Parity non conserving effects in 181Ta and 175Lu

Volume 35B, number 1

PARITY

PHYSICS LETTERS

NON

CONSERVING

26 April 1971

EFFECTS

IN

181Ta

AND

175Lu

B . D E S P L A N Q U E S and N. VINH MAU $ Institut de Physique Nucl~aire, Division de Physique Th$orique ~ , 91, Orsay, France Received 5 March 1971

The circular polarization of 482 keV transition in 181Ta and 396 keV transition in 175Lu has been calculated. Pairing effects and short range correlations have been considered. In the conventional weak interaction model the values of polarization are too small compared to the measured values.

A f t er the m e a s u r e m e n t of the c i r c u l a r p o l a r i zation of the 482 k e V - y t r a n s i t i o n in 181Ta by Lobashov et al. [1], s e v e r a l g r o u p s [2-6] have m e a s u r e d the s a m e t r a n s i t i o n and the 396 k e V t r a n s i t i o n in 175Lu. The r e s u l t s a r e s u m m a r i z e d in table 1. R e f s . [2-4] a g r e e with Lobashov but for e x a m p l e r e f . [5] and [6] r e p o r t a l a r g e r va lue for the p o l a r i z a t i o n . T h e o r e t i c a l a t t e m p t s [7-9] have been m a d e to c a l c u l a t e this effect in both nuclei. Although the f o r m of the r e s u l t s looks d i f f e r e n t , s i m i l a r n u m e r i c a l v a l u e s a r e obtained if we note 1) M c K e l l a r [7] u s e s an a v e r a g e d one p a r t i c l e p o t e n t i a l d e r i v e d by Michel [10] and Wahlborn [11] while o t h e r s c a l c u l a t e the p a r i t y a d m i x t u r e f r o m the two body i n t e r a c t i o n . F u r t h e r m o r e the sign of the a v e r a g e d p o t e n ti a l was i n c o r r e c t for the p - e x c h a n g e contribution to the p o t e n t i a l and the p o l a r i z a t i o n has to be a c c o r d i n g l y changed in r e f . [7]. At the State University of New York, Stony Brook. during part of this work; supported by A.E.C. contract AT (30-1)-4032 during this time. ~$ Laboratoire Associd au CNRS.

2) If c o m p a r e d with o t h e r s , the r e s u l t s of ref. [9] have to be modified, si n ce they c o r r e spond to a d i f f e r e n t choice of the e f f e c t i v e c h a r g e and the r e g u l a r t r a n s i t i o n amplitude. Once t h ese m o d i f i c a t i o n s a r e taken into account, the t h eo r e t i c a l p o l a r i z a t i o n s a r e given in table 2 (colu m n s A.B.C.) f o r 181Ta. In t h e s e c a l c u I a t i o n s , the N i l s s o n m o d el was a s s u m e d , the n o r m a l s t a t e s being d e s c r i b e d as p r o t o n single p a r t i c l e s t a t e s , the r e m a i n i n g p r o tons and n e u t r o n s filling by p a i r s the l o w e s t N i l s s o n s h e l l s . T h e s e s t a t e s w e r e mixed by the p a r i t y v i o l at i n g two body f o r c e with s t a t e s of opposite p a r i t y of the type a) b) and c) r e p r e sented in fig. 1 for 181Ta. In fact, s t a t e s like (1. b) do not c o n t r i b u t e to the p o l a r i z a t i o n , si n ce they give no i r r e g u l a r E 1 t r a n s i t i o n and s t a t e s like (1. c) will be mixed with the n o r m a l state only if the p a r i t y v i o l at i n g f o r c e allows an i n t e r action between p r o t o n s . In the conventional model, we have no such a d m i x t u r e and in m o d e l s with an e x t r a n e u t r a l c u r r e n t t h e i r a d m i x t u r e was found to be v e r y s m a l l [8]. One of the p u r p o s e s of our p r e s e n t work i s to

~s~t~ P~o~ core

, Io-1 ~/2+--e -~-

_

~states1 Fig. 1. Possible configurations of 7/2- and 5/2- states in 181Ta 28

PHYSICS

Volume 35B, number 1

LETTERS

26 April 1971

Table 1 C i r c u l a r polarization P × 106 m e a s u r e d in 181Ta and 175Lu transitions

