Analogous 32− levels in 43Ca and 41Ar

Volume 24B, number 1

PHYSICS L E T T E R S

ANALOGOUS

3-

LEVELS

IN 43Ca

9 January 1967

AND

41Ar*

D. B. FOSSAN State University of New York at Stony Brook, Stony Brook, New York Brookhaven National Laboratory, Upton, New York

and A. R. P O L E T T I Brookhaven National Laboratory, Upton, New York

Received 13 December 1966

Lifetime measurements of the -~- levels in 43Ca at 594 keV and 41Ar at 518 keV yield M1 hindrances within the predominantly f73 configurations of (~< 300) and 3000, respectively. These results are compared with M1 matrix elementg between the f72p3 admixtures obtained from recent theoretical calculations. T

P r o p e r t i e s of nuclei with n n e u t r o n s (protons) outside a closed shell of 20 and a closed proton (neutron) shell a r e in g e n e r a l d e s c r i b e d with fair s u c c e s s by f~n c o n f i g u r a t i o n s and e x p e r i mentally determined interaction matrix elements [1,2]. In p a r t i c u l a r for a p u r e f½3 n u c l e u s , the theory p r e d i c t s a ~- ground state, a low-lying ~ level, and a ~-- level at about 1 MeV. The higher spin s t a t e s of the f 33 configuration a r e expected at somewhat g r e a t e r e n e r g i e s . Notable exceptions to t h e s e p r e d i c t i o n s occur for 43Ca and 41Ar where the ~- m e m b e r s of the f~-3-neutron c o n f i g u r a t i o n s a r e r e s p e c t i v e l y at 594 and 518 keV. The additional two d~- p r o t o n s holes in 41Ar which a r e coupled to zero spin at low excitation e n e r g i e s , a r e not expected to a l t e r the d i s c u s s e d f½3-neutron level spacings [3]. In an a t t e m p t to explain this energy d i s c r e p a n c y for 43Ca and other e n e r g y - s p e c t r u m details of the f½n Ca i s o topes, England and O s n e s [4] and F e d e r m a n and T a l m i [5] have r e c e n t l y made c a l c u l a t i o n s allowing for f~n-1 p~ and f ~ n - 2 p ~ a d m i x t u r e s . F o r 4 3Ca spdcifically, t h e" i r r e s"u l t s showed I f~2(0)p~} and I f~2(2)p~) a d m i x t u r e s in the ~level which lowered its energy into a g r e e m e n t with the e x p e r i m e n t a l value. T h e s e a d m i x t u r e s , in addition, a r e c o n s i s t e n t with 42Ca(d,p)43Ca e x p e r i m e n t s where a weak l = 1 s t r i p p i n g d i s t r i bution is o b s e r v e d to this 3- level [6]; a s i m i l a r d i s t r i b u t i o n is o b s e r v e d in the 40Ar(d,p)41Ar r e a c t i o n [7]. The p u r p o s e of this l e t t e r is to r e * Work performed

in p a r t u n d e r t h e a u s p i c e s

Atomic Energy Commission. 38

of t h e US

port on a c o m p a r i s o n of e x p e r i m e n t a l lifetime m e a s u r e m e n t s for these 3- levels in 43Ca and 41Ar. The l i f e t i m e s can be i n t e r p r e t e d in t e r m s of the (~- ~ ~-) M1 t r a n s i t i o n p r o b a b i l i t i e s which allow a d i r e c t check on the f~3 purity of the wave functions. This check is e s p e c i a l l y s e n sitive to the a d m i x t u r e s , since the dominant f_73 configurations have no M1 c o n t r i b u t i o n [8]. 2 The l i f e t i m e m e a s u r e m e n t s in this e x p e r i m e n t were obtained from l o g a r i t h m i c slopes of t i m e delay d i s t r i b u t i o n s . The t i m e of f o r m a t i o n of the - l e v e l s was d e t e r m i n e d by the detection of p r o t o n s f r o m either the 43Ca(p,p'~)43Ca or 40Ar(d,pT)41Ar r e a c t i o n in a s o l i d - s t a t e detector, while the decay t i m e was m a r k e d by the d e t e c • 37. . . . . tlon of the (~ ~ ~ ) 7 r a y s m a p l a s t i c s c i n t i l l a tor. Thin t a r g e t s of 43CACO 3 or 40Ar gas were used. Decay s c h e m e s for the low lying l e v e l s of 43Ca and 41Ar a r e shown in fig. 1. T i m e - d e l a y p u l s e s were produced in a t i m e - t o - h e i g h t c o n v e r t e r with the u s u a l f a s t - s l o w coincidence a r r a n g e ment. The 41Ar t i m e s p e c t r u m included [9] a p r o m p t c o n t r i b u t i o n from the it½ < 100 ps) 1.36 MeV level. F o r the 43Ca m e a s u r e m e n t a c o m p a r i s o n p r o m p t r e s o l u t i o n function was obtained f r o m the 27Al(p,p'~/)27A1 r e a c t i o n u n d e r s i m i l a r e x p e r i m e n t a l conditions. T i m e c a l i b r a t i o n s were made with a i r d i e l e c t r i c l i n e s . The e x p e r i m e n t a l l i f e t i m e r e s u l t s a r e shown in fi B. 2. F o r the 43Ca m e a s u r e m e n t , the 594 keV ~- level was completely i s o l a t e d f r o m other decay t i m e s by the coincidence conditions with the r e s o l v e d i n e l a s t i c proton group. Although the (p,p') c r o s s section to this level was s m a l l , fair

9 January1967

PHYSICS L E T T E R S

Volume 24B, number 2

i

312-

I

594

374

i

i

I

I

[

x

I000

7/2-

43 Ca

.

