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Positive parity deformed states in 56Ni and 58Ni
V o l u m e 32B, n u m b e r 6
POSITIVE
PHYSICS
PARITY
DEFORMED
LETTERS
17 A u g u s t 1970
STATES
IN
56Ni
AND
58Ni
A. J A F F R I N Service de Physique Th~orique, Centre d'Etudes Nucl$aires de Saclay, B P . n o 2, 9 1 - G i f - s u r - Y v e t t e , France Received 25 June 1970
Positive parity states with a prolate deformation are constructed in the configuration space of 56 Ni and 58Ni by diagonalizing a residual interaction in the b a s i s of projected Slater determinants• A s a t i s factory description is obtained both for the 56Ni energy s p e c t r u m and for the 58Ni excitation s p e c t r u m seen in a - t r a n s f e r e x p e r i m e n t s . E v e n p a r i t y s t a t e s of d o u b l e c l o s e d s h e l l m e d i u m n u c l e i a r e b e g i n n i n g to b e u n d e r s t o o d in t e r m s of 2 p - 2 h a n d 4 p - 4 h e x c i t a t i o n s , w h i l e l i t t l e i s s t i l l k n o w n a b o u t t h e d e t a i l e d n a t u r e of low l y i n g p o s i t i v e p a r i t y s t a t e s of s i n g l e c l o s e d s h e l l n u c l e i . It i s now c o m m o n l y b e l i e v e d t h a t a c l a s s i c a l d e s c r i p t i o n of t h e s e s t a t e s in t e r m s of 2 q u a s i - p a r t i c l e (2qp) a n d 4qp e x c i t a t i o n s [ 1 - 3 ] hides a crucial core polarization effect behind t h e c o n c e p t of e f f e c t i v e f o r c e a n d e f f e c t i v e c h a r g e s [4,5]. T h e a i m of t h e p r e s e n t w o r k i s to i n v e s t i g a t e t h e p o s s i b i l i t y of f i n d i n g c o r e p o l a r i z e d s t a t e s in t h e v i c i n i t y of u s u a l 2qp s t a t e s . A c c o r d i n g t o p r e v i o u s c a l c u l a t i o n s of 0 + e x c i t e d s t a t e s in n i c k e l a n d t i n i s o t o p e s [6], a n d in v i e w of r e c e n t a l p h a - t r a n s f e r e x p e r i m e n t s in t h e r e g i o n of n i c k e l [7], 2 p - 2 h - 2 q p p o s i t i v e p a r i t y s t a t e s s e e m to e x i s t a t r a t h e r low e n e r g i e s . S i n c e t h e n i c k e l s o f f e r t h e o p p o r t u n i t y to s t u d y a t t h e same time a (pseudo-)double closed shell nucleus a n d n u c l e i w i t h a n e x c e s s of n e u t r o n s , it w a s f o u n d i n s t r u c t i v e to l o o k f o r a s i m u l t a n e o u s d e s c r i t p i o n of p o s i t i v e p a r i t y s t a t e s of 56Ni a n d 58Ni, t h e f i r s t o n e in t e r m s of 0 p - 0 h , 2 p - 2 h , 4 p - 4 h c o n figurations, the other one as 2 neutrons and 2 protons - 2 proton holes - 2 neutrons (2p-2~-2n) on a 56Ni c o r e . L i k e in [6], a m a x i m u m s y m m e t r y p r i n c i p l e w a s a p p l i e d to s e l e c t , a m o n g a l l 2 p - 2 h , 4 p - 4 h o r 4p-2h configurations, those which involve the m a x i m u m b i n d i n g e n e r g y • We c o m p a r e d , in particular, pairing configurations with aligned c o n f i g u r a t i o n s [8] of p r o l a t e o r o b l a t e s h a p e , a n d we v e r i f i e d t h e w e l l k n o w n p r o p e r t y t h a t t h e c o e x i s t e n c e of p r o t o n s a n d n e u t r o n s i s u n f i l l e d o r b i t s f a v o r s a d e f o r m a t i o n ; in t h e n i c k e l r e g i o n , t h e p r o l a t e d e f o r m a t i o n t a k e s o v e r t h e o b l a t e one. A typical prolate 4p-2h wave function expressed as a Slater determinant constructed on spherical orbits is the following: 448
I q~} = Det[q~P(j, ½) ~pP'(j,-½) ~pn(k, ½) ~pn'(k,-½)
× 9pI)(j,j) ~ p P ' ( j , j ) ]
w h e r e b a r s r e f e r to h o l e s • T h e v a l e n c e p a r t i c l e s w e r e r e s t r i c t e d to t h e lf7/2, 2P3/2, lf5/2 and 2Pl/2 orbits. Only one configurat,on, of.prolate shape, was retained m t h e c o n f i g u r a t i o n s p a c e f o r e v e r y d i s t r i b u t i o n of E M~, O÷ -
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F i g . 1. P o s i t i v e p a r i t y s t a t e s in 56Ni. a) S p e c t r u m obs e r v e d in the 58Ni(p, t)56Ni experiment; b)and c) Cal-
culated s p e c t r a with ~K - B" and "IGE" interactions.