[1]

[2]

5._+ /2 ~482 l T akeV; 7/2 +

-6± 1

-3.8±1.3

396keV _ + 9/2 ~ 7 / 2

40±10

62

-

_

[3] -4.1±1.3

[4]

[5]

-13±7

-32±8

[6] -21±11

±8

Table 2 Polarization of 482 keV transition in 181Ta calculated in the conventional model with an effective charge eef f = 0.6 e [7]

[8]

[9]

P r e s e n t work Nilsson model

P r e s e n t work : Nilsson + pairing ~ut short ~ short range c o r r . range c o r r .

A

B

C

D

E

PTr × 106

-5"

-6.8"

-8.4

-1.6

-0.26

Pp x 106

25 *

43.2 *

95.2

10.8

1.66

F ~ -0.26 ~

* These values involve some effects of s h o r t range c o r r e l a t i o n s which, in both calculations, s u p p r e s s tor ~ 2 and P n by ~ 10.15 % but values C,D and E do not involve such effects.

t a k e i n t o a c c o u n t t h e a d m i x t u r e of s t a t e s 1. d). T h e m e t h o d of c a l c u l a t i o n i s t h e s a m e a s d e s c r i b e d in r e f . [9]. We u s e the p a r i t y v i o l a t i n g f o r c e due to o n e p i o n and p m e s o n w e a k e x c h a n g e s [7,12,13] :

PNCv = VTr + Vp. In t h e c o n v e n t i o n a l C a b i b b o m o d e l :

4rr~/l m N

rl2

f is the p i o n - n u c l e o n weak coupling constant: f = 4.3 × 10 - 8 if t h e C a b i b b o a n g l e ~ i s t a k e n to be 0.22 exp(-mprl2)

Vp

=

-

4~:~2--~N

+ i(l+#v)

r 12

(al×a2)"

[

/)12,

exp(-mprl2)]f T~2 rl 2

0.17

Pp by a f a c -

h a s a l a r g e e f f e c t on t h e p o l a r i z a t i o n w h i c h i s greatly reduced. F u r t h e r m o r e , t h e e f f e c t s of t h e p a i r i n g f o r c e on the N i l s s o n s t a t e s w e r e c a l c u l a t e d . N e g l e c t i n g p a i r i n g b e t w e e n n e u t r o n s and p r o t o n s , t h e BCS equations were solved for N = 3,4,5 proton s t a t e s and N = 4 , 5 , 6 n e u t r o n s t a t e s . T h e s i n g l e particle energies are taken as Nilsson energies c o r r e s p o n d i n g to t h e e x p e r i m e n t a l d e f o r m a t i o n (5 = 0.22), e x c e p t t h o s e of p r o t o n s t a t e s n e a r the F e r m i l e v e l w h i c h a r e s h i f t e d to o b t a i n the k n o w n l e v e l s . T h e p a i r i n g s t r e n g t h i s a d j u s t e d to o b t a i n t h e gap A = 0.73 MeV. T h e n o r m a l s t a t e s , 5//2 + and 7 / 2 a r e d e s c r i b e d a s one q u a s i - p r o t o n s t a t e s and t h e i r a d m i x t u r e s with one and t h r e e q u a s i p r o t o n s t a t e s (5,/2 - and 7/12 - ) a r e c a l c u l a t e d . T h e c o r r e s p o n d i n g v a l u e s of PTT and are still s m a l l e r and g i v e n in t a b l e 2 ( c o l u m n E). In t a b l e 2, t h e s i g n of P~ c o r r e s p o n d s to p o s i t i v e f . In f a c t the s i g n o f f i s u n k n o w n and it i s c h o s e n p o s i t i v e to o b t a i n a g r e e m e n t with the e x p e r i m e n t a l s i g n of the p o l a r i z a t i o n . is

