Buehring, H.

Schopper, H.

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A Reevaluation of the Coupling Constants in Beta Decay H. Bühring, H. Schopper Februar 1965 KFK , ji 17 Insz-i .52~ f ü r  Bmerimentc l'e Xercph~sik A Reeva1uatZ.cn of t h e  Coil-1Lng Conz';mts i n  3ei;a 2 e c q  H, ~ ~ u i r i n ~ ~ ,  Y, Schcpp.31. + 11, Pnysikali sches I n s t ~ t - L ? ,  Heid?l*>erg -- Gesellschaft  f ü r  Kercionschü.ng 11?.'b.-'1, X- l s ruhe  k Reevaluation of  t he  Coupling Constants i n  Beta Decay A precise determination of the R decay coupling constants i s  of great  importance with respect  t o  the universal  Fermi in te rac t ion  and the CVC theory, The vector coupling con- s t a n t  gV i s  obtained from the f t  value of oq4 and other  0+-0+ t r ans i t ions  and the r a t i o  gA/gV from the  f t  value o f  the  neutron. For t h i s  purpose the f function must be known precisely.  I n  the pas t  calculations f o r  a point  charge ['I] were improved by applying corrections f o r  the  nuclear s i ze  and the screening by o r b i t a l  electrons.  Because of the approximations used some of the r e s u l t s ,  especial ly  f o r  the  screening correction,  d i f fe red  considerably [21. One of us [3] has developed an exact method t o  calculate  the  solut ion of the Disac equation ( f o r  an extended nuclear charge) taking electron screening i n t o  account. With the electron wave functions obtained i n  t h i s  way the function was calculated ( f o r  the def in i t ion  of FoLo See [ll] and 131). It i s  thought t h a t  the f values derived here a r e  t o  be preferred t o  those evaluated i n  the pas t  on the bas i s  of various approximations . The r e s u l t s  f o r  the  neutron and 014 are shown i n  the t ab le  together with values published by other authors. It might be i o t e r e s t i n g  t o  mention t h a t  the  e f f e c t  of  screening i s  very s m a l l  ( Y ,  2 x I O - ~ )  f o r  the  f t  value of 014. The influence o f  a change o f  the  nuclear radius R = (0.428/13?). A ' / ~ ^ _ I . ~  x 10 -I3 A " ~  cm has a lso been investigated since t h i s  i s  the only parameter relevant t o  the calculations.  A varia t ion of R by 10% i n  the case of oq4 o r  by 20% i n  the case o f  the neutron chmges the f t  value by l e s s  thon I O - ~ .  Several addit ional  e f fec ts  have t o  be taken i n t o  account. The most important are the radiat ive corrections which were calculated hy Kinoshita, Berman and S i r l i n  [4, 53, using perturbation theory. Durand e t  al. C61 evaluated the rad ia t ive  corrections with dispersion re l a t ions  but i n  t h i s  way only r e s u l t s  fo r  p a r t i a l l y  renormalized coupling constants are obtained. Therefore the numbers deduced by Kinoshita e t  a l .  were used (see t ab le ) .  Corrections originating from the nucleon s t ruc ture  and from the  competition o f  K capture were also applied* Corrections due t o  r e l a t i v i s t i c  e f fec t s  and contributions from second forbidden matrix elements are small and can be neglected C2, 61. The f values computed from the exact e lectron wave functions and with the corrections mentioned above are shown i n  the table .  From these and the experimental half l i f e s  the f t  values can be deduced. The r e s u l t s  a r e  a l s o  given i n  the table .  The constant gV can be calculated from the r e l a t i o n  The mahix  element MF can be computed f o r  0+-0+ t r ans i t ions  i f  i sospin  is a good quantum number, Although the inf  luence of Coulomb e f fec t s  on the matrix element i s  not ye t  comple- 2 tely c l a r i f i e d  (see C23, C63) w e  shal l  assume / M ~ [  = 2 f o r  014. We s h a l l  not consider other 0'-0' t r ans i t ions  since t h e i r  matrix elements are known with even l e s s  re- l i a b i l i t y .  Brom the f t  value given i n  the t ab le  one obtains Por the axial vectnr coupling constant one has and This value i s  somewhat lower than the values accepted thus far, % = 1.19 o r  1.25 [see 63 and higher than a recent value derived by Phalla,  -1 .I 5 (reported by C.S.  Wu a t  the  Par is  Conference 1964). We do not ye t  understand the difference between the value given by Bhalla and ours, s ince there i s  no screening i n  the case o f  the n e u t r m  and therefore the method of Rhalla C l 1 3  i s  equivalent to  ours. I f  gg i s  compared t o  g = (1.4350 - + 0.0011) X 10 -49 P erg. cm3 121 one obtains ( g  - gv)/gp = (2.02 0.25)%. P. This difference i s  i n  reasonable agreement with the pre- d ic t ion  of Cabbibo's theory o f  3.3%. It should be noted t h a t  tha e r ro r  of gV does not contain the uncertain- t y  of the rad ia t ive  correction which might be 0.5%. Li ter  ature Tables for the Analysis of Beta Spectra, NBS Ser. I 3  (3952) C.S.  Wu, Rev. mod. phys. 36, 618 (1964) W. Buhring, Nuclear Physics 61, 110 (1965) S.M. Berman and A.  S i r l i n ,  Ann. Phys. 20, 20 (1962) T. Kinoshita and A. S i r l i n ,  Phys. Rev. 113, 1652 (19.59) Durand, Landovitz and Marr, Phys. Rev. 130, 1 7 8 8  (1963) Bardin, Barnes, Fowler and Seeger, Phys. Rev- 127, - 583 (1962) Freeman, White, Montagne, Murray and Burcham, Phys. Lett .  8, 115 (1964) Sosnovsky, Spivak, Prokofiev, Kut:kpv and Dobrinin, Nuclear Phys. 10, 395 (1958) N. Cabbibo, Phys. Rev. Lett .  10,  531 (1963); ?2,  62 (1964) C.P. Bhalla and M.E. Rose, Phys. Rev. 128 (1962) 774; Table f uncorrected point charge f nuclear size, screening (Rose) f nuclear size, screening (Reitz) f exact wave function 1.695 2 0.005 42.9 - + 0.15 [this workl radiat ive corrections f + 1.8 % C43 + 1.7 % C53 A f - finite nucleon size f - 0.002 % [61 0.110 % C61 competition from K capture - 0.090 C61 total ~ f / f  + 1.8 O/o + l .90 % f (exact, corrected) 1.725 + 0.005 43.6 2 1.5 t sec 702 - + 18 C71 71.36 11 0.09 171 C61 ft sec 1211 -+ 37 3111 - + 15 

A reevaluation of the coupling constants in beta-decay

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A reevaluation of the coupling constants in beta-decay

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