xf ft33 Tie 3*. ^

ft33 Tie 3*. ^

xf

KFKI-71-52

I. S z en tp éte ry

J . S ziics M l T R A N SIT IO N

FROM a ANALOGUE TO A N T I-A N A L O G U E STA TE

9/2

IN 5 9 C

, 6 1 C

, 6 3 C e . 6 5 G a AND 6 7 G a N U C L E I

eKotingaxian S4cadem ^ o f (Sciences

CENTRAL RESEARCH

INSTITUTE FOR PHYSICS

BUDAPEST

К Ж 1 - 7 1 - 5 2

I . S z e n tp é t e r y and J u d it Szűcs

C en tra l R esearch I n s t i t u t e f o r P h y s ic s B u d ap est, Hungary N u clea r P h y s ic s Departm ent

Ml TRANSITION FROM gg /2 ANALOGUE ^{T O} ANTI-ANALOGUE STATE IN 59C u,61C u,6 5 C u,65Ga AND 67Ga NUCLEI

ABSTRACT

g q / o an a lo g u e r e so n a n c e s have b een found i n t h e

5 8 , 6 0 , 6 2 ^ 2 ^ 5 9 , 6 ! , 63Cu and 6 4 ,6 6 Zn ( pf Y) 6 5 ,6 7 Ga r e a c t io n S f w ith s t r o n g Ml t r a n s i t i o n s to th e c o rr e sp o n d in g a n t i-a n a lo g u e s t a t e s .

KIVONAT

g 9 /2 a n a ló g r e z o n a n c iá k a t t a lá l t u n k a 5 8 , 6 0 , 6 2 ^ ( р , у ) 5 9 ,6 1 ,6 3qu a 6 á ,6 6 Zn ( p >Y) ^5>,67Ga jnagreajfciók-ban, am elyek e r ő s Ml á t m e n e t t e l bomlanak a m e g f e le lő a n t ia n a ló g á lla p o to k b a .

РЕЗЮМЕ

Были найдены аналоговые резонансы gg/ 2 в ядерных реакциях 5 8 ,6 0 ,6 2n í(P ,y) 5 9 , 6 I , 6 3 Cu и 6^ ’6 6Zn(p,Y)^5 , 6 7 Gai которые распадают­

ся переходом MI в соответствующие антианалоговые состоян и я.

Ш t r a n s i t i o n s from th e i a o b a r i c r e so n a n c e s (IAR) t o th e a n ti-a n a lo g u e s t a t e s (AIAS) have r e c e n t l y r e c e i v e d much a t t e n t i o n from b o th e x p e r im e n ta l and t h e o r e t i c a l p o in t s o f v iew [1 -9 1 . I t h a s been p o in t e d out t h a t t h e s e t r a n s i t i o n s a r e s tr o n g i n 2 s - l d s h e l l n u c l e i and are h in d e r e d by s e v e r a l o r d e rs o f m agnitude i n th e low er p a r t o f th e l f - 2 p s h e l l . I n a p r e v io u s a r t i c l e IlO ] some p r e lim in a r y r e s u l t s were p u b lis h e d on th e ^8N i (p ,y)^9Cu r e a c t i o n w hich in d ic a t e d th a t th e IAR to AIAS Ml t r a n s i t i o n s t r e n g th r i s e s t o th e ord er o f th e s i n g l e p a r t i c l e s t r e n g t h a g a in . In o r d e r t o c o l l e c t more d e t a i l e d in fo r m a tio n on th e g e n e r a l b eh a v io u r o f t h e s e t r a n s i t i o n s we have exten d ed o u r i n v e s t i g a t i o n s t o ( p , y ) r e a c t io n s o f o th e r e v e n -e v e n n u c le i o f th e upper p a r t o f t h e lf - 2 p s h e l l , nam ely t o th e 5 8 , 6 0 , 6 2 ^ (p,y ) 5 9 » 6 1 ,6 5 Cu and 6 4 ,6 6 Zn

6 5 » 6 7 (ja r e a c t i o n s .

