Second-forbidden nonunique β − decays of Na 24 and Cl 36 assessed by the nuclear shell model

We have performed a systematic study of the $logft$ values, shape factors, and electron spectra for the second-forbidden nonunique ${\ensuremath{\beta}}^{\ensuremath{-}}$ decays of $^{24}\mathrm{Na}({4}^{+})\ensuremath{\rightarrow}^{24}\mathrm{Mg}({2}^{+})$ and $^{36}\mathrm{Cl}({2}^{+}){\ensuremath{\rightarrow}}^{36}\mathrm{Ar}({0}^{+})$ transitions under the framework of the nuclear shell model. We have performed the shell model calculations in the $sd$ model space, using more recent microscopic effective interactions such as Daejeon16, chiral N3LO, and JISP16. These interactions are derived from the no-core shell model wave functions using Okubo-Lee-Suzuki transformation. For comparison, we have also shown the results obtain from the phenomenological USDB interaction. To test the predictive power of these interactions first we have computed low-lying energy spectra of parent and daughter nuclei involved in these transitions. The computed results for energy spectra, nuclear matrix elements, $logft$ values, shape factors, electron spectra, and decomposition of the integrated shape factor are reported and compare with the available experimental data.