518

512

Z (5/2-1

#I 4tAr

165

7/8-.

I

I

0

41Ar

~I

I

43C0 43Co

t

TI

io

Fig. 1. Low-lying f~3 neutron levels of 43Ca and 41Ar. The y ray branching ratios are taken from refs. 10 and 11. s t a t i s t i c s were achieved; a l e a s t - s q u a r e s fit to the h a l f - l i f e slope yielded 160 + 10 ps. Because the slope of the p r o m p t r e s o l u t i o n function (factor of 2 in ~ 100 ps) does not fall off s i g n i f i c a n t ly f a s t e r than the l i f e t i m e slope, only an upper l i m i t can be stated with c e r t a i n t y , t½ --< 170 ps. F o r the 41Ar m e a s u r e m e n t , a fit to the lifetime slope in r e g i o n s not influenced by the p r o m p t c o n t r i b u t i o n r e s u l t e d in a h a l f - l i f e for the 518 keV ~ - level of t½ = 340 ~ 20 ps. The ~ r a y b r a n c h i n g for the decay [10,11] of the ~ - l e v e l s in 43Ca and 41Ar a r e e s s e n t i a l l y i d e n t i c a l as shown in fig. 1. The (3- ~ ~-) t r a n s i t i o n s a r e all E2, however the M1-E2 mixing r a t i o s for the (~- ~ ~-) b r a n c h a r e u n d e t e r m i n e d . B e c a u s e of the low t r a n s i t i o n e n e r g i e s , 220 keV for 43Ca and 353 keV for 41Ar, n o r m a l E2 s t r e n g t h s would y i e l d only s m a l l p e r c e n t a g e cont r i b u t i o n s to the o b s e r v e d t r a n s i t i o n p r o b a b i l i t i e s for these ( 3 ~-) b r a n c h e s even for f a i r l y l a r g e M1 h i n d r a n c e s . A s s u m i n g only M1 c o n t r i butions, the M1 h i n d r a n c e s r e l a t i v e to M o s z kowski e s t i m a t e s a r e --< 300 for 43Ca and 3000 for 41Ar. The c o r r e s p o n d i n g r e d u c e d t r a n s i t i o n p r o b a b i l i t i e s a r e B(M1) >/ 5.0 × 10 -3 nm2 for 43Ca and B(M1) = 0.59 x 10 -3 nm 2 for 41Ar. The g r e a t d i f f e r e n c e in magnitude of these t r a n s i t i o n p r o b a b i l i t i e s for the supposedly analogous levels in 43Ca and 41At is s u r p r i s i n g . Although l a r g e h i n d r a n c e s a r e c o n s i s t e n t with d o m i n a n t f7_3 conf i g u r a t i o n s which have no M1 contribution~, the question of whether the l a r g e r h i n d r a n c e in 41Ar

7

6

5

4

3

I

TIME DELAY (nsec)

Fig. 2. Time-decay curves for the 594 keV ~2 level of 43Ca and the 518 keV i2 level of 41Ar as shown with open circles. Comparison prompt-resolution functions are shown with solid circles. The time dispersion for the 43Ca measurement is twice that of the 41Ar measurement. An arbitrary zero time has been used. The prompt contribution in the 41Ar measurement is discussed in the text. indicates a purer f~3 configuration than that for Z 43Ca or whether just greater cancellation occurs in the M1 matrix element is unanswered. In respect to this question, it is interesting to see what M1 strength results from the f~2p~ admixtures which were required to fit the experimental energies in 43Ca; the wave functions [12]

are I~-> = 0.791 If l 3) + 0.194 If;2(0)p 3) -0.580 Jf~2(2)P3-) and I ~ z=0.870 f~3)z- 0.296 Lf}2(2)p] ) -0.396 IfL2(4)p3_)'. The only MI strength be~weenZthese wave2functi2ns arises from matrix elements between the fl2p_3 admixtures. There are no cross contributi~ns2from f2~2P~ admixtures to the dominant f 73 configurations since the single-particle M~I operator cannot change an l value. With a complete three particle calculation, these wave functions imply a B(MI) (3- --. ~)-5= 1.1 x 10-3 nm2. This theoretical value is a fac39

