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

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 $32.8\pm 0.7$~MeV and effective mass of $m^{\ast }/m\ge 0.75$ at the saturation density is the most likely to systematically reproduce the experimental data of $Q_{\beta }$ systematically.

Comments: 11 pages, 7 figures