γ-neutrino correlation in first forbidden nuclear μ-meson capture

γ-neutrino correlation in first forbidden nuclear μ-meson capture

Volume 15, number 3 PHYSICS L E T T E R S The r e s u l t s or these recent m e a s u r e m e n t s allow us to calculate the factors by which the p...

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Volume 15, number 3

PHYSICS L E T T E R S

The r e s u l t s or these recent m e a s u r e m e n t s allow us to calculate the factors by which the polarizations quoted in a number of publications should be multiplied. Tilese factors are: 1. F o r the p - c a r b o n data of Dickson and Salter [5]; 0.854 ± 0.017 2. F o r the r e c e n t p-nucleus data of Steinberg e t a l . [8]; 0.917 ± 0.012 3. F o r the p - p data of Taylor e t a l . [1]; 0.911 4 F o r the p - p data of P a l m i e r i e t a l . [3] and the p-He data of Cormack e t a l . [9]; 0.933 [10] 5. For the low energy p-p data of Christmas and Taylor [2]; 0.89 6. For the p-p data of Caverzasio et a l . [4]; 0.854 In cases (1) and (2) (above) the factor is intended to be multiplied into the tabulated relative polarization values quoted in refs. 5 and 8. The absolute e r r o r s are then found by combining the relative e r r o r s with the above normalization e r r o r s . F o r the eases (3) to (6) all the polarization values given in refs. 1-4, 9 should be multiplied by the appropriate factor but the absolute e r r o r on each point (expressed as a percentage) is unchanged. Fig. 1. shows the variation with energy of the corrected values of P(e) for p-p scattering at a c e n t r e - o f - m a s s angle 0 = 61.8o, together with a recent m e a s u r e m e n t at 140.7 MeV obtained at Harwell [ 11]. The curve drawn in fig. 1 gives

1 April 1965

the variation of p ( 8 = 61.8 o) with energy as predicted by the phenomenologlcal potential model of Hamadaand Johnston [12]. It is c l e a r that the variation of the polarization with energy is now reasonable and that the fit of the model to the data is considerably improved. I. A. E, Taylor, E. Wood and L. Bird, Nuol. Phys. 16

(1960) 320. 2. P.Chrlstmas and A.E.Taylor, Nucl.Phys. 41 • {1963) 388; and P. Christmas, D. Phil. Thesis (unpublished), University of Oxford, 1961. 3. J.N.Palmieri, A.M.Cormack, N.F.Ramsey and R. Wilson, Ann. Phys. 5 (1958) 299. 4. C.Caverzasio, A.Miohelowicz, K.Kurods, M. noulet and N. Poutcherov, J. Phys. Radium 24 (1963) 1048; and C.Caverzasio, Thesis, University of Paris (Orsay) 1964. 5. J.M.Diekson and D.C.Salter, Nuovo Cimento 6 (1957} ~ 5 . 6. R.Alphonce, A. Johansson and G.Tibell, Nucl.Phys. 4 (1957} 672. 7. R.Alphonce, A. Johansson and G.Tibell, Nucl.Phys. 3 (1957) 185. 8. D.J. Steinberg, J.N. Palmiert and A. M. Cormack, Nucl.Phys. 56 {1964) 46. 9. A.M.Cormack, J.N.Palmieri, N.F.Ramsey and R. Wilson, Phys. Roy. 115 (1955) 599. 10. R. Wilson and J.N. Palmteri, private communica-tion. 11. G.F.Cox, G.H.Eaton, O.N.Jarvis and B.Rose, unpublished. 12. T.Hamada and l.D.Jolmston, Nucl.Phys. 34 (1962) 382. 13. J.Tlalot and R.G.Warner, Phys.Rev. 124 0961) 890.

