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The lifetime of 18Ne and the second class current problem
Volume 32B, number 3
THE
LIFETIME
PHYSICS
OF
18Ne
AND
THE
LETTERS
SECOND
22 June 1970
CLASS
CURRENT
PROBLEM*
D. E. ALBURGER Brookhaven National Laboratory, Upton, New York, USA and D. H. WILKINSON
Nuclear Physics Laboratory, Oxford, UK Received 4 May 1970
The half-life of 18Ne is found to be 1.67 + 0.02 sec. T h e f t - v a l u e for the 18Ne transition to the ground state of 18F divided by that for the m i r r o r transition between 180 and 18F is 0.992 ± 0.015. This r e m o v e s a disturbing anomaly in a survey o f f t - v a l u e s for m i r r o r beta-decay directed towards testing for the p o s sible existence of second class c u r r e n t s .
A t t e n t i o n h a s r e c e n t l y b e e n d i r e c t e d [1] t o t h e h i g h i n t e r e s t t h a t r e s i d e s in t h e c o m p a r i s o n of mirror beta-decays. The naive expectation that mirror beta-decays should have identicalft-valu e s i s r e l i e v e d by a h o s t of f a c t o r s e s s e n t i a l l y t r i v i a l in n a t u r e if d i f f i c u l t of r e l i a b l e e s t i m a t i o n such as electromagnetic, second forbidden, isos p i n m i x i n g a n d b i n d i n g e n e r g y e f f e c t s but a l s o by o n e f u n d a m e n t a l f a c t o r n a m e l y t h e p o s s i b l e e x i s t e n c e o f s e c o n d c l a s s c u r r e n t s [2], s p e c i f i c ally the induced t e n s o r coupling gIT; gIT c o m b i n e s with gA with d i f f e r e n t sign for positon and n e g a t o n e m i s s i o n a n d so l e a d s to a d i f f e r e n c e in f t - v a l u e s f o r t h e two t h a t m a y b e w r i t t e n :
5 = ~ft)+ 1 ~ 4 (ft)- 3 g v / g A gIT(W+ +Wo) Should b o t h b o d i e s b e p o s i t o n e m i t t e r s W o+ + w o i s r e p l a c e d by t h e d i f f e r e n c e in t h e i r e n e r g y r e lease. T h e r e c e n t s u r v e y [1] c o m p r i s e d e l e v e n A - v a l ues and r e v e a l e d a significant positive t r e n d for 6, c o n s i s t e n t w i t h a l i n e a r d e p e n d e n c e on W + + W o. E v e n if s u c h a t r e n d w e r e w i t h o u t e x c e p t i o n t h e r e a l i t y of s e c o n d c l a s s c u r r e n t s would be far f r o m e s t a b l i s h e d until the " t r i v i a l " f a c t o r s w e r e b e t t e r u n d e r s t o o d . But t h e s u r v e y c o n t a i n e d two m a r k e d e x c e p t i o n s to t h e g e n e r a l t r e n d n a m e l y A = 20 a n d A = 18 f o r b o t h of w h i c h * R e s e a r c h at Brookhaven National Laboratory c a r r i e d out under the auspices of the U.S. Atomic Energy Commission. 190
5 was significantly negative. The case of A = 20 may possibly be resolved by later measurements [3] but A = 18 is particularly disturbing since all the states involved are of low excitation, the binding energies are quite high and the energy release is small (W++Wo = 5.5) so that the 'trivial' effects cannot be large. The survey value for A = 18, 5 = -0.12 +0.04, would not seem possible to comprehend. It is particularly important that 5 should be seen to behave properly close to the origin if its departures for large values of + + Wo are ever to be interpreted with confiWo dence. We have therefore undertaken a re-examination. The bodies in question are both positon emitters: the mirror decays are that of 18Ne to the ground state of 18F and the reverse of that of 18F to the ground state of 180. The case of 18F decay appears to be straightforward: the halflife is accurately given as 109.74 + 0.21 rain [4] and 109.87 + 0.12 rain [5], concordant values with a mean of 109.84 ± 0.10 min; the positon kinetic energy end point, derived from the standard masses [6] is 632.9 ± 0.7 keV; only the ground state of 180 is energetically accessible and the measured K-capture is 3.0 ± 0.2%~7]. These data lead tort = (1.230± 0.006) x i0 ° s (for the reverse 180 ~ 18F transition); here we have used, as elsewhere in this note, the standard definition of f, evaluating the point-charge Coulomb wavefunctions at a radius of 1.2A I/3 fro, and applying the usual "modified WKB" screening recipe [8].
