Nuclear Matrix Elements for AllowedβTransitions

Abstract

Nuclear matrix elements are evaluated for all allowed $\beta$ transitions in the strict $j-j$ coupling shell model, i.e., for states of lowest seniority. The wave functions for the $j^N$ configurations are obtained by algebraic means in the formalism of coefficients of fractional parentage. The matrix elements are given for the two assumptions, firstly that isotopic spin is a good quantum number, and secondly that the neutrons and are coupled separately to their lowest seniority states. The latter includes the case where the protons end in a $j=l+\frac{1}{2}$ shell, while the neutrons end in the $j=l-\frac{1}{2}$ shell. A similar explicit form is given for the magnetic moments of the states of the $j^N$ configuration with seniority one.