Background: 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. However, it remains unclear which nuclear bulk properties are most relevant for constraining $Q_{\beta }$ predictions.

Purpose: The aim of this work is to identify the nuclear bulk properties that are strongly correlated with $Q_{\beta }$ values, thereby clarifying the key nuclear characteristics that govern $\beta$-decay calculations.

Method: 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.

Results: The analysis shows that the symmetry energy at low densities exhibits a significant correlation with $Q_{\beta }$. 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 $32.8\pm 0.7\mathrm{MeV}$ and effective mass of $m^{*}/m\ge 0.75$ at the saturation density is the most likely to reproduce the experimental data of $Q_{\beta }$ systematically.

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• Beta decay
• Nuclear astrophysics
• Nuclear many-body theory
• Nuclear matter
• Nuclear matter in neutron stars
• Nuclear structure & decays
• Nucleosynthesis in explosive environments