Study of $\beta^+$/EC-decay properties of $sd$ shell nuclei using nuclear shell model

TL;DR

This paper uses the nuclear shell model with USDB and SDNN Hamiltonians to systematically compute beta decay properties of sd shell nuclei, including half-lives, Q-values, and transition strengths, with results aligning well with experiments.

Contribution

It provides a comprehensive shell model analysis of beta decay in sd shell nuclei, including quenching factors and electron capture effects, which was not extensively done before.

Findings

Quenching factors of approximately 0.79 and 0.82 for USDB and SDNN.

Calculated half-lives and transition parameters agree with experimental data.

Electron capture phase space has a minor impact on half-life calculations.

Abstract

Our study employs the nuclear shell model to systematically compute the half-lives of $\beta$ -decay for nuclei in the mass range of $A = 18-39$, encompassing the majority of $sd$ shell nuclei. This analysis utilizes the USDB and SDNN Hamiltonians. The theoretical outcomes contain calculations of various parameters such as $Q$ -values, half-lives, excitation energy, log$ft$ values, and branching ratios. We explore these results with axial-vector coupling constant for weak interactions, denoted as $g_A$$(= 1.27)$, and $\kappa$ value $(= 6289)$. We perform calculations of Gamow Teller matrix elements for 116 decay processes to calculate the quenching factor; we found a quenching factor of $q = 0.794\pm0.05 $ for the USDB interaction and $q = 0.815\pm0.04 $ for the SDNN interaction. We have also calculated superallowed transitions $0^+ \rightarrow 0^+$ for seven nuclei. Further, we have also included the electron capture phase space factor for the required nuclei to calculate the half-lives. This inclusion leads to small contribution in results, particularly for nuclei where electron capture (EC) plays a significant role. The overall results are in agreement with the experimental data.