Nuclear moments around the Z=40 shell closure:91mY,95Zr and97Nb

Hyperfine Interactions 75(1992)93- 100 93 N U C L E A R M O M E N T S A R O U N D T H E Z = 40 S H E L L C L O S U R E :

91my, 9SZr AND 97Nb

I. BERKES, M. DE JESUS, B. HLIMI*, M. MASSAQ, E.H. SAYOUTY**

Institut de Physique Nucl~aire de Lyon, IN2P3-CNRS et Universit~ Claude Bernard, 43 Bd du 11 Novembre 1918, 69622 Villeurbanne Cedex, France

and the NICOLE-ISOLDE Collaboration, CERN K. HEYDE

Institute for Theoretical Physics and Institute for Nuclear Physics, Proeftuinstraat 86, B-9000 Gent, Belgium

M a g n e t i c muments around the Z=/40 shell closure have been established using nuclear m a g n e t i c resonance on o r i e n t e d nuclei ( N M R / O N ) in iron. F r o m the resonance frequencies we established I #(91Y;9/2+) I = 5.%(6)# N,I #(95Zr;5/2+)[ =

1.103(23)#N, I #(97Nb;9/2+)1 = 6.153(5)#. N. F r o m the e l e c t r i c quadrupole a l i g n e m e n t of 95Zr + 95Nb in a Zr single c r y s t a l Q(95Zr) = + 0.29(5)b and Q (95Nb) <0 have been derived. The results o b t a i n e d are discussed using the Nilsson d e f o r m e d single p a r t i c l e m o d e h It is shown that for c e r t a i n d e f o r m a t i o n regions, a mea- s u r e m e n t of the m a g n e t i c m o m e n t can give i n f o r m a t i o n on the nuclear quadrupole d e f o r m a t i o n .

I. I N T R O D U C T I O N

The odd mass p r o t o n nuclei Y, Nb and Tc lie close to the Z=40 and N=50 closed shells. They are i n t e r e s t i n g candidates for the study of the dependence of the 9/2 + ground s t a t e m a g n e t i c m o m e n t s on the quadrupole d e f o r m a t i o n d e t e r m i n e d by the number of valence nucleons outside the closed shell c o n f i g u r a t i o n . Adding nucleons to the Z=40, N=50 c o n f i g u r a t i o n implies m o d i f y i n g the spherical shell model m a g n e t i c m o m e n t t h r o u g h c o n f i g u r a t i o n m i x i n g . One can e i t h e r use s p h e r i c a l p a r t i c l e - c o r e coupling c a l c u l a t i o n s , or s t a r t f r o m the beginning f r o m a d e f o r m e d s i n g l e - p a r t i c l e field like e.g. the Nilsson model. We study the v a r i a t i o n of the m a g n e t i c dipole m o m e n t tl versus the e q u i l i b r i u m ground s t a t e d e f o r m a t i o n both for odd mass p r o t o n and neutron nuclei.

One of the measures of the quadrupole d e f o r m a t i o n comes f r o m the k n o w l e d g e of the quadrupole m o m e n t . In n u c l e a r o r i e n t a t i o n this q u a n t i t y can be measured in two ways : a l i g n m e n t of the nuclei in a non-cubic single c r y s t a l ( i n t e g r a l method), or sublevel resonance in a m a g n e t i c single c r y s t a l (e.g. Co). Both methods require the k n o w l e d g e of the e l e c t r i c f i e l d g r a d i e n t of the i m p u r i t y in the host; in a d d i t i o n , the i n t e g r a l m e t h o d o f t e n suffers f r o m the presence of n o n - s u b s t i t u t i o n a l sites of the

~mpur~ty in the host. A n y h o w , the e x t r a c t i o n of the nuclear d e f o r m a t i o n f r o m the spectroscopic quadrupoJe m o m e n t is m o d e l - d e p e n d e n t .