The e x p e r im e n t s w e r e p e r fo r m e d w i t h t h e 4- MeV Van d e G r a a f f a c c e l e r a t o r o f t h e C e n tr a l R e s e a r c h I n s t i t u t e f o r P h y s i c s . The Zn t a r g e t s w e r e e v a p o r a t e d from n a t u r a l m e t a l l i c z i n c , t h e 5 8 , 6 0 ,6 2 щ . t a r g e t s , e n r i c h e d t o 9 7 . 6 , 9 5 . 1 a n d 9 0 . 6 %, r e s p e c ­ t i v e l y , w ere e l e c t r o p l a t e d o n t o t h i c k g o l d b a c k i n g s . The t o t a l ( b e a m + t a r g e t ) e n e r g y r e s o l u t i o n o f t h e s y s t e m w a s a b o u t 5 k e V I n e v e r y c a s e . A 7 . 5 x 7 . 5 cm^ NaI(T£) s c i n t i l l a t i o n d e t e c t o r w as u s e d f o r t h e s im u l t a n e o u s m ea su rem en t o f t h e e x c i t a t i o n f u n c t i o n s f o r Y - r a y s o f e n e r g y

( i ) Ey > Ех - 2 0 0 keV ( i i ) 'Ey > E2 + 5 0 0 keV

( i i i ) E2 + 500 > EY > E2 - 1 5 0 0 keV,

where E^ i s th e energy o f t h e f i r s t e x c i t e d s t a t e o f th e t a r g e t n u c le u s and E2 i s th e e x p e c t e d en ergy o f th e IAR-AIAS t r a n s i t i o n . The e x c i t a t i o n f u n c t io n s w ere m easured i n 2 .5 keV s t e p s o v e r a r e g io n o f about 150 keV around the e x p e c t e d p o s i t i o n o f th e IA R -s.

The d e t a i l e d Y - s p e c t r a w ere taken by a 50 cur* G e (L i) d e t e c t o r , S in ce a l l th e e x c i t a t i o n f u n c t i o n s , in c lu d in g t h o s e o f rype ( i i i ) showed v e r y complex s tr u c tu r e e x c e p t f o r t h o s e o f th e

^8N i (p,y) 59 Cu r e a c t io n ( s e e F ig . 1 o f r e f . [ 1 0 ] ) , i t was n e c e s ­

2

sa ry t o measure t h e y - s p e c t r a o f each r eso n a n ce fo u n d in th e

co v ered bombarding energy r e g i o n in o r d e r t o g et f u r t h e r argum ents fo r i d e n t i f i c a t i o n o f IAR-в beyond t h e i r p o s i t i o n . I n each n u c le u s s t u d ie d here r e s o n a n c e s were fo u n d whoee s p e c tr a w ere m arkedly d i f f e r e n t from t h o s e o f th e o t h e r s . T h is means t h a t o n ly t h e s e r e so n a n c e s decay t o th e l o w - l y i n g g ^ /2 s t a 'fce» an<3- fu rth erm o re

th e se t r a n s i t i o n s a r e th e s t r o n g e s t p rim a ry ones i n t h e s p e c t r a . In the f i n a l n u c le i t h e r e i s o n ly one known g g / 2 s ^a‘*=e w h ic h .is a c a n d id a te to be t h e AIAS. In o rd er to c h e ck th e Ml c h a r a c te r o f th e s e t r a n s i t i o n s th e asymmetry param eter I ^q. / Iq. was d eterm in ed f o r t h e Cu i s o t o p e s . The o b t a in e d v a lu e s a re in agreem ent w ith th e m ainly Ml ( 9 /2 + .-> 9 / 2 +) c h a r a c t e r e x p e c t e d . On th e b a s i s o f t h e above o b s e r v a t io n s th e r e s o n a n c e s o f s p e c i a l p r o p e r t ie s were i d e n t i f i e d as members o f th e IAR o f th e f i r s t gg^2 s t a t e in th e t a r g e t + n eutron sy ste m .

The r e s u l t s are summarized i n T a b le 1 . I t can be s e e n t h a t the IAR—s are v e r y c lo s e t o t h e e x p e c te d p o s i t i o n s c a l c u l a t e d from th e and the e s t im a t e d [2 2 ] C oulom b-energy s h i f t v a l u e s . While in 59CU and k^Ga o n ly one r e so n a n c e seems t o p o s s e s s t h e IAR s t r e n g t h , In th e o th e r n u c l e i th e IAR shows f i n e s t r u c t u r e s p l i t t i n g sp r ea d over a r e g io n o f s e v e r a l t e n keV. In T a b le 1 can be fo u n d th e e s t im a te d and m easured Coulom b-energy s h i f t s t o g e t h e r w ith th e deduced symmetry p o t e n t i a l v a l u e s . The Coulomb s h i f t s are i n good agreem ent w ith o t h e r e x p e r im e n ta l r e s u l t s [ 1 1 ,1 2 ] . The V1 symmetry p o t e n t i a l , s t r e n g t h s d e r iv e d from the e n e r g y s p l i t t i n g o f th e

