Isospin symmetry breaking (ISB) effects in the charge radius difference $\mathrm{\Delta }{R}_{\mathrm{ch}}$ of mirror nuclei are studied using the test example of ${}^{48}\mathrm{Ca}$ and ${}^{48}\mathrm{Ni}$. This choice allows for a transparent study of ISB contributions since pairing and deformation effects, commonly required for the study of mirror nuclei, can be neglected in this specific pair. The connection of $\mathrm{\Delta }{R}_{\mathrm{ch}}$ with the nuclear equation of state and the effect of ISB on such a relation are discussed according to an energy density functional approach. We find that nuclear ISB effects may shift the estimated value for the symmetry energy slope parameter $L$ by about 6 to 14 MeV while Coulomb corrections can be neglected. ISB effects on the ground-state energy and charge radii in mirror nuclei have been recently predicted by ab initio calculations to be relatively small, pointing to a negligible effect for the extraction of information on the nuclear EoS. These contrasting results call for a dedicated theoretical effort to solve this overarching problem that impacts not only the neutron-skin thickness or the difference in mass and charge radii of mirror nuclei but also other observables such as the isobaric analog state energy.

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• Equations of state of nuclear matter
• Nuclear density functional theory
• Symmetry energy