As ."nentioned above, the m a g n e t i c m o m e n t is an i n d i r e c t measure of the nuclear d e f o r m a t i o n , in low t e m p e r a t u r e nuclear o r i e n t a t i o n (NO) precise m a g n e t i c m o m e n t s can be established only w i t h nuclear m a g n e t i c resonance on o r i e n t e d nuclei ( N M R / O N ) . Several a t t e m p s have been made to resonate y t t r i u m nuclei, e i t h e r on y t t r i u m produced by d i r e c t recoil i m p l a n t a t i o n into iron w i t h the 85Rb(o.,2n)87my r e a c t i o n / 1 / or by p e r f o r m i n g NMIR/ON on r e c o i l - i m p l a n t e d 89Zr or on its decay product 8 9 m y / 2 / . N M R

Permanent address : * University Ibn Zohr, Fac. Sciences, Agadir, Morocco 9 * University Hassan tl, F a c . Sciences-l, Casablanca, Morocco

9 Baltzer A.G., Scientific Publishing Company

94 1. B e r k e s et at., N u c l e a r m o m e n t s a r o u n d Z = 40 shell c l o s u r e

railed in all these e x p e r i m e n t s . In f a c t , Zr and Y o x y d i z e easily e s p e c i a l l y )ust a f t e r i m p l a n t e d ions stop in a sli]l hot m t c r o e n v i r o n m e n t . T h e r e f o r e , in [isis e x p e r i m e n t all nuclei are decay p r o d u c t s of n e u t r o n rich Rb isotopes.

2. I}:XPERIMILN TS

2.1 Source p r e p a r a t i o n

l h e on-line isotope s e p a r a t o r ISOLDE-2 of CEF'N ~ields v e r y strong Rb beams o v e r a large range of masses /}',/. Mass 91, 95 and 97 r u b i d i u m isotopes have been i m p l a n t e d w i t h an energ} of 60 keV into pure iron foils. No stable isotopes are c o l l e c t e d at these masses, so the i m p l a n t a t i o n densities are low. The iron foils w e r e c o a t e d on t h e i r back sides w i t h Ga-ln e u t e t i c solder, pressed against the cold f i n g e r of the N I C O L E d i l u t i o n r e f r i g e r a t o r w i t h a thin p l a s t i c p l a t e and loaded t o g e t h e r w i t h a 6l]CoCo or a 6 0 C o r e

I

nuclear t h e r m o m e t e r into the r e f r i g e r a t o r . A d e t a i l e d d e s c r i p t i o n of this r e f r i g e r a t o r is published Jn / a / .

A Zr single c r y s t a l has been i r r a d i a t e d in the l O l a n / c m 2 s n e u t r o n f l u x of the Melusine r e a c t o r of G r e n o b l e . The sample has been annealed at IS0 ~ under Ar a t m o s p h e r e , then soldered w i t h an u l t r a s o n i c soldering iron w i t h In to the cold finger of the r e f r i g e r a t o r .

2. S [Data accumulation and results

F o r sources in iron and Zr m a t r i c e s pulse height s p e c t r a of g a m m a rays w e r e tal<en w i t h 2 or 3 i n t r i n s i c Ge d e t e c t o r s in the d i r e c t i o n of the p o l a r i z i n g field (0 ~ or 1UU ~ and p e r p e n d i c u l a r to it (90'b. The data w e r e r e g i s t e r e d on the m a g n e t i c mass storage unit of the data a c q u i s i t i o n system which c o n t r o l l e d the e x p e r i m e n t . The data of the 0 u and 180 ~ d e t e c t o r s were summed in the e v a l u a t i o n s .

] h e ~ a r i a t i o n of the g a m m a ray i n t e n s i t y w i t h t e m p e r a t u r e has been e v a l u a t e d for se~erat g a m m a rays. ] h e t e m p e r a t u r e of the sample has been o b t a i n e d f r o m the o r i e n t a t i o n of the 60Co nuclear t h e r m o m e t e r .

The NMP,/ON t e c h n i q u e is d e s c r i b e d in d e t a i l in / 5 / . The f r e q u e n c y of the Nix4R signal g e n e r a t o r was m o d u l a t e d w i t h a continuous up-down ramp at 30 H z . Supposing that the h ~ p e r f i n e field d i s t r i b u t i o n around the resonance f i e l d is gaussian, the measured cur~e takes the c o n v o l u t e d f o r m / 5 / .

t [ II

,~j.S v ( ^{V_VO 2}

f(v) ^{I e • -} _) dr'

t

This cur~e has been f i t t e d to the measured p e n i s .

The e x t e r n a l p o l a r i z i n g field for the NMF~/ON m e a s u r e m e n t s was a l w a y s 0.096(2)T.

The t e m p e r a t u r e of the 95Zr and 97Nb samples under rf. p o w e r was b e t w e e n 6.5 and 9 mK, and about 25 mK for 9 1 m y .

