Information content of the differences in the charge radii of mirror nuclei

Abstract

Differences in the charge radii of mirror nuclei have been recently suggested to contain information on the slope of the symmetry energy $L$. To test this hypothesis, we perform statistical correlation analysis using quantified energy density functionals that are consistent with our previous knowledge on global nuclear observables such as binding energies and charge radii. We conclude that the difference in charge radii between a mirror pair, $\mathrm{\ensuremath{\Delta}}{R}_{\mathrm{ch}}^{\mathrm{mir}}$, is an inferior isovector indicator compared to other observables, such at the neutron skin or electric dipole polarizability ${\ensuremath{\alpha}}_{\mathrm{D}}$. In particular, this quantity correlates poorly with both the neutron skin and $L$. We demonstrate that $\mathrm{\ensuremath{\Delta}}{R}_{\mathrm{ch}}^{\mathrm{mir}}$ is influenced by pairing correlations in the presence of low-lying proton continuum in the proton-rich mirror-partner nucleus. Considering the large theoretical uncertainties on $\mathrm{\ensuremath{\Delta}}{R}_{\mathrm{ch}}^{\mathrm{mir}}$, we conclude that the precise data on mirror charge radii cannot provide a stringent constraint on $L$.