Volume 24B, number 1

PHYSICS

t o r of 5 s m a l l e r than the 43Ca e x p e r i m e n t a l l i m i t and about a f a c t o r of 2 l a r g e r than the m e a s u r e d value for 41At. T h e i n d i v i d u a l t e r m s of t h i s c a l c u l a t i o n h a v e c o n s i d e r a b l e M1 s t r e n g t h ; if the a b s o l u t e v a l u e of a l l the t e r m s w e r e a d d e d , a B(M1) = 0.4 n m 2 is o b t a i n e d . With t h i s a m o u n t of c a n c e l l a t i o n , the l a r g e r e x p e r i m e n t a l B(M1) f o r 43Ca is p e r h a p s not i n c o n s i s t e n t with a d m i x t u r e s of t h i s t y p e , s i n c e s m a l l c h a n g e s in the v a r i o u s a m p l i t u d e s c o u l d p o s s i b l y be found which would c o r r e c t l y a l t e r the B(M1) without m a k i n g s i g n i f i c a n t c h a n g e s in the e n e r g y . L i k e w i s e , a g r e a t e r c a n c e l l a t i o n by a f a c t o r of 2 c o u l d p o s s i b l y be a c h i e v e d w h i c h would s a t i s f y the 41Ar e x p e r i m e n t a l r e s u l t . In o r d e r to d e m o n s t r a t e t h a t t h i s s i m p l e s h e l l - m o d e l d e s c r i p t i o n of an f~3 c o n f i g u r a t i o n p l u s s m a l l a d m i x t u r e s is a p p l i c a b l e to t h e s e n u c l e i , it w i l l be n e c e s s a r y to s h o w that a c o m p l e t e fit to a l l the t r a n s i t i o n p r o b a b i l i t i e s a s w e l l a s e n e r g i e s can be a c h i e v e d with one s e t of a m p l i t u d e s . An a l t e r n a t e a p p r o a c h to the s u r p r i s i n g l y d i f f e r e n t e x p e r i m e n t a l M1 h i n d r a n c e s would be to a r g u e that l a r g e c a n c e l l a t i o n s a r e u n l i k e l y and that t h e ~ r e a t e r h i n d r a n c e f o r 4 1 A r i n d i c a t e s a p u r e r f l ° c o n f i g u r a t i o n . F o l l o w i n g t h i s i d e a , it i s i n t e r e s t i n g to c o n s i d e r the c o n t r i b u t i o n s due to e x c h a n g e t e r m s in the M1 o p e r a t o r . A l t h o u g h t h e u s u a l a d d i t i v e s i n g l e - p a r t i c l e M1 o p e r a t o r h a s zero matrix elements within a pure configuration, an e x c h a n g e m a t r i x e l e m e n t f r o m t w o - p a r t i c l e o p e r a t o r s i s not z e r o [13]. A s s u m i n g p u r e f ! 3 c o n f i g u r a t i o n s in the (~ ~ 5- ) t r a n s i t i o n of 241Ar, a c o m p a r i s o n of the e x c h a n g e m a t r i x e l e m e n t 5 I 7 3 and the experimentalB(MI)results i ! t ~ ; I f o l l o w i n g l i m i t , ,_~612<

--< 4.3 × 10 -3 n m 2.

40

LETTERS

9 January 1967

Of c o u r s e , if t h e r e a r e a d m i x t u r e s p r e s e n t w h o s e M1 c o n t r i b u t i o n c a n c e l with the e x c h a n g e t e r m s , t h e a b o v e l i m i t w o u l d not n e c e s s a r i l y be v a l i d . T h e hope a s e x p r e s s e d by De S h a l i t [13], i s that if a s u f f i c i e n t n u m b e r of M1 m a t r i x e l e m e n t s could be experimentally determined for a given configuration, it would then be possible to isolate the exchange terms in the M1 operator.

References 1. I . T a l m i , Phys. Rev. 107 (1957) 326. 2. J . D . McCullen, B . F . Bayman and L. Zamick, Phys. Rev. 134 (1964) B515. 3. Y. Shadmi and I . T a l m i , Phys. Rev. 129 (1963) 1286. 4. T.Engeland and E.Osnes, Phys. Letters 20 (1966) 424. 5. P . F e d e r m a n and I . T a l m i , Phys. Letters 22 (1966) 469. 6. C.K. Bockelman, C.M. Braams, C . P . Browne and W.W.Buechner, Phys. Rev. 107 (1957) 176. 7. E. Kashy, A.M. Hoogenboom and W. W. Buechner, Phys. Rev. 124 (1961) 1917. 8. A.De-Shalit and I . T a l m i , Nuclear shell theory (Academic P r e s s , Inc., New York, 1962) p. 409. 9. D . B . F o s s a n a n d A . R . P o l e t t i , Phys. Rev. (to be published). 10. N. Benczer-Koller, A. Schwarzschild and C.S.Wu, Phys. Rev. 115 (1959) 108; C. Chasman, K.W. Jones and R.A. Ristinen ( to be published). 11. J . P . A l l e n , A . J . H o w a r d , D . A . B r o m l e y , J . W . Olness and E.K. Warburton, Phys. Rev. (to be published). 12. T.Engeland, private communication. 13. A.De-Shalit, Nuclear structure and electromagnetic interactions, Scottish Universities Summer School, ed. N. MacDonald (Plenum P r e s s , 1965) p. 1.