Resonance m high f r e q u e n c y c o u p l i n g b e t w e e n the r a d i o f r e q u e n c y system and the sample may increase the t e m p e r a t u r e of the sample in c e r t a i n f r e q u e n c y ranges and thus destroy, the n u c l e a r o r i e n t a t i o n . The absence of such t h e r m a l resonances has been c h e c k e d tn each m e a s u r e m e n t . We also ensured t h a t the r a d l o f r e q u e n c y p o w e r a p p l i e d was sufQc,en[ to s a t u r a t e the resonance s~gnal.

The results of N I v l R / O N m e a s u r e m e n t s are s u m m a r i z e d in Table 1. The e r r o r on

the resonance f r e q u e n c y e x t r a p o l a t e d to zero e x t e r n a l p o l a r i z i n g f i e l d IS increased to

l a k e rote account an e v e n t u a l small K n i g h t shift. It should be n o t e d t h a t the d e s t r u c t i o n

r a t i o of the a m s o [ r o p y +s low, p r o b a b l y due to dispersion of h y p e r f i n e fields around Hs

s u b s t i t u t i o n a l value. The resonance on 97NbFe Is p r e s e n t e d oil (fig. I). The light decrease

of lhe a n l s o t r o p y for decreasing frequencieS--is due to a t h e r m a l resonance lying b e l o w

the represented range.

1. B e r k e s et al.. N u c l e a r m o m e n t s a r o u n d Z = 4 0 s h e l l c l o s u r e 95

0 00

w

4-

v 0

x 1 0 5

7.1

7.0

6.9

6.8

I I I

, j I,, '#'tt

I I

6 . 7 i

2 7 4 2 7 5 276 2 7 7 2 7 8

FREQ (MHz)

Fig. I. Intensity of the 658 keV gamma radiation of 97NbFe in the direction of polarizing field, versus rf. frequency. Modulation : +_ 0.25 MHz. Fitted values : see table I.

Table 1

Results of NMR/ON Measurements State

9 1 m y (9/2 +)

95Zr (5/2 +)

9 7 N b (9/2')

v Vextr FWHM Bhf ref J 11/11N I

(iVlH z) (MHz) (iVlH z) (T) (B)

308.57(5) 309.54(6) 1.1 -30.67(36) 6 5.96(6)

96.55(4) 96.88(5) 1.1 -28.1(5) * 1.131(20)

275.92(4) 276.92(5) 0.55 -26.57(2) 7 6.153(5)

v : resonance frequency

Vextr: r e s o n a n c e frequency extrapolated to zero external polarizing field PrecJsions of F W H M and the destruction ratios D are about 10 %.

* see in the text.

96 I. B e r k e s et al., N u c l e a r m o m e n t s a r o u n d Z = 40 shell c l o s u r e

The h y p e r f i n e field of Zr in iron has been d e t e r m i n e d by p e r t u r b e d a n g u l a r d i s t r i b u t i o n at r o o m t e m p e r a t u r e / 8 / . This r o o m t e m p e r a t u r e v a l u e has been e x t r a p o - l a t e d to low t e m p e r a t u r e using the precise r a t i o for B h f ( F e F e ) f r o m the M8ssbauer e f f e c t /c)/ Bhf(,,0O K)/13hf(a K) 0.9746(]). As the t e m p e r a t u r e d q m n d e n c e of I~,hi(/rFe) ma.~ be s o m e w h a t d i f f e r e n t f r o m t h a t of iron, we increase the e r r o r on the c o r r e c t i o n f a c t o r 0.975110) and use for the e v a l u a t i o n of the m a g n e t i c m o m e n t B h f ( Z r F e , 0 K) = -2t/.l(', ~, T.

In the n e u t r o n - i r r a d i a t e d Zr single c r y s t a l 95Zr and its d a u g h t e r 95Nb w e r e o r i e n t e d at about 6.5 m K . The a n g u l a r d i s t r i b u t i o n c o e f f i c i e n t s for 95Nb are t a k e n f r o m /~,/, for the 757 keV 7/2 + 5/2 t r a n s i t i o n of 95Z r f r o m this paper. As the 95Zr a c l i v i t y is c r e a t e d in situ in the Zr c r y s t a l it is supposed t h a t a f t e r the a n n e a l i n g all Zr nuclei occup~ s u b s t i t u t i o n a l sites. The a b s o l u t e value of the e l e c t r i c f i e l d g r a d i e n t of Zr in Zr is t a k e n f r o m D P A D of 8 9 ' 9 0 Z r ( 8 +) / 1 0 / .

