Nuclear beta decay

Abstract

New formulae for nuclear beta decay are derived by using a modified expansion of the electron radial wave functions. This expansion is obtained by means of the integral equations which correspond to the Dirac radial differential equations. As a consequence new types of form factor coefficients or nuclear matrix elements occur which depend on the shape of the nuclear charge distribution. The implications of the new formulae for the analysis of experiments are discussed. The sensitivity to the detailed shape of the charge distribution turns out to be weak usually, even in the case of non-unique forbidden transitions. An elementary treatment of the induced interactions leads in a simple way to the formulae which express the form factor coefficients in terms of coupling constants and nuclear matrix elements. Expressions are given for the single-particle values of all the nuclear matrix elements in terms of radial integrals. References