Mirror energy differences (MED) between excited states in the $A=31, T=1/2$ mirror pair ${}^{31}\mathrm{S}$ and ${}^{31}\mathrm{P}$ have been measured up to high spin yrast states of positive and negative parity. The mirror nuclei were populated in the ${}^{24}\mathrm{Mg}({}^{12}\mathrm{C}, \alpha n$) and ${}^{24}\mathrm{Mg}({}^{12}\mathrm{C}, \alpha p$) reactions, respectively. For the first time the MED are described in the framework of the shell model in a valence space that includes three main shells. The theoretical MED values as a function of angular momentum indicate that the main contribution arises from the Coulomb interaction, however, the isospin symmetry breaking term is not at all negligible and needs to be considered to reproduce the experimental findings.

• Received 17 November 2020
• Revised 27 December 2020
• Accepted 1 June 2021

DOI:https://doi.org/10.1103/PhysRevC.104.024309