The sign of Vzz (Zr, Zr) is not k n o w n f r o m d i r e c t m e a s u r e m e n t s , but s y s t e m a t i c s of EFC i n d i c a t e t h a t it is p o s i t i v e / 1 1 / . As this sign is d e t e r m i n e d m a i n l y by the m a n • , we adopt the same sign also for V zz (Nb, Zr). The results of the q u a d r u p o l e

o r i e n t a t i o n m e a s u r e m e n t s are s u m m a r i z e d in Table 2.

Table 2

Results of NO m e a s u r e m e n t s in a Zr single c r y s t a l .

N u c l e u s e O V @

zz

(10 -26 J) (eb) 9 5 Z r . 1.74(2/4) + 0.29(5) 9 5 N b - 1.0(3) s i g n ( Q ) = -

The h y p e r f i n e field of Zr in Z r F e 2 can be r e e v a l u t e d f r o m the i n t e g r a l o r i e n t a t i o n m e a s u r e m e n t of K r a n e el: al / 1 2 / . ] B h f ( Z r , Z r F e 2 ) [ = 17(5) T.

F o r 97Nb our m o r e precise m a g n e t i c m o m e n t value lies w i t h i n the e r r o r bars q u o t e d by K r a n e eL al ; 7.5(1/4) #N.

Supposing t h a t the e l e c t r i c f i e l d g r a d i e n t ~n Zr does not change sign b e t w e e n Zr and Nb, the sign change of the q u a d r u p o l e i n t e r a c t i o n e n e r g y r e f l e c t s the o p p o s i t e signs of the n u c l e a r q u a d r u p o l e m o m e n t s of 95Nb, as p r e d i c t e d by our c a l c u l a t i o n s and M61ler and Nix / 1 3 / as w e l l .

3. D I S C U S S I O N

In nuclei near to d o u b l e - o r single- closed shell regions, the ground s t a t e c o n f i g u r a -

t m n w i l l be d o m i n a t e d in m o s t cases by s p e c i f i c and r a t h e r pure s p h e r i c a l s h e l l - m o d e l

c o n f i g u r a t i o n s . N e a r Z=40 and N=50 for o d d - p r o t o n c o n f i g u r a t i o n s , the l g _ , ~ o r b i t a l

d e t e r m i n e s the ground or m o m e r i e s t a t e s for m a n y odd-mass Y, Nb and Tc'~r~uZcJei. On

the o t h e r hand, the o d d - n e u t r o n c o n f i g u r a t i o n is not as pure a s i n g l e - p a r t i c l e c o n f i g u r a -

h o n as is the p r o t o n c o n f i g u r a t i o n , a l t h o u g h n e a r N=51,53 and e v e n N=55, the 2d5/2

o r b i t a l s t i l l c o n s t i t u t e s an i m p o r t a n t c o m p o n e n t in t h e 17T = 5/2 + g r o u n d s t a t e .

I. Berkes et al., N u c l e a r m o m e n t s around Z = 40 shell closure 97

The q u a d r u p o l e p r o t o n - n e u t r o n c o r r e c t i o n s can be t a k e n i n t o a c c o u n t by consl- demng a s l i g h t l y d e f o r m e d s i n g l e - p a r t i c l e Nilsson p o t e n t i a l . H e r e , the q u a d r u p o l e d e f o r - m a t i o n E 2 i m p l i e s a p a r t i c u l a r v a r i a t i o n of ! 1 for a g i v e n s N i l s s o n - m o d e l c o n f i g u r a t i o n . F o r o d d - p r o t o n nuclei, w h e r e the l g 9 / 2 s p h e r t c a l o r b i t a l is d o m i n a n t , the g r o u n d - s t a t e c o n f i g u r a t i o n and the m a g n e t i c m o m e n t w i l l depend v e r y much on the sign of the d e f o r m a t i o n . On the o b l a t e side (fig. 2.), the F e r m i l e v e l for Y and Nb nuclei stays v e r y close to [he ~n _ 9/2 + o r b i t a l and a v e r y pure s t a t e r e m a i n s o v e r a r a t h e r large d e f o r m a t i o n i n t e r v a l . F o r Y n u c l e i w i t h /46 < N < 52 small o b l a t e shapes o c c u r and thus an a l m o s t c o n s t a n t m a g n e t i c m o m e n t results. This is also c o n s i s t e n t w i t h the e •

tal r a t i o b e t w e e n the m o m e n t s of 8 7 m y and 9 1 m y d e r i v e d d i r e c t l y f r o m the r a t i o s of the resonance f r e q u e n c i e s I ~ ( 8 7 m y ) / lz ( 9 1 m y ) I = 1.016(1) (this m e a s u r e m e n t and /6/).

