How do mirror charge radii constrain density dependence of the symmetry energy?

It has recently been suggested that differences in the charge radii of mirror nuclei (ΔR_ch^mirr) are strongly correlated with the neutron-skin thickness (R_skin) of neutron-rich nuclei and with the slope of the symmetry energy (L). To test this assumption, we present ab initio calculations of R_skin in ⁴⁸Ca and ²⁰⁸Pb, ΔR_ch^mirr in ³⁶Ca−³⁶S, ³⁸Ca−³⁸Ar, ⁴¹Sc−⁴¹Ca, ⁴⁸Ni−⁴⁸Ca, ⁵²Ni−⁵²Cr, and ⁵⁴Ni−⁵⁴Fe mirror pairs, and L. Employing the recently developed 34 chiral interaction samples, identified by the history matching approach, we conduct rigorous statistical analysis of correlations among ΔR_ch^mirr, R_skin and L, accounting for quantified uncertainties from low-energy constants of chiral interaction, chiral effective field theory truncation and many-body method approximation. The ab initio results reveal an appreciable ΔR_ch^mirr−L correlation in fp-shell mirror pairs. However, contrary to previous studies, the present calculation finds that the studied sd-shell mirror pairs do not exhibit any ΔR_ch^mirr−L correlation.