y-NEUTRINO CORRELATION IN F I R S T F O R B I D D E N NUCLEAR #-MESON CAPTURE

Z. OZII~WICZ and N. P. POPOV A. F. loffe Physico-Techni~,al Institute, Leningrad, USSR Receivec~ 15 February 1965 In a previous paper [1] a general expression was obtained for angular yv correlation in nuclear , meson capture for partial transitions of any order of forbiddenness, which was reduced to a form which is convenient for con ?aring with experiment for allowed transitions. However the possibilities of an experimental study of r v correlation are limited in the case of p - m e s o n capture by the B I0 nucleus, having a small 3/v correlation coefficient [2]. Nevertheless, there is a wide possibility of the study of the first forbidden transitions IAjl = 0, 1, 2 (yes) (for example y - m e s o n capture by the C 12 nucleus). Ill the partic,Jlar case of the first forbidden transitions the angular ~,v correlation is defined by the formula: 273

Volume 15, number $

w = -, . ~ .

PHYSICS

LETTERS

1 April 1965

( s . ~ P2([email protected] + ~,)~e) + ~)([o x q].k) + (c~+¢[o x % k)Ps(ke) - (~-xo~)P4([email protected]

where @ is the ~-meson polarization vector at the instant of the capture, q and k are unit vectors in the direction of emission of the neutrino and ),-ray quantum respectively, Pi(ql~ is the Legendre polyuomlal,

ap o

.

AS) -~C~ + ~ ( ~ -4~'~ D~-E ~) - ~ P 0

i~a~- ~ - ~

.22,.t D2 +46DE +4E 2) +~/~A12(B-42 A)(43D-.,/2E)-A02C~.,/2D+43 E)

~'2 ~ + A2 W~ BD'~BE +~J2AE) +~43AO2CE" 24~ A 2 2 ( ~ 1 D 2 " M ~/~

:

~,~.11._ 2 A 2 (Z~ -

~B2+j2AB) A{2(~j3AD+J2AE+~DE)+~AO2c(43D..j2E)+

+ ~ , / 1 4 " 2 2 ' ' D2+J~ DE r~2 ~,T 12

II

DE" E2) " ~Po

BA*+

E2)+~.PO

' 3 D+2JZE)*] " 4 ~ A ~2 Im[S~eD +~~E)*-A(~4

Im

C(JSD-J2E)* +

+ ~,/~A~2ImDE+~-~PO * PO :

-34[~A242(TD2 +J~ DE- E2) 22

" Po : -WlOS a4 ~m DE*

~I~ = - ~ XP 0 -

A242(2~DE

+~z E~

-~a A4~2E2

Here P0 is proportional to the probability of ~ capture and is given by Morita and Fujii [3]. The fvuctions A, B, etc. have the following form: A =, ~ C~011] -~- CA[ 111] +4~ CvqM°l[011] + ~qCvA~r~l+~p-/~n) [ 111+] - 4 3 CvM-I[ 1019] B : ~, 3 C~011] + ~J2 CA[ t11] +4~ CvqM-l[011-]-~J~ qCvM-l(1 + ~p-~n)[ 111-] -4~ CvM'I [ 121p]

C = ~ CA{ 1101+ 4~ (CA-C)qltf1[110+]+42 CA M" 1[000p] D = 4} CA[112]- ~''~ -,/~-tlrs r Cv(I+/~p-/~n)- C A + %]qM" 1[,12-]+ ~[Cv(l+~tp-gn)+ CA-%]qM" I[132+] + ~,'~Cv:~-l[122p]+ ~45 CAM-1[022p] E=, i cA[13~-]+~[ Cv(l +~p-~n) + CA - %]qM'11112-]- ~4~[~Cv(I + ~p- ~n) - CA + %]¢M'11132+] + • ~ ' 1 5 CvM-I[ 1229] +4~CA~-I[022p] Ci is the weak interaction constant, ~IP ~n are the anomalous magnetic moments of the proton and neutron, respectively, q is the energy oftne neutrino; M is the mass o! "~he wacleon. The reduced .uuc!e~_r matri.x elements [001] etc. are given in table II taken from ref. 3. For electric multipole radiation of cb~racter 2 L in a transition J0 ~ Jl .T_.J2 we have • .

. ,.

.



