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 (Δ Rᵐⁱʳʳch) are strongly correlated with the neutron-skin thickness (Rₛₖᵢₙ) of neutron-rich nuclei and with the slope of the symmetry energy (L). To test this assumption, we present ab initio calculations of Rₛₖᵢₙ in ⁴⁸Ca and ²⁰⁸Pb, Δ Rᵐⁱʳʳch 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 Δ Rᵐⁱʳʳch, Rₛₖᵢₙ 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 Δ Rᵐⁱʳʳch-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 Δ Rᵐⁱʳʳch-L correlation.