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

TL;DR

This study uses the nuclear shell model with various effective interactions to analyze second-forbidden nonunique $eta^-$ decays of $^{24}$Na and $^{36}$Cl, comparing theoretical predictions with experimental data.

Contribution

It provides a systematic shell model analysis of these rare decays using modern microscopic interactions and compares results with phenomenological models and experimental data.

Findings

Calculated energy spectra agree with experimental data.

Predicted log$ft$ values and shape factors match observed values.

Demonstrated the effectiveness of microscopic interactions in decay predictions.

Abstract

We have performed a systematic study of the log$ft$ values, shape factors and electron spectra for the second-forbidden nonunique $\beta^-$ decays of $^{24}$Na$(4^+) \rightarrow ^{24}$Mg$(2^+)$ and $^{36}$Cl$(2^+) \rightarrow ^{36}$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.