1/2 § 912 § 112-

(,D 5.4 . . . . , . 5 r 2.

"" 3/2"

~ 3 1 2 ~ ., ... !112-

z . . . . i

~3 4 . 6 / ~ " .... ""1"f5/2"" . . . " " " "':

3/2,,i .

171

I J2 > : +

- 0 . 4 - 0 . 2 0.0 0.2 0.4

Q U A D R U P O L E DEFORMATION

Fig.2. Part of the Nilsson model single-particle level scheme for the nucleus 80 40Zr as function of the quadrupole deformation c 2. On the horizontal axis we

indicate, however, (c2, ~4 ), since we have calculated along a line minimi- zing the total energy surface in the hexadecapole deformation ~4" The Fermi level ~ for the corresponding Z and N values of Y, Nb, Tc and Rh isotopes is also drawn.

We h a v e c a l c u l a t e d the m a g n e t i c d i p o l e m o m e n t s for the ground or i s o m e r i c states t h r o u g h o u t the r e g i o n around Z=40 and N=50. F o r o d d - p r o t o n n u c l e i , we use the Ni]sson model w i t h g - f a c t o r s g~, = 1.0, gs = 5.58, gR = 0. The need to take into a c c o u n t a q u e n c h i n g for the n e u t r o n gs f a c t o r stems f r o m the f a c t t h a t in this casej above N=50~

the n e u t r o n 2d5/2 § 2d3/2 s p i n - f l i p t r a n s i t i o n c o r r e c t i o n s occur q u i t e low in e n e r g y and

c o n t r i b u t e in an i m p o r t a n t way to c o r e - p o l a r i z a t i o n c o r r e c t i o n s for the spin gs f a c t o r .

A t the p r o t o n Z=40 shellj the l g 9 / 2 -* l g 7 / 2 s p i n - f l i p e x c i t a t i o n needs a much l a r g e r

e n e r g y (a s p h e r i c a l shell gap of As ~ 5 MeV) and s u b s e q u e n t l y does not i n f l u e n c e the

p r o t o n gs f a c t o r in an i m p o r t a n t w a y / 1 4 / .

98 I. B e r k e s et al., N u c l e a r m o m e n t s a r o u n d Z : 40 s h e l l c l o s u r e

In Fig. 3. we present the m a g n e t i c m o m e n t s for the I ;T : 9/2 ~ states as a f u n c t i o n of the e q u i l i b r i u m d e f o r m a t i o n E 2 taken f r o m M611er and N i x / 1 3 / . H e r e too, and in par- t i c u l a r for the odd-mass Nb nuclei, o n e o b s e r v e s a steady decrease of 11(9/2 ~) w i t h p r o l a t e q u a d r u p o t e d e f o r m a t i o n as was the case in the p a r t i c l e core c o u p l i n g approach, in Fig. 3 we also i n d i c a t e the pure s i n g l e - p a r t i c l e s h e l l - m o d e l value of

H L lqo/2) : Q~*tgs/2) = 6.79 for gs - _5.58 : gs,free

= 5.95 gs = 0"7gs,free

as a r e f e r e n c e value. These e x t r e m e spherical s h e l l - m o d e l values give an i n d i c a t i o n that some quenching in the p r o t o n gs f a c t o r is present. As a l r e a d y p o i n t e d out, the v a r i a t i o n of the m a g n e t i c m o m e n t wLth d e f o r m a t i o n is very small and thus, lrl this region, m a g n e t i c m o m e n t s are poor i n d i c a t o r s for a d e t e r m i n a t i o n of the quadrupole d e f o r m a - tion. For p r e l a t e d e f o r m a t i o n , on the o t h e r hand (see fig.2, for the F e r m i level position), which becomes d o m i n a n t near N=56 in most nuclei and a l r e a d y below N=56 for Rh nuclei, m o r e d e l i c a t e s i t u a t i o n s occur. The F e r m i level is s i t u a t e d near the s 1 / 2 +