Volume 32B, number 3
PHYSICS
T h e c a s e of 18Ne d e c a y is m o r e c o m p l i c a t e d . S e v e r a l s t a t e s of 18F a r e e n e r g e t i c a l l y a c c e s s i b l e to the p o s i t o n d e c a y of w h i c h the g r o u n d s t a t e k i n e t i c e n e r g y r e l e a s e is [6] 3424.9 =~4.7 keV. H o w e v e r , the g r o u n d s t a t e d e c a y d o m i n a t e s and so the 5 - a n o m a l y , if it is to be r e s o l v e d , m u s t i n v o l v e an e r r o r in the v a l u e of t h e h a l f - l i f e of 1.46 + 0.06 s u s e d in the s u r v e y [1]. T h i s l i f e t i m e d e r i v e d f r o m the two m o s t r e c e n t , c o n c o r d ant, v a l u e s of 1.46 + 0.07 s [9] and 1.47 + 0.10 s [10]. A p a r t f r o m the g r o u n d s t a t e d e c a y , t r a n s i t i o n s t a k e p l a c e to the J ~ = 1 + s t a t e at 1701 k e V (0.17+ 0.05% [11]) and to the jTr = 0 + T = 1 a n a l o g u e at 1042.2 ± 0.5 keV [12]. T h e f o r m e r t r a n s i t i o n is v e r y w e a k w h i l e t h e s t r e n g t h of the l a t t e r is not g r e a t and m a y be a c c u r a t e l y c o m p u t e d u s i n g CVC so the e x p e r i m e n t a l p r o b l e m r e d u c e s to t h a t of the l i f e t i m e m e a s u r e m e n t w h i c h we h a v e t h e r e fore tackled. A t h i c k t a r g e t of P b O 2 w a s b o m b a r d e d w i t h 5.5 MeV 3He p a r t i c l e s f r o m t h e B r o o k h a v e n R e s e a r c h Van de G r a a f f . T h e b e a m w a s m e c h a n i c a l l y i n t e r r u p t e d on a c y c l e of 4 s on, 102 s off and t h e t a r g e t e x a m i n e d f o r e l e c t r o n a c t i v i t y t h r o u g h o u t t h e " o f f " p e r i o d with a p l a s t i c s c i n t i l l a t o r b i a s s e d a b o v e 2 MeV. T h e output of the s c i n t i l l a t o r w a s a n a l y z e d by a m u l t i - s c a l e r s t e p ped at 0.2 s by a q u a r t z - c r y s t a l c l o c k . U n d e r t h e s e c o n d i t i o n s the only b o d i e s m a d e f r o m o x y gen o r c a r b o n i s o t o p e s to w h o s e d e c a y we a r e s e n s i t i v e a r e 140, I 8 N e , 1 9 N e and 2 0 F . To e x t r a c t t h e d e s i r e d h a l f - l i f e of 18Ne the c o m p o s i t e d e c a y c u r v e w a s a n a l y z e d with a c o m p u t e r p r o g r a m * c o n t a i n i n g the known h a l f - l i v e s of 140, I 9 N e [13] and 2 0 F [ 3 ] plus a c o n s t a n t b a c k g r o u n d and t h e unknown l g N e . We m a d e t h r e e e x t e n d e d r u n s w h i c h y i e l d e d 18Ne h a l f - l i v e s of 1.701 + 0.032, 1.650 + 0 . 0 3 3 a n d 1 . 6 5 8 + 0.025 s, r e s p e c t i v e l y . As m a y h a v e b e e n a n t i c i p a t e d , the 140 and 19Ne a c t i v i t i e s w e r e n e g l i g i b l e ; the i n i t i a l a c t i v i t y of 20F was a few p e r c e n t of that of 18Ne. T h e X2 f i t s w e r e e n t i r e l y a c c e p t a b l e . A r u n at a h i g h e r b i a s r e v e a l e d an i n c r e a s e d p r o p o r t i o n of 20F a s e x p e c t e d f r o m i t s h i g h e r e n d - p o i n t ~ n e r g y . We quote t l / 2 = 1.67 + 0.02 s. W e h a v e l e a r n t f r o m our c o l l e a g u e s in S t r a s b o u r g [11] that t h e y had e a r l i e r , f o l l o w i n g K a v a n a g h ' s r e m a r k i n g upon t h e s a m e a n o m a l y [14], r e m e a s u r e d the 18Ne h a l f - l i f e , finding 1.69 ± 0.04 s. T h i s v a l u e i s e n t i r e l y c o n c o r d a n t w i t h o u r p r e s e n t m e a s u r e m e n t and we w e i g h t it with o u r s in the s u b s e q u e n t a n a l y s i s . We c o m p u t e the l i f e t i m e f o r t h e s u p e r a l l o w e d F e r m i t r a n s i t i o n of 18Ne to i t s a n a l o g u e in 18F * We are indebted to Mr. B. E. F. Macefield for help with this analysis.
