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

TL;DR

This study investigates whether differences in charge radii of mirror nuclei can inform about the symmetry energy slope L, finding it to be a poor indicator compared to other observables due to theoretical uncertainties.

Contribution

The paper provides a statistical analysis showing that mirror charge radii differences are less effective as isovector indicators for L than other measures like neutron skin or dipole polarizability.

Findings

R_mir correlates poorly with neutron skin and L.

Pairing correlations affect R_mir in proton-rich nuclei.

Large uncertainties limit the use of R_mir to constrain L.

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