Existence of isobaric states and beta decay of heavier nuclei

Abstract

It was already pointed out that the experimental discovery of well-defined isobaric states suggests that the heavier nuclei have the supermultiplet structure to a certain extent. The purpose of this note is to investigate the systematics of nuclear matrix elements for the allowed beta decay on the basis of the pairing model including nuclear interactions between unlike nucleons. We discuss two different approaches: (a) the conventional pairing model, which additionally includes the effect of the short or long range residual proton-neutron interactions; (b) the modified pairing model, in which the supermultiplet-like structure is assumed in the zeroth approximation and partially destroyed by the spin-dependent interactions such as the spin-orbit forces. The results are compared with experimental data on the SnSb transitions. It is concluded that the main part of the hindrance factor can be attributed to the p-n interaction. In the course of study, the theory of isobaric peaks in (p, n) reactions is reformulated by using the so-called Ahrens-Feenberg approximation method. Several formulae of a general validity are derived, which are especially useful in treating the normal allowed matrix elements.