Correlations of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msub><mml:mi>Q</mml:mi><mml:mi>β</mml:mi></mml:msub></mml:math> values with symmetry energy and effective mass studied within Skyrme energy-density functionals

Background: The $\ensuremath{\beta}$-decay half-lives of nuclei are sensitive to the values of ${Q}_{\ensuremath{\beta}}$. For accurate theoretical predictions, it is essential to develop an effective interaction or an energy-density functional (EDF) that can systematically reproduce experimental ${Q}_{\ensuremath{\beta}}$ values. However, it remains unclear which nuclear bulk properties are most relevant for constraining ${Q}_{\ensuremath{\beta}}$ predictions.Purpose: The aim of this work is to identify the nuclear bulk properties that are strongly correlated with ${Q}_{\ensuremath{\beta}}$ values, thereby clarifying the key nuclear characteristics that govern $\ensuremath{\beta}$-decay calculations.Method: We employ the Skyrme energy-density functionals to find correlations between ${Q}_{\ensuremath{\beta}}$ 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 ${Q}_{\ensuremath{\beta}}$ and various nuclear properties.Results: The analysis shows that the symmetry energy at low densities exhibits a significant correlation with ${Q}_{\ensuremath{\beta}}$. This correlation becomes stronger for functionals with an effective mass close to 1, but it weakens at higher nuclear densities.Conclusions: From our analysis, we found that a symmetry energy of $32.8\ifmmode\pm\else\textpm\fi{}0.7\phantom{\rule{0.28em}{0ex}}\mathrm{MeV}$ and effective mass of ${m}^{*}/m\ensuremath{\ge}0.75$ at the saturation density is the most likely to reproduce the experimental data of ${Q}_{\ensuremath{\beta}}$ systematically.