PHYSICS LETTERS
Volume 32B, number 6 o Mev
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Fig. 2. Positive parity states in 58Ni. a) Spectrum observed in the 56Fe(160,12C)58Ni experiment; b) and e) Calculated spectra with " K - B" and 'IGE" interactions. p a r t i c l e s and h o l es in the v a l e n c e o r b i t s . Each c o n f i g u r a t i o n , a S l a t e r d e t e r m i n a n t , was then p r o j e c t e d on its c o m p o n e n t s of good a n g u la r m o m e n t u m b e f o r e d i ag o n a l iz in g the r e s i d u a l i n t e r action. The p r o j e c t i o n method c o n s i s t s in p e r f o r ming finite r o t a t i o n s on the s t a t e s and in s o l v i n g two s e t s of l i n e a r equations, one f o r the n o r m s and one fo r the e n e r g i e s [9]. P o t e n t i a l s of diff e r e n t n a t u r e w e r e used: (i) a s e t of now s t a n d a r d ' bare" matrix elements generated from a HamadaJohnston potential by Kuo and Brown [10], denoted h e r e by " K - B " ; (ii) an e f f e c t i v e i n t e r a c t i o n , denoted by "IGE", with a G a u s s i a n r a d i a l d e p e n de nc e and with p a r a m e t e r s d e t e r m i n e d f r o m BCS c a l c u l a t i o n s in t h e n i c k e l r e g i o n [11], n a m e l y a depth Vo = - 2 4 MeV and the following spin and i s o s p i n m i x t u r e : (S = 0 , T = I ) / ( S = 1 , T = 0 ) / ( S = O, T = O ) / ( S = 1, T = 1) = 1 . / 1 . 2 5 / 1 . / - 0 . 4 . The s i n g l e p a r t i c l e eneirgies w e r e e x t r a c t e d f r o m e x p e r i m e n t a l s p e c t r a of 57Ni and 59Cu and the l f 7 / 2 - 2p 3/2 s.p. e n e r g y s e p a r a t i o n was t r e a t e d
17August 1970
as a p a r a m e t e r . An additional d e g r e e of f r e e d o m was n e c e s s a r y in the c a s e of the IGE e f f e c t i v e potential to c o r r e c t f o r the fact it is e f f e c t i v e in a d i f f e r e n t co n f i g u r at i o n space; the d i s t a n c e b et w een the 2P3/2 o r b i t and the next o r b i t s was i n c r e a s e d by 0.4 MeV. Th e s i n g l e p a r t i c l e adopted v a l u e s a r e given in table 1. The r e s u l t s of the diagonalization in the c o n f i g u r a t i o n sp ace of 56Ni is p r e s e n t e d in fig. 1. Solid lines in fig. l b and l c a r e the t h e o r e t i c a l e n e r g y v a l u e s p r e s e n t e d as s u c c e s s i v e "bands" made of a m i x t u r e of 0p-0h, 2p-2h and 4p-4h conf i g u r a t i o n s and c a l c u l a t e d with the " K - B " and the "IGE" i n t e r a c t i o n s r e s p e c t i v e l y . Dashed l i n es a r e the r e s u l t of a s e p a r a t e l p - l h c a l c u l a t i o n with s a m e f o r c e and s a m e p a r a m e t e r s . T h e s e c a l c u lated s p e c t r a a r e to be c o m p a r e d with the e x p e r i mental s p e c t r u m of ref. [12] given in fig. l a. The f i r s t 0 + e x c i t e d st at e is adjusted by m e a n s of the ( l f 7/2 - 2P3/2) e n e r g y s e p a r a t i o n p a r a m e t e r . The value of this p a r a m e t e r , 4.0 MeV, is r e a s o n a b l y c l o s e to the o b s e r v e d value (4.8 MeV) which i n cludes c o r r e l a t i o n s of all kinds. The ground s t a t e is found to be 95% 0p-0h. The g o o d a g r e e m e n t between the o b s e r v e d 2~ and 4 ~ s t a t e s and the m e m b e r s of the f