+

Pp

Pp

where T~2 = T (1) v(2) +T (1)~_ (2) -

4-

+

-

*

Pp

T h e c o n t r i b u t i o n s PTr and to t h e c i r c u l a r p o l a r i z a t i o n in the 482 k e V t r a n s i t i o n o f 181Ta ' due to Vu and w e r e c a l c u l a t e d taking into a c c o u n t t h e a d m i x t u r e of all s t a t e s r e p r e s e n t e d in fig. 1 w i t h odd p a r i t y p r o t o n s in N = 3 and 5 s h e l l s . T h e y a r e p r e s e n t e d in t a b l e 2 ( c o l u m n D)o T h e a d m i x t u r e of two p a r t i c l e - one h o l e s t a t e s

Table 3 Polarization of 396 keV transition in 175Lu calculated in the conventional model with eeff = 0.6 e - E is the sign of the regular E 1 transition p r e s e n t work p r e s e n t work : Nilsson+pairing Nilsson model without s h o r t with s h o r t range c o r r . range c o r r .

Vp

P~. xLO 6

2.7E

2.4E

~

2.4E

Pp ×106

-35.5~

-30.6~

~

-3E

29

Volume 35B. n u m b e r 1

PHYSICS

p o s i t i v e , a n d t h u s h a s t h e w r o n g s i g n , if we a s s u m e G > 0 a s g i v e n by t h e i n t e r m e d i a t e b o s o n e x c h a n g e m o d e l of w e a k i n t e r a c t i o n s [8]. A l t h o u g h P n a n d P p a r e m u c h s u p p r e s s e d by a m o r e a c c u r a t e d e s c r i p t i o n of n u c l e a r s t a t e s , Pp is always much larger than Pu in the conventional model and then gives the wrong sign for t h e p o l a r i z a t i o n . A c t u a l l y , it h a s b e e n s h o w n i n r e f . [9] t h a t , w h e n i n d e p e n d e n t p a r t i c l e w a v e f u n c t i o n s a r e u s e d , t h e Vn - m a t r i x e l e m e n t s a r e s u p p r e s s e d by a n o v e r a l l f a c t o r of a b o u t 8 if t h e p i o n m a s s i s r e p l a c e d by t h e p - m a s s . T h u s , if we take into account the difference between the s t r e n g t h s of Vu a n d Vp, Pp w i l l a l w a y s b e in t h e r a n g e of 5 P ~ - 6 P ~ w h e n o n e a s s u m e s a n u c l e a r m o d e l b a s e d on i n d e p e n d e n t p a r t i c l e w a v e f u n c tions. However, such models omit short range c o r r e l a t i o n s b e t w e e n n u c l e o n s . B e c a u s e of t h e v e r y s h o r t r a n g e of t h e p e x c h a n g e p o t e n t i a l , such correlations will affect greatly the calcul a t e d v a l u e of P p w h i l e P n i s c e r t a i n l y l e s s s e n s i t i v e [8,9]. T h e s e e f f e c t s h a v e b e e n r o u g h l y e s t i m a t e d [7,8] to s u p p r e s s Pp by a f a c t o r two but this was an underestimate. Hadjimichael and one of u s (NVM) h a v e r e c a l c u l a t e d * t h e r a d i a l i n t e grals with approximated correlated two-nucleon w a v e f u n c t i o n s a n d f o u n d t h a t P p c o u l d be s u p p r e s s e d by a f a c t o r w h i c h c o u l d b e a s l a r g e a s 9 - 1 0 . In t h e p r o c e s s n+p ~ d+y, t h e p o l a r i z a t i o n , g i v e n o n l y by t h e p - e x c h a n g e f o r c e f o r s l o w n e u t r o n s i s s i m i l a r l y s u p p r e s s e d [14]. T h e s u m of a l l t h e e f f e c t s c o n s i d e r e d a b o v e g i v e s r i s e in t h e c o n v e n t i o n a l m o d e l , to a t h e o retical polarization much smaller than experimental values. Furthermore, we h a v e t a k e n a n e f f e c t i v e c h a r g e e e f f = e N/A ~ 0.6 e , but t h e real effective charge for E 1 transition is cert a i n l y m u c h s m a l l e r [19] and w i l l e n h a n c e t h i s discrepancy. We h a v e p e r f o r m e d t h e s a m e c a l c u l a t i o n s f o r t h e 396 k e V t r a n s i t i o n ( 9 / 2 - ~ 7 / 2 +) i n 175Lu. T h e r e s u l t s a r e p r e s e n t e d in t a b l e 3 a n d s h o w t h e same behaviour and the same discrepancy bet w e e n c a l c u l a t i o n s a n d m e a s u ~ ' e m e n t s . In t h i s c a s e , we h a v e no e x p e r i m e n t a l i n f o r m a t i o n on t h e s i g n of t h e r e g u l a r E 1 t r a n s i t i o n a m p l i t u d e . If we h a v e c o n f i d e n c e i n b o t h m e a s u r e m e n t s * This work has not been published.

