Parity impurities in 19F

Volume 23, number 1O

PHYSICS LETTERS

l e a s t two and in g e n e r a l t h r e e e x p e r i m e n t a l p a r a m e t e r s m u s t be e s t a b l i s h e d , a single d i r e c tional c o r r e l a t i o n m e a s u r e m e n t cannot be u s e d to set a l i m i t on any of th e m , as has been done by Lawson and Segal [4] in t h e i r c o n s i d e r a t i o n of 180Hf m. If t h e r e a r e only two p a r a m e t e r s , a s in the c a s e c o n s i d e r e d above, a matching of t h r e e d i m e n s i o n a l plots (Ak(n) v e r s u s q and 5, k = 2,4) i s p o s s i b l e a s a n a t u r a l extension of the usual method of d e t e r m i n i n g mixing r a t i o s . T h i s would p r o v i d e l i m i t s on the allowable range of q and 5, and can be u s e d in conjunction with other m e a s u r e m e n t s to e s t a b l i s h the magnitude of p a r i t y mixing effects.

5 December 1966

The a u t h o r s w i s h e s to thank P r o f e s s o r E . Bodenstedt and the m e m b e r s of his i n s t i t u t e f o r t h e i r hospitality, and for s e v e r a l s t i m u l a t i n g discussions. 1. F.C.Michel, Phys. Rev. 133 (1964) B329; S.Wahlborn, Phys. Rev. 138 (1965) B530. 2. H. Blumberg, K.H. Speidel, H. Sehlenz, R. L. Rasera and E. Bodenstedt~ Physics Letters 22 (1966) 328, and references cited therein. 3. H. Frauenfelder and R.M.Steffen, in: Alphs-, betaand gamma-ray spectroscopy, ed. K.Siegbahn (North-Holland Publ. Co., Amsterdam, 1965) Ch. XIX. A. 4. R.D. Lawson and R.E.Segel, Phys. Rev. Letters

16 (1966) 1006.

PARITY

IMPURITIES

IN

19F

E. MAQUEDA*

School of Mathematical and Physical Sciences, The University of Sussex, Brighton, England Received 28 October 1966

The effect of nuclear parity impurities in the 110 keV transition in 19F is investigated.

The t h e o r e t i c a l i n t e r p r e t a t i o n of e x p e r i m e n t s a i m e d at finding p a r i t y i m p u r i t i e s in n u c l e a r s t a t e s i s in g e n e r a l i m p a i r e d by the c o m p l e x s t r u c t u r e of the n u c l e i involved. T h i s has been the c a s e in r e c e n t studies of g a m m a t r a n s i t i o n s in 181Ta, 175Lu and l l 4 C d . In this note we c o n s i d e r the ½- ~ ½+ 110 keV y - t r a n s i t i o n in 19F, which i s m o r e a c c e s s i b l e to t h e o r e t i c a l i n v e s t i g a t i o n b e c a u s e of the r e l a t i v e s i m p l i c i t y of the r e l e v a n t n u c l e a r s t a t e s . The t r a n s i t i o n a l s o s a t i s f i e s the conditions f o r an e n h a n c e m e n t of the p a r i t y i m p u r i t y effect since the r e g u l a r (parity allowed) m u l ti p o le t r a n s i t i o n is hinde re d, the i r r e g u l a r t r a n s i t i o n is c o m p a r a tively l a r g e and the p e r t i n e n t e n e r g y d e n o m i n a t o r is small. In the a b s e n c e of a p a r i t y non c o n s e r v i n g t e r m in the n u c l e a r potential the initial and final s t a t e s of this e l e c t r i c dipole (El) t r a n s i t i o n have jTr = ½- and j~r = ½+ r e s p e c t i v e l y . As t h e r e is no oth e r J = ½ state in the low e n e r g y s p e c t r u m , the

* Fellow of the Consejo Nacional de Investigaciones Cient1"ficas y T6cnicas of Argentina.

only i m p o r t a n t p a r i t y m i x i n g o c c u r s between those two s t a t e s . Th e p e r t u r b e d i n i t i a l and final s t a t e s can then be w r i t t e n a s

#i = ~(½-) + (~E)-I <½-}Q~]½+) ~(½+)

(I)

~f

(2)

=

~(½+)- (~)-i<½+ - ~} I~, - >~(½-)

respectively, where AE = 0.110 MeV and QYstands for the parity non conserving potential. The reduced matrix element mI for the irregular M1 transition will be

ml =<~f I l~(Ml)l l'i> =

(3)

= (L~E)-I{(½+i~)7~(MI)I 1½+)-(½- I~ M I ) 1{½->}<½+h~}- >

or in terms of static magnetic moments mI = (3/4f~) (AE)-I{~(½+) ~(½-)}<~ i+ l~l -

½->. (4)

The parity non conserving effects due to the interference between irregular and regular parts of the transition are given by The ~-ray-e3rcxYi~r polarization P=~, but if a forward-backward asymmetry in the angular distribution is to be detected, the asymmetry factor ot =~B1, with B 1 equal to the degree of polarization of the initial state. 571

Volume 23, number 10

2rnl 3 1 {p,(½+)r/ = e--i- = f ~ - ~ el

PHYSICS LETTERS

..(½-) } <~÷ - ~l~

½->.

