s h i f t e d ,n) spectrum.

- ;i ;: 6x10-3- E - -

44x16~ a," - g Z ~ I O - ~ b

=J

For 1- s t a t e s the calculated cross sec t ions a r e proport ional t o n e i t h e r t h e AL=l, A S 0 s t reng th nor t o t h e AL=l, A S 1 s t reng th ( f ig . 4). Yet t h e analog of t h e GDR i s exc i ted s t rongly i n a l l cases. In f i g s . 5 and 6 s e c t r a a r e shown from t h e 9 ( He, t ) reac t ions on 24Mg and 28 Si i n which even the f i n e s t r u c t u r e s of t h e GDR a r e recognized.

m . . rn

-

Mn apln fltp d~wla

- rpln fllp dlpole . . m

Fig. 6 Top: Spectrum from t h e 28 ~ i ( ~ ~ e , t ) * ~ p reac t ion with the Coulomb s h i f t e d (y ,n) spectrum a s a n i n s e r t . Bottom: Calculated s t reng th d i s t r ibu- t i o n s with A I i l .

-z m span fllp rnonwla . SPln fllP quadrapole 2 6x10-' - E

0 2 4

strength (frn2)

Fig. 4. Top: Cross sec t ions ca lcu la ted f o r t h e lp-lh wave funct ions _of Gillet-Vinh Mau a r e p lo t ted versus A I ~ = ~ , AL-1, A S O (non spin-f l ip) and A > l , A 5 1 (spin-blip) di- pole s t reng th , calculated from t h e same wave - functions, Bottom: Idem f o r t h e -hIn=2 and AI'=O s t rength.

Fig. 7 shows a 4 0 ~ a ( 3 ~ e , t ) 4 0 ~ c spectrum compared with a (y ,n) spectrum (middle) and a TDA- s t r e n t h d i s t r i b u t i o n <top). Like i n l fF, t h e lowest 2 s t a t e i n 'OSc (0.772 MeV) i s s t rong ly exc i t ed while t h e remaining 2- s t r e n g t h i s expected somewhat lower than t h e GDR. The bottom p a r t of f i g . 7 shows t h e t r i t o n spectrum, coincident wi th protons decaying t o 3 9 ~ a (g.s.) (d3,2 ). This f i g u r e i l l u s t r a t e s t h e power of t h e coincidence technique. P a r t of t h e continuum s t r u c t u r e i n t h e s i n g l e s spectrum i s due t o a breakup-transfer mechanism 1111 i n which a spectator-proton escapes. n e s e a r e mostly confined t o t h e forward hemisphere and by de tec t ing t h e protons a t a backward ang le t h i s breakup-transfer background i s e f f i c i e n t l y suppressed.

It i s s t r i k i n g t h a t t h e GDR shows l i t t l e decay i n t o t h e ground s t a t e . The s t r u c t u r e s seen i n t h e coincidence spectrum might be mostly 2- a s suggested by t h e c a l c u l a t i o n (top). Analysis on t h i s nucleus i s s t i l l i n progress.

Fig. 7. Top: Calculated AL=1 s t r e n g t h d i s - t r i b u t i o n s f o r 40Sc. Middle: Spectrum of t h e 4 0 ~ a ( 3 ~ e , t ) 4 0 Sc r e a c t i o n and t h e (y ,n) spectrum s h i f t e d over 7.66 MeV. Bottom: Spectrum of t r i t o n s co inc iden t wi th proton- decay t o 3 9 ~ a (g.s.1

* Permanent address: F lo r ida A&M Univers i ty , Tal lahassee, USA ** Present address: Univers i tas Gadjah Mada, Yogyakarta, Indonesia.

References: 1. C. Gaarde e t a l . , Nucl.Phys. -(1981)258 2. S.L. Tabor e t a l . , Phys.Rev. =(1982)1253 3 . W.A. Sterrenburg e t al., Nucl.Phys. m ( 1 9 8 3 ) 109 4. 3 . Arens e t a l . , Nucl.Phys. =(1975)479; B.L. Berman and S.C. Fu l t z ,

Rev.Mod.Phys. *(1975)713 5. T. deForest Jr. e t a l . , Phys.Lett. =(1965)311 6. V. G i l l e t and N. Vinh Mau, Nucl.Phys. 2 ( 1 9 6 4 ) 3 2 1 7. D. Kurath and J. Mil lener , p r i v a t e communication 8. 3. Raynal, DWBA82, unpublished 9. from: V. G i l l e t e t a l . , Nucl.Phys. 8tJ(1966)321

10. R. Schaeffer, Nucl.Phys. %(1971)145 11. E.H.L. Aarts e t a l . , Phys.Lett. =(1981)307