Renormalization of the axial-vector coupling constant in nuclear β-decay (III)

Abstract

Axial-vector β-decay of nuclei of A ≦ 22 is analyzed in the light of recent work on relativistic corrections to the axial matrix element and to the isoscalar magnetic moment. After allowance for relativity it appears that the average decay amplitude found in practice is (7.3 ± 3.8)% below that predicted by the best explicit wave-functions that are confined to the nominal major shell; this is about one half of the renormalization that has been predicted on the basis of the tensor component of the NN potential and about equal to that predicted from PCAC and empirical pion-nucleus properties. Analysis of the isoscalar magnetic moments suggests a “tensor force renormalization” of perhaps a little less than this and also that the renormalization of the effective axial coupling constant, additional to that due to the tensor force or to equivalent “pion-nucleus” effects, is small and possibly of the opposite sign, i.e. an enhancement of the decay rate. A form of the relativistic isoscalar magnetic moment associated with a potential that generates a realistic spin-orbit splitting is favoured by the analysis of the isoscalar moments. Some qualitative discussion is given of possible relationships between the theoretical renormalization effects.