(5)

The magnitude of the r e d u c e d m a t r i x e l e m e n t e 1 f o r the r e g u l a r t r a n s i t i o n can be obtained f r o m the m e a s u r e d h a l f - l i f e of the 110 keV l e v e l (T½ = = 1.0 nsec). The 19F ground state m a g n e t i c m o m e n t i s known (/I(½ +) = 2.6287 n.m. ) and the m a g net i c m o m e n t of the 110 keV e x c i t e d state m u s t be s i m i l a r to the 15N ground state m a g n e t i c m o ment (/~(½-) ~ -0.2831 n.m.). Substituting t h e s e e x p e r i m e n t a l v a l u e s into (5) one obtains

171 = 261(½+ Icl21½-> (MeV) -1

(6)

and only the matrix element of the parity non conserving potential is left to be theoretically estimated. Conversely, a measurement of ~? would determine the magnitude of a parity non conserving effective interaction. To predict the sign of 7/,

EXACT

5December 1966

the sign of the h i n d e r e d E l - t r a n s i t i o n r e d u c e d m a t r i x e l e m e n t m u s t be d e t e r m i n e d . By u si n g a single p a r t i c l e p a r i t y non c o n s e r v ing p o t en t i al [1] ~ = F(~/MR o) a ' p ) the f o l l o w ing e s t i m a t e can be obtained

I~1 = 1350 F = 4.3x

10-4

w h e r e a v al u e of F = 3.2 × 10 -7 has been used. The magnitude of the above p r e d i c t i o n c o m p a r e s f a v o u r a b l e with the v a l u e s p r e d i c t e d and m e a s u r e d in the h e a v i e r nuclei a l r e a d y mentioned, D e t a i l e d c a l c u l a t i o n s with a m o r e r e a l i s t i c , two-body p a r i t y non c o n s e r v i n g potential a r e in preparation.

References 1. F.C.Michel, Phys. Rev. 133 (1964) B 329.

DETERMINATION OF GAMOW-TELLER MATRIX FOR SUPERMULTIPLET STATES

ELEMENTS

M. KUSHNER*$ and J . QUINTANILLA*$

Instituto de F$'sica, Universidad de M~xico Received 1 November 1966

The allowed Gamow-Teller beta decay matrix elements for supermultiplet states are derived exactly using the representations of the generators of the U4 group. The transition between the ground states of 18F and 180 is evaluated explicitly.

In r e c e n t p u b l i c a t i o n s [1,2] the s u p e r m u l t i p l e t c l a s s i f i c a t i o n of s t a t e s [3] has c o m e back into f a v o r as an i n t e r m e d i a t e step in the SU3 s c h e m e . In this c l a s s i f i c a t i o n the n p a r t i c l e s t a t e s a r e denoted by the ket [2,3]

]aL, {v lV2V3V4}~ST, JM )

(1)

w h e r e {v lV 2v3v4} i s the p a r t i t i o n of n c h a r a c t e r izing the i r r e d u c i b l e r e p r e s e n t a t i o n of the U 4 group a s s o c i a t e d with the four single p a r t i c l e spin i s o s p i n s t a t e s , L, J,S, T a r e r e s p e c t i v e l y the o r b i t a l and total a n g u l a r m o m e n t u m , spin and i s o s p i n , a,/3 a r e additional quantum n u m b e r s [2,3]. * Fellow of the Comision Nactional de Energia Nuclear. $ Fellow of the Instituto Nacional de la Investigaci6n Cmntlfma. 572

We a r e i n t e r e s t e d in d e t e r m i n i n g the m a t r i x e l e m e n t s of al l o w ed beta o p e r a t o r s with r e s p e c t to the s t a t e s (1). T h i s is t r i v i a l f o r allowed F e r m i t r a n s i t i o n s si n ce the one body o p e r a t o r n

tt~),'

q = 4-1

i=1 w h er e t=(i) is the q component of the i s o s p i n of p a r t i c l e q i , can be e x p r e s s e d in t e r m s of the total i s o t o p i c spin which i s an i n t e g r a l of motion of (1). F o r the G a m o w - T e l l e r al l o w ed t r a n s i t i o n s the situation i s not so s i m p l e . The one body o p e r a t o r i s given by [4],