Abstract
Nuclear matrix elements are evaluated for all allowed $\ensuremath{\beta}$ transitions in the strict $j\ensuremath{-}j$ 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 $j=l\ensuremath{-}\frac{1}{2}$ shell. A similar explicit form is given for the magnetic moments of the states of the ${j}^{N}$ configuration with seniority one.
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