i r s t band c l e a r l y s u p p o r t s the p r e s e n t choice of f o r c e s . F u r t h e r m o r e , the f i r s t 2 + and 4 + s t a t e s turn out to be n i c e l y d e s c r i b e d as l p - l h st at es. T h i s is to be opposed to Wong and D a v i e s ' c o n c l u s i o n s on 56Ni [13]. The r e s u l t s of the d i a g o n a l i z a t i o n in the space of 58Ni a r e shown in fig. 2. Since we a r e m a i n l y i n t e r e s t e d in the 2 p - 2 h - 2 q p p a r t of the s p e c t r u m , fig. 2a shows the e x c i t a t i o n s p e c t r u m o b s e r v e d in the 54Fe(160, 12C)58Ni e x p e r i m e n t [6]. Fig. 2b and 2c show c a l c u l a t e d s p e c t r a with " K - B " and "IGE" potentials. Dashed lines a r e s t a t e s with p r e d o m i n a n t 2n c o n f i g u r a t i o n s and solid l i n es i n dicate "bands" f o r m e d m a i n l y with 2p-2~-2n c o n f i g u r a t i o n s . The c a l c u l a t i o n p r e d i c t s 4p-2h s t a t e s as low as 3 MeV; and this is e x p e r i m e n t a l l y conf i r m e d : the 62Zn e x c i t a t i o n s p e c t r u m s e e n in a r e c e n t 58Ni(160, 12C)62Zn e x p e r i m e n t [14] r e p r o duces, above the ground state, a p a t t e r n v e r y s i m i l a r to what is o b s e r v e d in 58Ni above 3 MeV. T h e s e 3 MeV r e f l e c t what a 2p-2h c o r e e x c i t a t i o n c o s t s in 58Ni. It s e e m s t h e r e f o r e r e a s o n a b l e to a d m i t that the o b s e r v e d s p e c t r u m as a whole is u n d e r s t o o d in t e r m s of 4p-2h s t a t e s : the s m a l l density of o b s e r v e d s t a t e s is r e p r o d u c e d and s u c c e s s i v e groups of peaks can be i n t e r p r e t e d as s u c c e s s i v e "bands" c o n s t r u c t e d on v a r i o u s 4p-2h c o n f i g u r a t i o n s (or v a r i o u s m i x t u r e s ) . T h e s e "bands" do not exhibit any s t r i c t r o t a t i o n a l c h a r a c t e r . Until one gets m o r e i n f o r m a t i o n about the a n g u l a r d i s t r i b u t i o n of t h e s e s t a t e s , it s e e m s 449
Volume 32B, n u m b e r 6
PHYSICS
LETTERS
17 August 1970
Table 1 lf7/2 nK - B " t protons neutrons
nIGE •
2P3/2
lf5/2
2p 1/2
- 3.8(56Ni), - 4.0(58Ni)
0
0.90
0.50
3.8(56Ni), - 0.4(58Ni)
0
0.76
1.08
-
i protons
- 4.0
0
1.30
0.90
! neutrons
- 4.0
0
1.16
1.48
Single p a r t i c l e e n e r g i e s used with the ~K - B" and the "IGE " potentials values a r e in MeV, 2P3/2 is taken as origin. p r e m a t u r e to go f u r t h e r i n t h i s d e t a i l e d a n a l y s i s . A s a c o n c l u s i o n , it i s p o s s i b l e , w i t h i n a t r a d i tional frame based on a shell model picture and t h e u s e of r e a s o n a b l e f o r c e s , to g e t a s a t i s f a c t o r y d e s c r i p t i o n of 56Ni a n d 58Ni a n d to j u s t i f y t h e 4 p - 2 h n a t u r e of t h e s t r o n g p e a k s o b s e r v e d i n 58Ni in a l p h a - t r a n s f e r e x p e r i m e n t s . K n o w i n g t h e p r e c i s e p o s i t i o n of s u c h 4 p - 2 h s t a t e s m a y h e l p u n d e r s t a n d i n g t h e p a r t i c u l a r f e a t u r e s of t h e low l y i n g p o s i t i v e p a r i t y s t a t e s of t h e n i c k e l i s o t o p e s i n t e r m s of a d m i x t u r e s of l p - l h a n d 2 p - 2 h e x c i t a t i o n s of t h e p r o t o n c o r e .