LETTERS
22 June 1970
u s i n g f t = 3060 + 20 s, the e r r o r c o v e r i n g the e x p e r i m e n t a l s p r e a d of the w e l l - s t u d i e d t r a n s i t i o n s of t h i s CVC c l a s s [e.g. 15]. (The w e a k n e s s of the b r a n c h d o e s not w a r r a n t a m o r e r e f i n e d t r e a t m e n t . ) W e f i n d t l / 2 = 2 2 . 6 8 + 0.25 s and so, c o r r e c t i n g a l s o f o r t h e v e r y w e a k t r a n s i t i o n to the 1.701 keV s t a t e , a p a r t i a l h a l f - l i f e f o r t h e g r o u n d s t a t e t r a n s i t i o n of 1.811 + 0.022 s to w h i c h c o r r e s p o n d s f t = (1.226+0.017) x 103s. (We m a y n o t e en p a s s a n t that t h e s e r e s u l t s i m p l y a g r o u n d s t a t e b r a n c h of 92.6 + 0.1% with w h i c h the d i r e c t e x p e r i m e n t a l f i g u r e of 92.4 * 1.7% [9,10] is c o n cordant. ) T h e a c c u r a c y of the m e a s u r e m e n t s w a r r a n t s the a p p l i c a t i o n , b e f o r e t h e i r i n t e r c o m p a r i s o n , of r a d i a t i v e c o r r e c t i o n s (but not of s e c o n d - f o r b i d d e n e f f e c t s ) . In the i n t e r c o m p a r i s o n of m i r r o r t r a n s i t i o n s the " i n n e r ", m o d e l d e p e n d e n t , r a d i a t i v e c o r r e c t i o n s , w h i c h m e r e l y r e n o r m a l i z e the c o u p l i n g c o n s t a n t s , f a l l away and we a r e l e f t w i t h only the " o u t e r " , m o d e l i n d e p e n d e n t , c o r r e c t i o n s [16]; t h e s e g i v e a s p e e d i n g up of the t r a n s i t i o n s by 1.57% f o r 18F and 1.10% f o r 18Ne. With t h i s f i n a l c o r r e c t i o n we find 5 -- -0.008 + 0.015. T h i s v a l u e of 5 we m u s t c o m p a r e with 5 = 0 f o r g I T = 0 and with 5 ~ 0.01 f o r g I T ~ + 2 x 1 0 - 3 ; t h e l a t t e r c o r r e s p o n d s to the " u n c o r r e c t e d " i n t e r p r e t a t i o n of t h e g e n e r a l t r e n d of 5 w i t h W~ + W ~ r e v e a l e d by the s u r v e y [1]. T h e A = 18 a n o m a l y is r e m o v e d and the m i r r o r transition problem receives a sure anchor near the o r i g i n . It would be d e s i r a b l e to i m p r o v e the a c c u r a c y of the o t h e r a n c h o r point, A = 30, w h i c h has an e v e n l o w e r v a l u e of W~o + W ~ n a m e l y 3.7; i t s s u r v e y v a l u e , 5 = 0.02 + 0.05, s h o w s no a n o m a l y and i t s i m p r o v e m e n t is m o r e d i f f i c u l t than f o r A = 18 s i n c e the g r o u n d s t a t e b r a n c h d o e s not d o m i n a t e .
