Search for isospin-symmetry breaking in the $A=62$ isovector triplet

The assignment of the first $2^+$ state in $^{62}$Ga has long been debated, due to its implications in triplet energy difference systematics in this mass region. An experiment has been performed at the IFIN-HH 9-MV Tandem accelerator using the ROSPHERE array in a mixed configuration of LaBr$_3$(Ce) and HPGe detectors, as well as an additional array of liquid scintillator neutron detectors. Excited states in $^{62}$Ga were populated through a $2n$ fusion-evaporation channel and an anisotropy ratio was obtained from neutron-filtered HPGe statistics of transitions observed at different angles. A $2^+$ state has been confirmed at an excitation energy of 978.1(1) keV. Theoretically, the interplay between isospin-symmetry breaking and shape-coexistence effects in the $A = 62$ isovector triplet is self-consistently treated within the beyond-mean-field complex excited Vampir variational model with symmetry projection before variation using an effective interaction obtained from a G matrix based on the charge-dependent Bonn CD potential adding the Coulomb interaction between the valence protons. Results are presented on Coulomb energy differences, mirror energy differences, triplet energy differences, and the superallowed Fermi $\beta$ decay of the ground state of $^{62}$Ge and $^{62}$Ga.