Nuclear Matrix Elements of Second-Forbidden Beta Transitions and thej−jCoupling Model

The ratios of nuclear matrix elements compatible with the experimental shape factors of the second-forbidden beta transitions in the decay of ${\mathrm{Cl}}^{36}$, ${\mathrm{Fe}}^{59}$, ${\mathrm{Tc}}^{99}$, ${\mathrm{I}}^{129}$, ${\mathrm{Cs}}^{135}$, and ${\mathrm{Cs}}^{137}$ are computed. In each case a solution is found which agrees with the predictions $\frac{\int i{A}_{\mathrm{ij}}}{\int R_{\mathrm{ij}}}$ of the conserved vector current theory and is close to the extreme single-particle estimate of $\frac{\int i{T}_{\mathrm{ij}}}{\int R_{\mathrm{ij}}}$. Deviations are analyzed by introducing small amounts of configuration mixing. The standard matrix elements $\int \frac{R_{\mathrm{ij}}}{R^2}$ are computed and compared to their single-particle estimate.