; / 2 ' , 5/2 + levels, (the small f~ c o m p o n e n t s o r i g i n a t e f r o m the l g 9 / 2 o r b i t a l ) thus ( o r i o l l s m i x i n g starts to play an i m p o r t a n t role and has been taken into account in all c a l c u l a t i o n s . This is i l l u s t r a t e d by the large v a r i a t i o n in the m o m e n t s for 99Nb, 99Rh and 101p.h. F o r 101Rh, in p a r t i c u l a r , a small v a r i a t i o n in E 2 a n d / o r the core e x c i t a t i o n unergJes g ~ e s a substantial ~ a r i a t i o n in l• as i l l u s t r a t e d by the h a t c h e d region in fig.3.

The e • m o m e n t s , p l o t t e d in the same f i g u r e , c o n f i r m the t r e n d of the c a l c u l a t e d m o m e n t s , but the v a r i a t i o n s are less sharp.

z< Z 5 8

7 fLCJs,free 6 o - 7 g s , f m e

4

5

85,87,9 t/<-~ 93Tc 97 ~ 9 5 Tc

87.9'1 y m 99R h ~ . ~ b

2 J 1

- 0 . 4 --0.3 - 0 . 2 -0.1 0.0 0.1 0.2 0.3

E 2

Fig. 3. Calculated m a g n e t i c dipole m o m e n t s (full dots) for the 9/2 + Nilsson model configuration (oblate shape) and for the aligned 9/2 + s t a t e (from ~ = 1/2 +, 3/2 + Nilsson configurations) with prelate d e f o r m a t i o n . The spherical I g9/2 proton value is also given for gs=gs,free and gs = 0.7 gs, free"

The abscissa is the calculated c 2 equilibrium value / 1 3 / f o r the corresponding

nucleus. Experimental m a g n e t i c m o m e n t s f r o m / 6 and 15/ and f r o m this

paper are indicated by full triangles. Coriolis mixing is tak'en into account in

all calculated values.

I. B e r k e s et al., N u c l e a r m o m e n t s a r o u n d Z = 40 shell closure 9 9

F o r the odd n e u t r o n Zr n u c l e i lhe l ~ 5/2 g r o u n d s l a t e o[ / r ts ~ery m u c h d e t e r m i n e d by the s p h e r i c a l 2d,~/2 s h e l l - m o d e l c o n f l g u r a l ~ o n w h m h r)i~.es u, 2d!,/2: qs/2

o f f

a n d polnls t o w a r d s a q u e n c h e d n e n l r t } n qs f a ( t l o r of (). t).7 gS,[l'ee s ;irl(! a subsequent, v a l u e of H(5/2 +) = - 1 . } } 7 lZN, q u i t e close to l h e e x p e r i m e n t a l g r o u n d .';late m o m e n t of 9 1 Z r : -1.305 i• N / 1 6 / . The v a r i a t i o n of 1• Jn l h e NIIsson m o d e l shows a g a i n a s m o o t h d e p e n d e n c e as E 2 i H c r e a s c s , w i t h an I n c r e a s l n q d e v i a t i o n f r o m a l i n e a r d e p e n d e n c e as E 2 t n c r e a s e s . ] h t s s h o w s t h e k m p o r t a n c e o f l h e l a r q e i m p u r i t y in the [;T = 5 / 2 * N t l s s o n c o n f i g u r a t i o n w i t h g r o w i n g r reduced b~, the i n c r e a s i n g i m p o r t a n c e of C o r i o l l s a d m l x l u r e a c c e n t u a t t n g this I r e n d . in Ihe hghl of the q u i t e c o n - sl ant -?~l e x c l l a l i o n enerc]\.. In the e v e n - e v e n Zr n u c l e i w i t h I x ~ I Iris'V. t~ne w o u l d nol e x p e c t a l a r g e v a r l a l l o n tr~ q u a d r u p o l e d e f o r m a t i o n e f f e c t s on tU',./2' ;, e o n t r a r ) I o I h e i m p o r t a n t , n c r e a s e tn e q u i l i b r i u m q u a d r u p o l e d e l o r m a t ~ o n as c a l c u l a t e d by M611er and N i x / 1 } / . It Is only f r o m N = 6 0 o n w a r d s t h a t a r a p i d m o d i f i c a t i o n o f Ihe low l y i n g e x c i t e d s t a t e s m e v e n Zr n u c l e i shows up. Thus, In w o r k i n g b a c k w a r d s , one e x p e c t s a d e f o r m a t i o n of ~2 = ( 0 . 0 6 5 - 0 . 0 7 ) m o r d e r to c o r r o b o r a t e w i t h l h e o b s e r v e d v a l u e ofl p (s/2+)1 = 1.103{23)iz N f o r 9 5 Z r .

