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

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, Delta R-ch(mir), is an inferior isovector indicator compared to other observables, such at the neutron skin or electric dipole polarizability alpha(D). In particular, this quantity correlates poorly with both the neutron skin and L. We demonstrate that Delta R-ch(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 Delta R-ch(mir), we conclude that the precise data on mirror charge radii cannot provide a stringent constraint on L.

Automated summary

Differences in charge radii of mirror nuclei are suggested to contain information on the slope of the symmetry energy. However, statistical correlation analysis shows that the difference in charge radii, Delta R-ch(mir), is an inferior indicator compared to other observables such as neutron skin or electric dipole polarizability. The presence of pairing correlations and low-lying proton continuum affects Delta R-ch(mir). Therefore, the precise data on mirror charge radii cannot provide a stringent constraint on the slope of the symmetry energy L.