Correlations of $Q_{\beta}$-values with symmetry energy and effective mass studied within Skyrme energy--density functionals

TL;DR

This study investigates how $Q_{eta}$-values correlate with nuclear symmetry energy and effective mass using Skyrme energy-density functionals, aiming to improve theoretical predictions of $eta$-decay half-lives.

Contribution

It identifies key nuclear bulk properties, especially symmetry energy and effective mass, that influence $Q_{eta}$ predictions within Skyrme EDFs, guiding better functional development.

Findings

Symmetry energy at low densities correlates with $Q_{eta}$ values.

Effective mass close to 1 enhances the correlation.

Optimal symmetry energy is around 32.8 MeV with effective mass ≥0.75.

Abstract

The $\beta$-decay half-lives of nuclei are sensitive to the values of $Q_{\beta}$. For accurate theoretical predictions, it is essential to develop an effective interaction or an energy density functional (EDF) that can systematically reproduce experimental $Q_{\beta}$ values. The challenge lies in identifying an appropriate EDF for an accurate $Q_{\beta}$ prediction. To address this, we focus on the bulk properties of nuclei that have correlations with $Q_{\beta}$. The primary objective of this study is to determine which nuclear bulk properties are sensitive to $Q_{\beta}$, providing information on the key nuclear characteristics that influence $\beta$-decay calculations. We employ the Skyrme energy-density functionals to find correlations between $Q_{\beta}$ and the nuclear bulk properties, assuming spherical symmetry. Using $42$ different Skyrme EDFs, we analyze these correlations by evaluating Pearson linear coefficients, focusing particularly on the relationship between $Q_{\beta}$ and various nuclear properties. We found that the symmetry energy at low densities shows a correlation with the $Q_{\beta}$ value. In particular, this correlation becomes stronger for functionals with an effective mass close to $1$. However, as the nuclear density increases, the correlation weakens. From our analysis, we found that a symmetry energy of $32.8\pm0.7$~MeV and effective mass of $m^{*}/m\ge0.75$ at the saturation density is the most likely to systematically reproduce the experimental data of $Q_{\beta}$ systematically.