30

LETTERS

26 April 1971

and present calculations, the disagreement w h i c h o c c u r s a l s o i n t h e i n t e r p r e t a t i o n of t h e p r o c e s s n + p ~ d + r [ 1 5 , 1 6 ] , c o u l d p o s s i b l y be r e m o v e d by c o n s i d e r i n g : 1) T h e 2u e x c h a n g e c o n t r i b u t i o n to P N C V w h i c h s e e m s to be i m p o r t a n t [17] a n d w h i c h , b e c a u s e of i t s r a t h e r l o n g r a n g e , c o u l d d o m i n a t e the polarization 2) a l a r g e e n h a n c e m e n t of t h e p i o n - n u c l e o n w e a k c o u p l i n g c o n s t a n t . Such a n e n h a n c e m e n t i s p r e d i c t e d by m o d e l s c o n t a i n i n g a n e x t r a n e u t r a l c u r r e n t [12,18]. We a r e v e r y g r a t e f u l to P r o f s . G . E . B r o w n , A. K. K e r m a n a n d A. J a c k s o n f o r h e l p f u l a n d s t i m . ulating discussions.

References [1] v . M. Lobashov, V. A. Nazareno, L. F. Saenko, L. M. Smotritskii and G. I. Kharevich, J E T P L e t t e r s 3 (1966) 47, 173, 5 (1967) 59. [2] F. Boehm and E. Vanderleeden, Phys. L e t t e r s 30B (1969) 467. [3] P. Bock and B. J e n s c h k e , Nucl. Phys. A 160 (1971) 550. [4] H. Diehl, G. Hopfenstitz, E. Kankeleit and E. Kuphal, Proc. of the 3rd Int. Conf. on High En. Phys. and Nucl. Structure, New York (1969}. [5] E. Bodenstedt, L. Ley, H. O. Schlenz and U. Wehman, Phys. L e t t e r s 29B (1969) 165. [6] P. de Saintignon, J . J . Lucas, J. B. Viano, M. Chabre and P. Depommier, NueI. Phys. A 160 (1971) 53. [7] B. H. F. McKellar, Phys. Rev. L e t t e r s 20 (1968) 1542. [8] B. Eman and D. Tadic, P r e p r i n t Zagreb 1970. [9] N. Vinh Man and A. M. Bruneau, Phys. L e t t e r s 29B (1969) 408. [10] F. C. Michel, Phys. Rev. 133 (1964) 329. [11] S. Wahlborn, Phys. Rev. 138B (1965) 530. [12] E. Fishbach, D. Tadic and K. T r a b e r t , Phys. Rev. 186 (1969) 1688. [13] E. M. Henley, Ann. Rev. of Nuel. Sc. 19 (1969) 367 [14] E. Hadjimichael, private communication. [15] E. Hadjimichael, P r e p r i n t Stony Brook (1970). [16] V. M. Lobashov, A. E. Egorov, D.M. K a m i n k e r , Vo A. Nazarenko, L. F. Saenko, L. M. Smotritskii, G. I. Kharkevieh and V. A. Knyaz'kov, J E T P L e t t e r s 11 (1970) 78. [17] D. Pignon, p r i v a t e communication. [18] E. F i s h b a e h and K. T r a b e r t , Phys. Rev. 174 (1968) 1843 and e a r l i e r r e f e r e n c e s quoted in this paper. [19] This was pointed out to us by G. E. Brown.