i s o s p i n d o u b le ts [3 ] are r e a s o n a b le . The a c c e p ta b le v a lu e s o f th e symmetry p o t e n t i a l are c o n s i s t e n t w ith t h e assu m p tion th a t th e AIAS s tr e n g t h i s m a in ly c o n c e n tr a te d in th e o n ly known lo w - ly i n g g ^ /2 s t a t e o f th e f i n a l n u c l e i .

The v a lu e s d eterm in ed f o r th e IAR-ALAS Ml t r a n s i t i o n s from t h e measured y i e l d s a r e p r e se n te d t o g e t h e r w it h th e s i n g l e ­ p a r t i c l e e s t im a t io n s in T a b le 2 [3,14-] • There are two t h e o r e t i c a l .

v a l u e s f o r e $ o h t r a n s i t i o n s one i s c a lc u la t e d w ith th e Schm idt g - f & c t o r , the o t h e r w ith th e measured e f f e c t i v e g - f a c t o r v a lu e

[1 5 ,1 6 ] . The e x p e r im e n ta l Гу r a d ia t i o n w id th s were d e r iv e d on th e a ssu m p tio n th a t Гр «• I t o t a l . Tb is a p p ro x im a tio n i s su p p o rted by th e f o l l o w i n g r e a s o n in g , p in c e the n e u tr o n channel i s c lo s e d i n a l l c a s e s , o n ly th e e l a s t i c ( Гр)м and i n e l a s t i c p ro to n w id th ( Гр , ) and Гу. could make an e s s e n t i a l c o n t r ib u t io n t o r t o t a l*

H owever, th e m easured Y - y i e l d o f th e (p ,p*y) r e a c t io n I n d ic a t e s th a t Гр, << Гр . The s in g le p a r t i c l e e s t im a t io n s on th e o th e r hand,

g iv e v a lu e s o f ab o u t 100 eV and 10 eV f o r th e p r o to n w id th s o f th e gQ/~ IAR-s i n Gu and Ga i s o t o p e s , r e s p e c t i v e l y (rIAR =, s r ^

\ P 2Т0 ч- 1 s . p . r hence << Гр , and so th e approach rp ^ r t o t a l seems t o Ъе 600^«

Comparing th e t h e o r e t i c a l and e x p e r im e n ta l v a l u e s o f F i g . 1 and T able 2 , i t i s c l e a r l y s e e n t h a t th e IAR-AIAS t r a n s i t i o n

s t r e n g t h i s h ig h a g a in in th e n u c l e i w it h a c l o s e d f r y s h e l l ,

a lth o u g h th e d e v i a t i o n from th e s i n g l e p a r t i c l e e s t im a t io n in c r e a s e s w ith th e mass number, l . e . w ith in c r e a s in g number o f n u c le o n s o u tsid e th e d o u b le - c lo s e d c o r e . S . Maripuu [5 ] and M. H ir a ta [81 h ave made t h e o r e t i c a l c a l c u l a t i o n s t o e x p la in t h e str o n g h in d ra n ce o f th e IAR-AIAS Ml t r a n s i t i o n in t h e low er p a r t o f th e l f - 2 p s h e l l . Accord­

in g t o th e s e m o d els th e a n t i- a n a lo g u e c o n f ig u r a t io n i s e x p e c t e d to mix w ith d i f f e r e n t c o r e - p o la r iz e d c o n f ig u r a t io n s i n which t h e a c t iv e n u c le o n s o f th e d o u b le - c lo s e d in e r t p a r t o f th e c o r e are c o u p le d to a s p in _v d i f f e r e n t from z e r o . The adm ixture o f su ch com ponents can s t r o n g ly reduce t h e M l- t r a n s it io n p r o b a b i l i t y . T hese c o r e - p o la r iz e d s t a t e s p ro b a b ly do n o t p la y a v e r y im p o rta n t r o l e i n th e n u c l e i j u s t above th e c lo s e d f r y g ßh e l l , an a ssu m p tio n su p p o rted by th e s tr o n g reap pearan ce o f th e IAR-AIAS t r a n s i t i o n s . On th e o th e r hand, th e in f lu e n c e o f th e c o r e - p o la r iz e d s t a t e s can keep grow ing i n im por­