References [1] D. H. Wilkinson, Phys. Letters 31B (1970) 447. [2] S. Weinberg, Phys. Rev. 112 (1958) 1375; [3] [4]
[5] [6] [7] [8] [9] [i0]
J. N. Huffaker and E. Greuling, Phys. Rev. 132 (1963) 738. D. H. Wilkinson and D. E. Alburger, to be published. J. D. Mahony and S. S. Markowitz, University of California Radiation Laboratory report, UCRL10512. T.G. Ebrey and P.R. Gray, Nucl. Phys. 61 (1965) 479. J.H.E.Mattauch, W. Thiele and A.H. Wapstra, Nucl. Phys. 67 (1965) I. R.W.P. Drever, A. Moljk and J. Scobie~ Phil. Mag. 1 (1956) 942. L. Durand Phys. Rev. 135 (1964) B310. J. W. Butler and K. L. Dunning, Phys. Rev. 121 (1961) 1782. G. Frick et al., Phys. Rev. 132 (1963) 2169.
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Volume 32B, n u m b e r 3
PHYSICS
[11] E. A s l a n i d e s , F. Jundt and A. Galtmann, private communication. [12] C. C h a s m a n , K.W. J o n e s . R . A . Ristinen and E . K . Warburton, Phys. Rev. 137 (1965) B1445; E . K . Warburton, J . W . O l n e s s and A. R. Potetti, Phys. Rev. 155 (1967) 1164; A. E. Blaugrund, D.H. Youngbtood, G. C. M o r r i s o n and R . E . S e g e l , Phys. Rev. 158 {1967) 893; S. Gorodetzky, E. Astanides, A. G a l t m a n n and G.
192
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22 June 1970
Frick, Nuct. Phys. A109 (1968) 417. [13] F. Ajzenberg-Selove, Nuc[. P h y s . , to be published. [14] R.W. Kavanagh, Nucl. P h y s . A129 (1969) 172. [15] R. J. B[in-Stoyle, Ch.4 of Isospin in l~uclear P h y s ics ed. D. H. Wilkinson (North-Holland, A m s t e r d a m 1969). [16] A. Sirlin, Phys. Rev. 164 (1967) 1767; D. H. Wilkinson and B. E. F. Macefietd, to be published.
THE
LIFETIME
PHYSICS
OF
18Ne
AND
THE
LETTERS
SECOND
22 June 1970
CLASS
CURRENT
PROBLEM*
D. E. ALBURGER Brookhaven National Laboratory, Upton, New York, USA and D. H. WILKINSON
Nuclear Physics Laboratory, Oxford, UK Received 4 May 1970
The half-life of 18Ne is found to be 1.67 + 0.02 sec. T h e f t - v a l u e for the 18Ne transition to the ground state of 18F divided by that for the m i r r o r transition between 180 and 18F is 0.992 ± 0.015. This r e m o v e s a disturbing anomaly in a survey o f f t - v a l u e s for m i r r o r beta-decay directed towards testing for the p o s sible existence of second class c u r r e n t s .
