Second-forbidden nonunique $β^-$ decays of ${}^{24}$Na and ${}^{36}$Cl assessed by the nuclear shell model

Abstract

We have performed a systematic study of the log$ft$ values, shape factors and electron spectra for the second-forbidden nonunique $β^-$ decays of ${}^{24}$Na$(4^{+}){\to }^{24}$Mg$(2^{+})$ and ${}^{36}$Cl$(2^{+}){\to }^{36}$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, log$ft$ values, shape factors, electron spectra and decomposition of the integrated shape factor are reported and compare with the available experimental data.

11 pages. 4 figures, 5 tables