References [1] R. Arvieu and E. Salusti, Nucl. Phys. 66 (1965) 305. [2] S. Cohen et al., Phys. Rev. 160 (1967) 903.
450
[3] L. S. Hsu and J. B. French, P h y s . L e t t e r s 19 (1965) 135. [4] V. Gillet, B. Giraud and M. Rho, Phys. Rev. 178 (1969) 1695. [5] J. Richert, J. de Physique 30 (1969) 609. [6] A. Jaffrin, P r o c . 1969 SPLIT S u m m e r School (Gordon and Breach), to be published. [7] J. C. Faivre and H. F a r a g g i et al., Phys. Rev. L e t t e r s 24 (1970) 1188. [8] M. Danos and V. Gillet, Phys. Rev. 161 (1967) 1034. [9] J. Raynal, J. de Physique 31 (1970} 3 and 135. [10] T. T. S. Kuo and G. E. Brown, Nucl. Phys. Al14 (1968) 241. [11] V. Gillet, B. Giraud and M. Rho, Nucl. Phys. A103 (1967) 257 and p r i v a t e communication. [12] W.G. Davies et al., Phys. L e t t e r s 27B (1968} 363. [13] S. S. Wong and W. G. Davies, Phys. L e t t e r s 28B (1968) 77. [14] J. C. Faivre, H. Faraggi et al., to be published.
POSITIVE
PHYSICS
PARITY
DEFORMED
LETTERS
17 A u g u s t 1970
STATES
IN
56Ni
AND
58Ni
A. J A F F R I N Service de Physique Th~orique, Centre d'Etudes Nucl$aires de Saclay, B P . n o 2, 9 1 - G i f - s u r - Y v e t t e , France Received 25 June 1970
Positive parity states with a prolate deformation are constructed in the configuration space of 56 Ni and 58Ni by diagonalizing a residual interaction in the b a s i s of projected Slater determinants• A s a t i s factory description is obtained both for the 56Ni energy s p e c t r u m and for the 58Ni excitation s p e c t r u m seen in a - t r a n s f e r e x p e r i m e n t s . E v e n p a r i t y s t a t e s of d o u b l e c l o s e d s h e l l m e d i u m n u c l e i a r e b e g i n n i n g to b e u n d e r s t o o d in t e r m s of 2 p - 2 h a n d 4 p - 4 h e x c i t a t i o n s , w h i l e l i t t l e i s s t i l l k n o w n a b o u t t h e d e t a i l e d n a t u r e of low l y i n g p o s i t i v e p a r i t y s t a t e s of s i n g l e c l o s e d s h e l l n u c l e i . It i s now c o m m o n l y b e l i e v e d t h a t a c l a s s i c a l d e s c r i p t i o n of t h e s e s t a t e s in t e r m s of 2 q u a s i - p a r t i c l e (2qp) a n d 4qp e x c i t a t i o n s [ 1 - 3 ] hides a crucial core polarization effect behind t h e c o n c e p t of e f f e c t i v e f o r c e a n d e f f e c t i v e c h a r g e s [4,5]. T h e a i m of t h e p r e s e n t w o r k i s to i n v e s t i g a t e t h e p o s s i b i l i t y of f i n d i n g c o r e p o l a r i z e d s t a t e s in t h e v i c i n i t y of u s u a l 2qp s t a t e s . A c c o r d i n g t o p r e v i o u s c a l c u l a t i o n s of 0 + e x c i t e d s t a t e s in n i c k e l a n d t i n i s o t o p e s [6], a n d in v i e w of r e c e n t a l p h a - t r a n s f e r e x p e r i m e n t s in t h e r e g i o n of n i c k e l [7], 2 p - 2 h - 2 q p p o s i t i v e p a r i t y s t a t e s s e e m to e x i s t a t r a t h e r low e n e r g i e s . S i n