High-precision $Q_{EC}$-value measurement of the superallowed $β^+$ emitter $^{22}$Mg and an evaluation of the $A=22$ isobaric triplet

A direct $Q_{EC}$-value measurement of the superallowed $β^+$ emitter $^{22}$Mg was performed using TRIUMF's Ion Trap for Atomic and Nuclear science (TITAN). The direct ground-state to ground-state atomic mass difference between $^{22}$Mg and $^{22}$Na was determined to be $Q_{EC}=4781.40(22)$~keV, representing the most precise single measurement of this quantity to date. In a continued push towards calculating superallowed isospin-symmetry-breaking (ISB) corrections from first principles, ab-initio shell-model calculations of the $A=22$ IMME are also presented for the first time using the valence-space in-medium similarity renormalization group formalism. With particular starting two- and three-nucleon forces, this approach demonstrates a level of agreement with the experimental data that suggests reliable ab-initio calculations of superallowed ISB corrections are now possible.