ta n ce w ith in c r e a s in g number o f n u c le o n s o u ts id e th e d o u b le - c lo s e d in e r t p a r t o f th e c o r e , and t h i s i s a p o s s i b l e e x p la n a t io n o f th e d e c r e a se o f th e Ml t r a n s i t i o n p r o b a b i l i t y . U n fo r tu n a te ly , t h e r e i s no d i r e c t e x p e r im e n ta l e v id e n c e y e t , f o r th e e x i s t e n c e o f c o r e - p o la r iz e d s t a t e s i n th e s e n u c l e i , a lth o u g h t h e i r p r e s e n c e i s i n d i ­ c a te d by th e r e l a t i v e l y low v a lu e s o f t h e s p e c t r o s c o p ic f a c t o r s o f AIAS-s m easured i n proton t r a n s f e r r e a c t i o n s [17 •- 2 0 ] . I t w ould be d e s ir a b le to se a r c h f o r t h e c o r e - p o la r iz e d s t a t e s and t o perform s h e l l m odel c a l c u l a t i o n s a c c o r d in g t o [ 5» 8] f o r t h i s n u c le a r r e g io n .

The a u th o r s are v e r y g r a t e f u l t o Dr. J . Z im ényi f o r v a lu ­ a b le d is c u s s i o n s and c r i t i c a l rea d in g o f th e m an u scrip t and a r e in d e b te d to Dr. J . P . S c h i f f e r f o r h i s s t im u la t in g i n t e r e s t i n t h i s work.

REFERENCES

t i ] P.M. E n d t, in N u c le a r S t r u c t u r e , e d s . A. H o ssa in e t a l . /N o r th -H o lla n d , Amsterdam, 1 9 6 7 /

[2] P.M. E n d t , i n N u c l e a r I s o s p i n , e d s . . J . D . A n d e rso n e t a l . /A cadem ic P r e s s , New York and L o n d o n , 1 9 6 9 /

[?] S . M aripuu, N u c l.P h y s. A123 / 1 9 6 8 / 357

[4] S. Maripuu and G.A. Hokken, N u c l.P h y s . A14-1 /1 9 7 0 / 4-81.

[5 ] S. M aripuu, P h y s . L e t t e r s 31B / 1 9 7 0 / 18''

[6] Ilo n a Fodor e t a l . , N u c l.P h y s. A116 /1 9 6 8 / 167

t7 i I« D em eter e t a l . , A c t a P h y s i c a H u n g a r i c a j50 /1 9 7 1 / 1 [8] M. H ir a ta , P h y s .L e t t e r s 3 23 / 1 9 7 0 / 656

[91 H.Y. K la p d o r, C o n tr ib u tio n to t h e " T o p ica l C onference on the S tr u c tu r e o f Ifrw o N u c le i" , Padua, 1971* to he

p u b lis h e d . ''

[10] Ilo n a Fod or e t a l . , P h y s .L e t t e r s 32B /1 9 7 0 / 689 [11] J . E. F u c h s, d o c t o r a l t h e s i s , S tr a sb o u r g / 1 9 7 1 / [12] J. C. Browne e t a l , , N u c l.P h y s. A153 / 1 9 7 0 / 481 [13 ] S . M aripuu, N u c l.P h y s . A151 / 1 9 7 0 / 465

[14-] I . Talmi and I . Unna, A n n .R ev .N u cl.S e i 10 / i 9 6 0 / 355 [1 5 ] H .B e r tsc h a t e t a l . , N u c l.P h y s. A150 / 1 9 7 0 / 282

[16] K. S ie g b a h n , in A l f a - , B eta - and Gamma-Ray S p e c tr o sc o p y /N o r th -H o lla n d , Amsterdam, 1 9 6 5 /

[1 7 ] D. J. P u lle n and B . R o sn er, P h y s.R e v . 170 / 1 9 6 8 / 1034-

*

[1 8 ] N uclear D ata T a b le s В . , Y ol. 2 , n o . 5 / 1 9 6 8 / [19] R.G. Couch e t a l . , P h y s.R ev . C2 / 1 9 7 0 / 14-9 [20] A. W eidin ger e t a l . , N u c l.P h y s. A149 / 1 9 7 0 / 241 [21] H.V. K la p d o r, P h y s. L e t te r s 35B /1 9 7 1 / 4-05 [22] J. D. A nderson e t a l . , P h y s.R ev . I 38B / 1 9 6 5 / 615