c e t h e n i c k e l s o f f e r t h e o p p o r t u n i t y to s t u d y a t t h e same time a (pseudo-)double closed shell nucleus a n d n u c l e i w i t h a n e x c e s s of n e u t r o n s , it w a s f o u n d i n s t r u c t i v e to l o o k f o r a s i m u l t a n e o u s d e s c r i t p i o n of p o s i t i v e p a r i t y s t a t e s of 56Ni a n d 58Ni, t h e f i r s t o n e in t e r m s of 0 p - 0 h , 2 p - 2 h , 4 p - 4 h c o n figurations, the other one as 2 neutrons and 2 protons - 2 proton holes - 2 neutrons (2p-2~-2n) on a 56Ni c o r e . L i k e in [6], a m a x i m u m s y m m e t r y p r i n c i p l e w a s a p p l i e d to s e l e c t , a m o n g a l l 2 p - 2 h , 4 p - 4 h o r 4p-2h configurations, those which involve the m a x i m u m b i n d i n g e n e r g y • We c o m p a r e d , in particular, pairing configurations with aligned c o n f i g u r a t i o n s [8] of p r o l a t e o r o b l a t e s h a p e , a n d we v e r i f i e d t h e w e l l k n o w n p r o p e r t y t h a t t h e c o e x i s t e n c e of p r o t o n s a n d n e u t r o n s i s u n f i l l e d o r b i t s f a v o r s a d e f o r m a t i o n ; in t h e n i c k e l r e g i o n , t h e p r o l a t e d e f o r m a t i o n t a k e s o v e r t h e o b l a t e one. A typical prolate 4p-2h wave function expressed as a Slater determinant constructed on spherical orbits is the following: 448
I q~} = Det[q~P(j, ½) ~pP'(j,-½) ~pn(k, ½) ~pn'(k,-½)
× 9pI)(j,j) ~ p P ' ( j , j ) ]
w h e r e b a r s r e f e r to h o l e s • T h e v a l e n c e p a r t i c l e s w e r e r e s t r i c t e d to t h e lf7/2, 2P3/2, lf5/2 and 2Pl/2 orbits. Only one configurat,on, of.prolate shape, was retained m t h e c o n f i g u r a t i o n s p a c e f o r e v e r y d i s t r i b u t i o n of E M~, O÷ -
8
0*
_
_
4
4+
2 +=
+ ~
4+
•
s
I-
~
0+ ~
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+
Q+
+
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.
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F i g . 1. P o s i t i v e p a r i t y s t a t e s in 56Ni. a) S p e c t r u m obs e r v e d in the 58Ni(p, t)56Ni experiment; b)and c) Cal-
culated s p e c t r a with ~K - B" and "IGE" interactions.
PHYSICS LETTERS
Volume 32B, number 6 o Mev
-
-
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2
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.
.
.
.
.
.
.,,-
. . . . =-2+= -
~
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4 .
~
.
--
.
*
__0 _
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_
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.
-
....
_
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-
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.
.
. . . .
2 +. . . .
0 ....
_ _ _ _ 2 + _ _ _
2 ~-. . . .
. . . .
. . . .
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.
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.
.
.
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.