L0

A~S ' = [ 1 - S(S + 1)/2L(L + 1)] J[(2S + 1)(2L + 1)] (2j I + 1)W(~(f 1[S,? j 1)W()2LJ 1Su 1L)CLos0 L0 VV(abcd; el) is theRacah function, CL0S0 is the Clebsch-Gordan coefficient. For the case of mixed magnetic multipole radiation of character 2L and electric radiation of character The probable complexity of the weak interaction constants was taken into consideration only when calculating ~ and aorresponding to the correlations which are not invartant under time reversal. 274

Volume 15. m m b e r 3

PHYSICS LETTERS

1 A~r/l 1 ~

2 L + l we have to m a k e a substitution u s i n g the f o r m u l a (13) f r o m the p a p e r by Dolginov and Toptigin [4]. In the c a s e of t h e unique [Aj[ = 2 (ytm) t r a n s i t i o n s A = B = C : 0, and the g e n e r a l exp~'ession f o r the a n g u l a r c o r r e l a t i o n is simplified. In the c a p t u r e of a n unpolarized ~ - m e s o n t h e r e r e m a i n s only the contribution of the ~P20k~ and ~ 4 ( k q ) c o r r e l a t i o n s . F o r a q u a l i t a t i v e c o n s i d e r a t i o n we m a y put [112-] ~ [112] and n e g l e c t the o t h e r n u c l e a r m a t r i x e l e m e n t s which a r e s m a l l e r than [112.] by one o r two o r d e r s of magnitude. As it is shown in the papers [5, 2], the exact calculation taking into consideration all the nuclear matrix elements differs l i t t l e from the approximate estimate. Thus, the dependence,on n u c l e a r s t r u c t u r e v a n i s h e s in the ~ and g coefficients, w h i c h now have become functions of the weak i n t e r a c U o n c o n s t a n t s i n . c a p t u r e only. H in the r e a c t i o n /~ + C 12 - . B 12. + v u the vald~s of the spin and L~rlty for one of tl~e excitation levels of the B 12 nucleus p r o v e to be equal to 2" [6], the value ~ will r e a c h approxim a t e l y 30 p e r c e n t ( E l radiation) having a very I weak dependence on the p s e u d o s c a l a r . At the s a m e time the P4(kq) c o r r e l a t i o n (the d e t e r Fig. 1. The dependence of the correlq~on coefficient on mining radiation is the M2) greatly depends on Cp/CA in a 0~ P-. 2= v I transition (/~z = }~/~), for the magnitude of the p s e u d o s c a l a r contribution, Cv/C A = -0.8 and ~p-U~ = 3.7. having s i m u l t a n e o u s l y a high ~,v c o r r e l a t i o n coefficient (see fig. 1), and t h e r e f o r e an e x p e r i mental study of this c o r r e l a t i o n may s e r v e as a very s e n s i t i v e way to d e t e r m i n e the magnitude of the p s e u d o s c a l a r constant. It should be noted that in the c a s e of a O k ~ 1 ~ t r a n s i t i o n C = D = E = 0, and the dependence of the c o r r e l a t i o n s on Cp vanishes. The study of the ~ o q and ~v2(kq) c o r r e l a t i o n s together with the probability of . - m e s o n c a p t u r e may provide m o r e a c c u r a t e i n f o r m a t i o n on the magnitude of the F e r m i c o n s t a n t in .-meson capture.

/I

The a u t h o r s a r e deeply g r a t e f u l to V. M. Shekhter and I. M. Shmushkevich for valuable diPcussion.

References 1. N.P. Pcpov, Zh. Eksp. i Teor. Fiz. 44 {1963) 1679. 2. (3. M. Bukat and N. P. Popov0 Zh. Eksp. i Teor. Fiz. 46 0964) 1782. 3. M.Morita and A.FuJii, Phys. Rev. 118 {1960) 606. 4. A.Z.Dolginov and I.N.Toptigin: Nuol. Phys. 2 {1956) 147. 5. G.J.Korenman and R.A.Ermndzyan, preprint (I)ubns) R-I160, 1962. 6. M. Ruel and J.G. Bronnan, Phys.Rev. 129 {1963) 866.

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