FIGURE CAFTIOÍT

F i g . 1 . A n a lo g u e t o a n t i - a n a l o g u e Ml t r a n s i t i o n s t r e n g t h s i n W e is s k o p f u n i t s . S q u a r e s i n d i c a t e f r y2 ^7 / 2 t r a n s i t i o n s l c i r c l e s V3 / 2 P3 / 2 t r a n s i t i o n s . ; t r i a n g l e s g g/ 2 + 8 9 /2 t r a n s i t i o n s . The o p e n s i g n s a r e e x p e r im e n t a l v a l u e s [ 1 , 2 , 4 , 5 , 9 , 1 3 » 2 1 ] ; f i l l e d s i g n s a r e v a l u e s f o r s i n g l e - p a r t i c l e t r a n s i t i o n s w i t h a s p i n l e s s c o r e c a l c u l a t e d w i t h S c h m id t g - f a c t o r s [ J ] .

»

T a b l e 1

Summary o f ex p erim en ta l r e s u l t s

T arget P arent s t a t e AIAS

E L a b

p . r e s .

(keV )a (keY) (keY)b

ДЕахР ‘ (keY)

V (MeV)

Г Г

P Y ^{H VO} 0 0

T T "

(keY) (2 J + l)fi E

(keV) (2J+1)c2S

Гt o t a l

(eY) V

3071 1 0 .6 5030 3 3538 6898 9441 9408 149 1 .0 +0 .0 9 0 .5 6 + 0 .0 6

3719 8458 9326 0 .8 2 + 0 .0 8 0 .7 2 + 0 .0 8

b0Ni 2133 8 .4 5 27I I 1 .4 3725 8466 9326 9334 138 0 . 61+0 .0 7 0 .7 5 + 0 .0 8

3735 8476 9346 О.32+0-.04 ₀.5 6+0 . 0 9

3751 9817 9233 0 .1 + 0 .0 4 ^—

3774 . 9839 9256 O.2I+O.O5 -

62M 1299 6 .1 2509 2 .9 3786 9851 9213 9268 13О О.4 5 +О.О5 0 .6 + 0 .1

3790 9855 9272 0 .6 6 + 0 .0 6 0 .6 + 0 .1

3806 9871 9288 0 .2 4 + 0 .0 4 0 .5 + 0 .1 5

2926 6828 9806 О.29+О.О5

^ Z n 1064 7 .8 2034 4 9823 123

2937 6839 9817 0 .2 +O.O5 ^-

66Zn 602 8 .4 2063 4 .6 2 3335 8550 9712 9729 122 0 . 32+0 .0 6 ^-

a / E rro r o f th e s e v a lu e s +_ 4 keY V see r e f . [22]

Table 2

E x p e r im e n t a l a n d t h e o r e t i c a l v a l u e s i n W . u . . f o r t h e Ml ( 9 / 2 + -»■ 9 / 2 + ) IAE - AIAS t r a n s i t i o n s *

5 9 c u 6 1 CU 6 *Cu 6 ^Ga 6 ?Ga

E xp erim en tal 0 . 8 3 0 .4 4 0 . 2 0 . 2 1 0 . 0 6

T h e o r e t ic a l, c a lc u la t e d w i t h Schm idt g - f a c t o r s

2 . 7 1 . 9 1 . 5 1 . 9 1 . 5

T h e o r e t ic a l, c a lc u la t e d w i t h e f f e c t i v e g - f a c t o r s

1 . 7 ^{1 .2} 0 . 9 3 ^{1 . 2} • 0 . 9 3

к

The ex p e rim en ta l v a lu e s a r e summed up f o r th e members o f th e f i n e s t r u c tu r e s p l i t t i n g .

- 8 -

5 :

6 i , 4 i h

K iadja a K özponti F i z i k a i K utató I n t é z e t F e l e l ő s k ia d ó : Erő J á n o s, a KFKI

M a g fiz ik a i Tudományos Tanácsának e ln ö k e Szakmai l e k t o r : Zimányi J ó z s e f

N y e lv i l e k t o r : T. W ilk in son

Példányszám : 230 Törzsszám : 7 1 -5 9 5 0 K é sz ü lt а К FKI s o k s z o r o s ít ó üzemében, Budapest

1 9 7 1 . s z e p t e m b e r hó