The s,gns of the q u a d r u p o l e m o m e n l s in the g r o u n d s t a t e s of "J"Zr arid 95Nb can be u n d e r s t o o d using s , m p l e s h e l l - m o d e l a r g u m e n t s . Whereas O (95Nb; ts m a i n l y d e t e r m , n e d by Ihe o d d - p r o t o n p a r t i c l e m o v , n g ,n the I g 9 / 2 o r b i t a l ( g i v i n g rtse Io a n e q a t , v e S~l n in 9 f o r 9'}Zr the 5/2 * g r o u n d s t a t e car, (tuJte ,.'loll be m t e r p r e l e d as a n e u t r o n - h o l e m o v , n g ~n the 2d5/2 s h e l l - m o d e l orbtLal ( g i v i n g rose to a p o s t t ~ . e sign in 9 l h e p u r e s,ngle p a r t i c l e q u a d r u p o l e m o m e n l e e l f < r - > (2j-])/~'2j+2) f o r the p u r e 2d,)/2 hoh:.

c o n f i g u r a t i o n a m o u n t s to , 0. l/4 eb, using e e l f = e as an e f f e c l i , , e c h a r g e and harmonLc o s c l l l a l o r w a v e l u n c t l o n s ul o r d e r to e v a l u a t e the r a d , a l i n t e g r a l , la, e.s~des the sn~gh.-par- t l c l e p a r t , c o l l e c t , v e c o r e a d m i x t u r e s can b e c o m e v e r y i m p o r t a n t and r e s u l t ,nto e x t r a p o l a r i z a t i o n c h a r g e s such t h a t p r o t o n and n e u t r o n e f f e e t L v e c h a r g e s b e c o m e close to e a c h o l h e r / 1 6 / . Thus a hole mo~,,ng in 96Zr reduces a p o l a r , z a t l o n ('i~arge whu:h {:an e a s i l y e x c e e d the s i n g l e - p a r t + c l e v a l u e b v a f a c t o r of 2 such t h a t e e f f ~ 2o, c~en f o r a n e u t r o n hole. The same a r g u m e n t has also been d c v e l o p p e d b,, I,tauha',.an el al / I O / tr~

o r d e r to e x p l a i n the 8* q u a d r u p o l e m o m e n t s in 8 8 ' 9 0 Z r and Ih~s e f f e c t i v e thai'Hi ~ e x p l m n s the m e a s u r e d quadrtJpole m o m e n l of 9 b Z r Ioo.

The p o l a r i z a t i o n c h a r g e t:arl a['.;O t3e i n t e r t ) r P l e d w i l h i l l the single-parlic:n~ rnuih'l as a s l i g h t d e v i a t i o n f r o m the s p h e r i c a l e q u i l i b r i u m shape as d e d u c e d f r o m the r m e a s u r e m e n t .

ACKNOWLEDC,EMENTS

A u t h o r s are i n d e b t e d to P r o f . P. H e r z o g f o r the iron foils, to Dr. E. Z e c h f o r the

Zr single c r y s t a l , to D r . R. E d e r f o r help tn the m e a s u r e m e n t s , to Ihe l s o l d e t e a m f o r

the Rb b e a m to lvIM. D.P. H a d j o u t and R. B o u , , i e r f o r t e c h n t c a l s u p p o r t . One of us (I<.H.)

a c k n o w l e d g e s a N A T O r e s e a r c h g r a n t N. IS, C,. N A T O ;38/0/452 and f m a n c t a ] support f r o m

N F W O and IIKW.

100 I. B e r k e s et al., N u c l e a r m o m e n t s a r o u n d Z = 40 s h e l l c l o s u r e

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C o n t r i b u t i o n to this c o n f e r e n c e