Correlations of $Q_β$-values with symmetry energy and effective mass studied within Skyrme energy--density functionals

Abstract

The $β$-decay half-lives of nuclei are sensitive to the values of $Q_β$. For accurate theoretical predictions, it is essential to develop an effective interaction or an energy density functional (EDF) that can systematically reproduce experimental $Q_β$ values. The challenge lies in identifying an appropriate EDF for an accurate $Q_β$ prediction. To address this, we focus on the bulk properties of nuclei that have correlations with $Q_β$. The primary objective of this study is to determine which nuclear bulk properties are sensitive to $Q_β$, providing information on the key nuclear characteristics that influence $β$-decay calculations. We employ the Skyrme energy-density functionals to find correlations between $Q_β$ 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 $Q_β$ and various nuclear properties. We found that the symmetry energy at low densities shows a correlation with the $Q_β$ 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 $Q_β$ systematically.