A t t e n t i o n h a s r e c e n t l y b e e n d i r e c t e d [1] t o t h e h i g h i n t e r e s t t h a t r e s i d e s in t h e c o m p a r i s o n of mirror beta-decays. The naive expectation that mirror beta-decays should have identicalft-valu e s i s r e l i e v e d by a h o s t of f a c t o r s e s s e n t i a l l y t r i v i a l in n a t u r e if d i f f i c u l t of r e l i a b l e e s t i m a t i o n such as electromagnetic, second forbidden, isos p i n m i x i n g a n d b i n d i n g e n e r g y e f f e c t s but a l s o by o n e f u n d a m e n t a l f a c t o r n a m e l y t h e p o s s i b l e e x i s t e n c e o f s e c o n d c l a s s c u r r e n t s [2], s p e c i f i c ally the induced t e n s o r coupling gIT; gIT c o m b i n e s with gA with d i f f e r e n t sign for positon and n e g a t o n e m i s s i o n a n d so l e a d s to a d i f f e r e n c e in f t - v a l u e s f o r t h e two t h a t m a y b e w r i t t e n :
5 = ~ft)+ 1 ~ 4 (ft)- 3 g v / g A gIT(W+ +Wo) Should b o t h b o d i e s b e p o s i t o n e m i t t e r s W o+ + w o i s r e p l a c e d by t h e d i f f e r e n c e in t h e i r e n e r g y r e lease. T h e r e c e n t s u r v e y [1] c o m p r i s e d e l e v e n A - v a l ues and r e v e a l e d a significant positive t r e n d for 6, c o n s i s t e n t w i t h a l i n e a r d e p e n d e n c e on W + + W o. E v e n if s u c h a t r e n d w e r e w i t h o u t e x c e p t i o n t h e r e a l i t y of s e c o n d c l a s s c u r r e n t s would be far f r o m e s t a b l i s h e d until the " t r i v i a l " f a c t o r s w e r e b e t t e r u n d e r s t o o d . But t h e s u r v e y c o n t a i n e d two m a r k e d e x c e p t i o n s to t h e g e n e r a l t r e n d n a m e l y A = 20 a n d A = 18 f o r b o t h of w h i c h * R e s e a r c h at Brookhaven National Laboratory c a r r i e d out under the auspices of the U.S. Atomic Energy Commission. 190
5 was significantly negative. The case of A = 20 may possibly be resolved by later measurements [3] but A = 18 is particularly disturbing since all the states involved are of low excitation, the binding energies are quite high and the energy release is small (W++Wo = 5.5) so that the 'trivial' effects cannot be large. The survey value for A = 18, 5 = -0.12 +0.04, would not seem possible to comprehend. It is particularly important that 5 should be seen to behave properly close to the origin if its departures for large values of + + Wo are ever to be interpreted with confiWo dence. We have therefore undertaken a re-examination. The bodies in question are both positon emitters: the mirror decays are that of 18Ne to the ground state of 18F and the reverse of that of 18F to the ground state of 180. The case of 18F decay appears to be straightforward: the halflife is accurately given as 109.74 + 0.21 rain [4] and 109.87 + 0.12 rain [5], concordant values with a mean of 109.84 ± 0.10 min; the positon kinetic energy end point, derived from the standard masses [6] is 632.9 ± 0.7 keV; only the ground state of 180 is energetically accessible and the measured K-capture is 3.0 ± 0.2%~7]. These data lead tort = (1.230± 0.006) x i0 ° s (for the reverse 180 ~ 18F transition); here we have used, as elsewhere in this note, the standard definition of f, evaluating the point-charge Coulomb wavefunctions at a radius of 1.2A I/3 fro, and applying the usual "modified WKB" screening recipe [8].
Volume 32B, number 3
PHYSICS