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B
C
Fig. 2. Positive parity states in 58Ni. a) Spectrum observed in the 56Fe(160,12C)58Ni experiment; b) and e) Calculated spectra with " K - B" and 'IGE" interactions. p a r t i c l e s and h o l es in the v a l e n c e o r b i t s . Each c o n f i g u r a t i o n , a S l a t e r d e t e r m i n a n t , was then p r o j e c t e d on its c o m p o n e n t s of good a n g u la r m o m e n t u m b e f o r e d i ag o n a l iz in g the r e s i d u a l i n t e r action. The p r o j e c t i o n method c o n s i s t s in p e r f o r ming finite r o t a t i o n s on the s t a t e s and in s o l v i n g two s e t s of l i n e a r equations, one f o r the n o r m s and one fo r the e n e r g i e s [9]. P o t e n t i a l s of diff e r e n t n a t u r e w e r e used: (i) a s e t of now s t a n d a r d ' bare" matrix elements generated from a HamadaJohnston potential by Kuo and Brown [10], denoted h e r e by " K - B " ; (ii) an e f f e c t i v e i n t e r a c t i o n , denoted by "IGE", with a G a u s s i a n r a d i a l d e p e n de nc e and with p a r a m e t e r s d e t e r m i n e d f r o m BCS c a l c u l a t i o n s in t h e n i c k e l r e g i o n [11], n a m e l y a depth Vo = - 2 4 MeV and the following spin and i s o s p i n m i x t u r e : (S = 0 , T = I ) / ( S = 1 , T = 0 ) / ( S = O, T = O ) / ( S = 1, T = 1) = 1 . / 1 . 2 5 / 1 . / - 0 . 4 . The s i n g l e p a r t i c l e eneirgies w e r e e x t r a c t e d f r o m e x p e r i m e n t a l s p e c t r a of 57Ni and 59Cu and the l f 7 / 2 - 2p 3/2 s.p. e n e r g y s e p a r a t i o n was t r e a t e d
17August 1970
as a p a r a m e t e r . An additional d e g r e e of f r e e d o m was n e c e s s a r y in the c a s e of the IGE e f f e c t i v e potential to c o r r e c t f o r the fact it is e f f e c t i v e in a d i f f e r e n t co n f i g u r at i o n space; the d i s t a n c e b et w een the 2P3/2 o r b i t and the next o r b i t s was i n c r e a s e d by 0.4 MeV. Th e s i n g l e p a r t i c l e adopted v a l u e s a r e given in table 1. The r e s u l t s of the diagonalization in the c o n f i g u r a t i o n sp ace of 56Ni is p r e s e n t e d in fig. 1. Solid lines in fig. l b and l c a r e the t h e o r e t i c a l e n e r g y v a l u e s p r e s e n t e d as s u c c e s s i v e "bands" made of a m i x t u r e of 0p-0h, 2p-2h and 4p-4h conf i g u r a t i o n s and c a l c u l a t e d with the " K - B " and the "IGE" i n t e r a c t i o n s r e s p e c t i v e l y . Dashed l i n es a r e the r e s u l t of a s e p a r a t e l p - l h c a l c u l a t i o n with s a m e f o r c e and s a m e p a r a m e t e r s . T h e s e c a l c u lated s p e c t r a a r e to be c o m p a r e d with the e x p e r i mental s p e c t r u m of ref. [12] given in fig. l a. The f i r s t 0 + e x c i t e d st at e is adjusted by m e a n s of the ( l f 7/2 - 2P3/2) e n e r g y s e p a r a t i o n p a r a m e t e r . The value of this p a r a m e t e r , 4.0 MeV, is r e a s o n a b l y c l o s e to the o b s e r v e d value (4.8 MeV) which i n cludes c o r r e l a t i o n s of all kinds. The ground s t a t e is found to be 95% 0p-0h. The g o o d a g r e e m e n t between the o b s e r v e d 2~ and 4 ~ s t a t e s and the m e m b e r s of the f i r s t band c l e a r l y s u p p o r t s the p r e s e n t choice of f o r c e s . F u r t h e r m o r e , the f i r s t 2 + and 4 + s t a t e s turn out to be n i c e l y d e s c r i b e d as l p - l h st at es. T h i s is to be opposed to Wong and D a v i e s ' c o n c l u s i o n s on 56Ni [13]. The r e s u l t s of the d i a g o n a l i z a t i o n in the space of 58Ni a r e shown in fig. 2. Since we a r e m a i n l y i n t e r e s t e d in the 2 p - 2 h - 2 q p p a r t of the