Mesic Effect in the Beta-Decay in a Nucleus

Abstract

The mesic effect to the beta-decay in a nucleus is investigated. The Villars' type tribution which is compared with the ordinary axial vector coupling is estimated by the perturbation method. The comparable value with the fourth component of the ordinary · axial vector couplin'g is obtained. § I. Introduction The problem of the mesic effect in the beta-decay has been considered by many authors. For the renormalization of the vector coupling constant, con­ served vector current theory m) seems to be consistent with several experiments. For the axial vector coupling several attempts 2 l have been made but the problem is not well clarified. K. Kawarabayashi and the author examined the renormali­ zation of the axial vector coupling constant in the free nucleon beta-decal) by considering the virtual process, p->n + e + v, where the effective coupling constant was calculated by the nucleon loop. The result was in good accord with the experiments. The virtual process p-7-Jr + e + v, would also contribute to the mesic correction in the beta-decay in the nucleus. In this note we estimate the Villars' type contribution to compare it with the ordinary axial vector coupling constant by the perturbation method. First, we derive the two-body operator by taking p meson and pion as the intermediate state. Only the fourth com­ ponent is considered for simplicity. Then the Fermi gas model, closed shell plus a neutron, is chosen as the model of the nucleus which is a good approxi­ mation for heavy nuclei. The expectation value of the two-body operator is estimated in the above mentioned model and the result is compared with the· fourth component of the one-body axial vector operator. With a reasonable choice of the coupling constant of p meson with the nucleon, it is shown that the comparable value with the one-body operator is obtained.