T h e c a s e of 18Ne d e c a y is m o r e c o m p l i c a t e d . S e v e r a l s t a t e s of 18F a r e e n e r g e t i c a l l y a c c e s s i b l e to the p o s i t o n d e c a y of w h i c h the g r o u n d s t a t e k i n e t i c e n e r g y r e l e a s e is [6] 3424.9 =~4.7 keV. H o w e v e r , the g r o u n d s t a t e d e c a y d o m i n a t e s and so the 5 - a n o m a l y , if it is to be r e s o l v e d , m u s t i n v o l v e an e r r o r in the v a l u e of t h e h a l f - l i f e of 1.46 + 0.06 s u s e d in the s u r v e y [1]. T h i s l i f e t i m e d e r i v e d f r o m the two m o s t r e c e n t , c o n c o r d ant, v a l u e s of 1.46 + 0.07 s [9] and 1.47 + 0.10 s [10]. A p a r t f r o m the g r o u n d s t a t e d e c a y , t r a n s i t i o n s t a k e p l a c e to the J ~ = 1 + s t a t e at 1701 k e V (0.17+ 0.05% [11]) and to the jTr = 0 + T = 1 a n a l o g u e at 1042.2 ± 0.5 keV [12]. T h e f o r m e r t r a n s i t i o n is v e r y w e a k w h i l e t h e s t r e n g t h of the l a t t e r is not g r e a t and m a y be a c c u r a t e l y c o m p u t e d u s i n g CVC so the e x p e r i m e n t a l p r o b l e m r e d u c e s to t h a t of the l i f e t i m e m e a s u r e m e n t w h i c h we h a v e t h e r e fore tackled. A t h i c k t a r g e t of P b O 2 w a s b o m b a r d e d w i t h 5.5 MeV 3He p a r t i c l e s f r o m t h e B r o o k h a v e n R e s e a r c h Van de G r a a f f . T h e b e a m w a s m e c h a n i c a l l y i n t e r r u p t e d on a c y c l e of 4 s on, 102 s off and t h e t a r g e t e x a m i n e d f o r e l e c t r o n a c t i v i t y t h r o u g h o u t t h e " o f f " p e r i o d with a p l a s t i c s c i n t i l l a t o r b i a s s e d a b o v e 2 MeV. T h e output of the s c i n t i l l a t o r w a s a n a l y z e d by a m u l t i - s c a l e r s t e p ped at 0.2 s by a q u a r t z - c r y s t a l c l o c k . U n d e r t h e s e c o n d i t i o n s the only b o d i e s m a d e f r o m o x y gen o r c a r b o n i s o t o p e s to w h o s e d e c a y we a r e s e n s i t i v e a r e 140, I 8 N e , 1 9 N e and 2 0 F . To e x t r a c t t h e d e s i r e d h a l f - l i f e of 18Ne the c o m p o s i t e d e c a y c u r v e w a s a n a l y z e d with a c o m p u t e r p r o g r a m * c o n t a i n i n g the known h a l f - l i v e s of 140, I 9 N e [13] and 2 0 F [ 3 ] plus a c o n s t a n t b a c k g r o u n d and t h e unknown l g N e . We m a d e t h r e e e x t e n d e d r u n s w h i c h y i e l d e d 18Ne h a l f - l i v e s of 1.701 + 0.032, 1.650 + 0 . 0 3 3 a n d 1 . 6 5 8 + 0.025 s, r e s p e c t i v e l y . As m a y h a v e b e e n a n t i c i p a t e d , the 140 and 19Ne a c t i v i t i e s w e r e n e g l i g i b l e ; the i n i t i a l a c t i v i t y of 20F was a few p e r c e n t of that of 18Ne. T h e X2 f i t s w e r e e n t i r e l y a c c e p t a b l e . A r u n at a h i g h e r b i a s r e v e a l e d an i n c r e a s e d p r o p o r t i o n of 20F a s e x p e c t e d f r o m i t s h i g h e r e n d - p o i n t ~ n e r g y . We quote t l / 2 = 1.67 + 0.02 s. W e h a v e l e a r n t f r o m our c o l l e a g u e s in S t r a s b o u r g [11] that t h e y had e a r l i e r , f o l l o w i n g K a v a n a g h ' s r e m a r k i n g upon t h e s a m e a n o m a l y [14], r e m e a s u r e d the 18Ne h a l f - l i f e , finding 1.69 ± 0.04 s. T h i s v a l u e i s e n t i r e l y c o n c o r d a n t w i t h o u r p r e s e n t m e a s u r e m e n t and we w e i g h t it with o u r s in the s u b s e q u e n t a n a l y s i s . We c o m p u t e the l i f e t i m e f o r t h e s u p e r a l l o w e d F e r m i t r a n s i t i o n of 18Ne to i t s a n a l o g u e in 18F * We are indebted to Mr. B. E. F. Macefield for help with this analysis.