s p e c t r u m , fig. 2a shows the e x c i t a t i o n s p e c t r u m o b s e r v e d in the 54Fe(160, 12C)58Ni e x p e r i m e n t [6]. Fig. 2b and 2c show c a l c u l a t e d s p e c t r a with " K - B " and "IGE" potentials. Dashed lines a r e s t a t e s with p r e d o m i n a n t 2n c o n f i g u r a t i o n s and solid l i n es i n dicate "bands" f o r m e d m a i n l y with 2p-2~-2n c o n f i g u r a t i o n s . The c a l c u l a t i o n p r e d i c t s 4p-2h s t a t e s as low as 3 MeV; and this is e x p e r i m e n t a l l y conf i r m e d : the 62Zn e x c i t a t i o n s p e c t r u m s e e n in a r e c e n t 58Ni(160, 12C)62Zn e x p e r i m e n t [14] r e p r o duces, above the ground state, a p a t t e r n v e r y s i m i l a r to what is o b s e r v e d in 58Ni above 3 MeV. T h e s e 3 MeV r e f l e c t what a 2p-2h c o r e e x c i t a t i o n c o s t s in 58Ni. It s e e m s t h e r e f o r e r e a s o n a b l e to a d m i t that the o b s e r v e d s p e c t r u m as a whole is u n d e r s t o o d in t e r m s of 4p-2h s t a t e s : the s m a l l density of o b s e r v e d s t a t e s is r e p r o d u c e d and s u c c e s s i v e groups of peaks can be i n t e r p r e t e d as s u c c e s s i v e "bands" c o n s t r u c t e d on v a r i o u s 4p-2h c o n f i g u r a t i o n s (or v a r i o u s m i x t u r e s ) . T h e s e "bands" do not exhibit any s t r i c t r o t a t i o n a l c h a r a c t e r . Until one gets m o r e i n f o r m a t i o n about the a n g u l a r d i s t r i b u t i o n of t h e s e s t a t e s , it s e e m s 449
Volume 32B, n u m b e r 6
PHYSICS
LETTERS
17 August 1970
Table 1 lf7/2 nK - B " t protons neutrons
nIGE •
2P3/2
lf5/2
2p 1/2
- 3.8(56Ni), - 4.0(58Ni)
0
0.90
0.50
3.8(56Ni), - 0.4(58Ni)
0
0.76
1.08
-
i protons
- 4.0
0
1.30
0.90
! neutrons
- 4.0
0
1.16
1.48
Single p a r t i c l e e n e r g i e s used with the ~K - B" and the "IGE " potentials values a r e in MeV, 2P3/2 is taken as origin. p r e m a t u r e to go f u r t h e r i n t h i s d e t a i l e d a n a l y s i s . A s a c o n c l u s i o n , it i s p o s s i b l e , w i t h i n a t r a d i tional frame based on a shell model picture and t h e u s e of r e a s o n a b l e f o r c e s , to g e t a s a t i s f a c t o r y d e s c r i p t i o n of 56Ni a n d 58Ni a n d to j u s t i f y t h e 4 p - 2 h n a t u r e of t h e s t r o n g p e a k s o b s e r v e d i n 58Ni in a l p h a - t r a n s f e r e x p e r i m e n t s . K n o w i n g t h e p r e c i s e p o s i t i o n of s u c h 4 p - 2 h s t a t e s m a y h e l p u n d e r s t a n d i n g t h e p a r t i c u l a r f e a t u r e s of t h e low l y i n g p o s i t i v e p a r i t y s t a t e s of t h e n i c k e l i s o t o p e s i n t e r m s of a d m i x t u r e s of l p - l h a n d 2 p - 2 h e x c i t a t i o n s of t h e p r o t o n c o r e .
References [1] R. Arvieu and E. Salusti, Nucl. Phys. 66 (1965) 305. [2] S. Cohen et al., Phys. Rev. 160 (1967) 903.
450
[3] L. S. Hsu and J. B. French, P h y s . L e t t e r s 19 (1965) 135. [4] V. Gillet, B. Giraud and M. Rho, Phys. Rev. 178 (1969) 1695. [5] J. Richert, J. de Physique 30 (1969) 609. [6] A. Jaffrin, P r o c . 1969 SPLIT S u m m e r School (Gordon and Breach), to be published. [7] J. C. Faivre and H. F a r a g g i et al., Phys. Rev. L e t t e r s 24 (1970) 1188. [8] M. Danos and V. Gillet, Phys. Rev. 161 (1967) 1034. [9] J. Raynal, J. de Physique 31 (1970} 3 and 135. [10] T. T. S. Kuo and G. E. Brown, Nucl. Phys. Al14 (1968) 241. [11] V. Gillet, B. Giraud and M. Rho, Nucl. Phys. A103 (1967) 257 and p r i v a t e communication. [12] W.G. Davies et al., Phys. L e t t e r s 27B (1968} 363. [13] S. S. Wong and W. G. Davies, Phys. L e t t e r s 28B (1968) 77. [14] J. C. Faivre, H. Faraggi et al., to be published.