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22 June 1970
u s i n g f t = 3060 + 20 s, the e r r o r c o v e r i n g the e x p e r i m e n t a l s p r e a d of the w e l l - s t u d i e d t r a n s i t i o n s of t h i s CVC c l a s s [e.g. 15]. (The w e a k n e s s of the b r a n c h d o e s not w a r r a n t a m o r e r e f i n e d t r e a t m e n t . ) W e f i n d t l / 2 = 2 2 . 6 8 + 0.25 s and so, c o r r e c t i n g a l s o f o r t h e v e r y w e a k t r a n s i t i o n to the 1.701 keV s t a t e , a p a r t i a l h a l f - l i f e f o r t h e g r o u n d s t a t e t r a n s i t i o n of 1.811 + 0.022 s to w h i c h c o r r e s p o n d s f t = (1.226+0.017) x 103s. (We m a y n o t e en p a s s a n t that t h e s e r e s u l t s i m p l y a g r o u n d s t a t e b r a n c h of 92.6 + 0.1% with w h i c h the d i r e c t e x p e r i m e n t a l f i g u r e of 92.4 * 1.7% [9,10] is c o n cordant. ) T h e a c c u r a c y of the m e a s u r e m e n t s w a r r a n t s the a p p l i c a t i o n , b e f o r e t h e i r i n t e r c o m p a r i s o n , of r a d i a t i v e c o r r e c t i o n s (but not of s e c o n d - f o r b i d d e n e f f e c t s ) . In the i n t e r c o m p a r i s o n of m i r r o r t r a n s i t i o n s the " i n n e r ", m o d e l d e p e n d e n t , r a d i a t i v e c o r r e c t i o n s , w h i c h m e r e l y r e n o r m a l i z e the c o u p l i n g c o n s t a n t s , f a l l away and we a r e l e f t w i t h only the " o u t e r " , m o d e l i n d e p e n d e n t , c o r r e c t i o n s [16]; t h e s e g i v e a s p e e d i n g up of the t r a n s i t i o n s by 1.57% f o r 18F and 1.10% f o r 18Ne. With t h i s f i n a l c o r r e c t i o n we find 5 -- -0.008 + 0.015. T h i s v a l u e of 5 we m u s t c o m p a r e with 5 = 0 f o r g I T = 0 and with 5 ~ 0.01 f o r g I T ~ + 2 x 1 0 - 3 ; t h e l a t t e r c o r r e s p o n d s to the " u n c o r r e c t e d " i n t e r p r e t a t i o n of t h e g e n e r a l t r e n d of 5 w i t h W~ + W ~ r e v e a l e d by the s u r v e y [1]. T h e A = 18 a n o m a l y is r e m o v e d and the m i r r o r transition problem receives a sure anchor near the o r i g i n . It would be d e s i r a b l e to i m p r o v e the a c c u r a c y of the o t h e r a n c h o r point, A = 30, w h i c h has an e v e n l o w e r v a l u e of W~o + W ~ n a m e l y 3.7; i t s s u r v e y v a l u e , 5 = 0.02 + 0.05, s h o w s no a n o m a l y and i t s i m p r o v e m e n t is m o r e d i f f i c u l t than f o r A = 18 s i n c e the g r o u n d s t a t e b r a n c h d o e s not d o m i n a t e .
References [1] D. H. Wilkinson, Phys. Letters 31B (1970) 447. [2] S. Weinberg, Phys. Rev. 112 (1958) 1375; [3] [4]
[5] [6] [7] [8] [9] [i0]
J. N. Huffaker and E. Greuling, Phys. Rev. 132 (1963) 738. D. H. Wilkinson and D. E. Alburger, to be published. J. D. Mahony and S. S. Markowitz, University of California Radiation Laboratory report, UCRL10512. T.G. Ebrey and P.R. Gray, Nucl. Phys. 61 (1965) 479. J.H.E.Mattauch, W. Thiele and A.H. Wapstra, Nucl. Phys. 67 (1965) I. R.W.P. Drever, A. Moljk and J. Scobie~ Phil. Mag. 1 (1956) 942. L. Durand Phys. Rev. 135 (1964) B310. J. W. Butler and K. L. Dunning, Phys. Rev. 121 (1961) 1782. G. Frick et al., Phys. Rev. 132 (1963) 2169.
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[11] E. A s l a n i d e s , F. Jundt and A. Galtmann, private communication. [12] C. C h a s m a n , K.W. J o n e s . R . A . Ristinen and E . K . Warburton, Phys. Rev. 137 (1965) B1445; E . K . Warburton, J . W . O l n e s s and A. R. Potetti, Phys. Rev. 155 (1967) 1164; A. E. Blaugrund, D.H. Youngbtood, G. C. M o r r i s o n and R . E . S e g e l , Phys. Rev. 158 {1967) 893; S. Gorodetzky, E. Astanides, A. G a l t m a n n and G.
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Frick, Nuct. Phys. A109 (1968) 417. [13] F. Ajzenberg-Selove, Nuc[. P h y s . , to be published. [14] R.W. Kavanagh, Nucl. P h y s . A129 (1969) 172. [15] R. J. B[in-Stoyle, Ch.4 of Isospin in l~uclear P h y s ics ed. D. H. Wilkinson (North-Holland, A m s t e r d a m 1969). [16] A. Sirlin, Phys. Rev. 164 (1967) 1767; D. H. Wilkinson and B. E. F. Macefietd, to be published.