Isospin symmetry breaking in the $T=3/2$ mirror pair $^{73}$Sr - $^{73}$Br

Recently, Hoff {\it et al.} reported the results of a measurement carried out at MSU-NSCL [1], in which the decay of the proton-rich, $T=3/2$, $T_{z}$=-3/2, isotope $^{73}$Sr was studied. The experimental data is consistent with a $I^{\pi}$= 5/2$^{-}$ ground state, which inverts relative to its mirror $T_{z}$=3/2 partner $^{73}$Br which has $I^{\pi}$= 1/2$^{-}$. In this work, we propose an explanation within the framework of the shell model for the nuclear part of the problem, plus a detailed treatment of the Coulomb and other isospin-symmetry breaking effects in line with the findings of Refs.~[2,3]. In the present calculation we use the ${0f_{7/2}}$, ${1p_{3/2}}$, ${0f_{5/2}}$, ${1p_{1/2}}$, ${0g_{9/2}}$ and ${1d_{5/2}}$ valence space with the single particle energies taken directly from the experimental spectra of $^{41}$Ca. We show that the large scale shell-model results reproduce well the observed inversion, with the Coulomb interaction playing a dominant role in breaking the isospin symmetry in the $^{73}$Sr - $^{73}$Br mirror pair.\\ [1] E. M. Hoff, {\it et al.}, Nature {\bf 580} 52 (2020).\\ [2] A.P.Zuker, {\it et al.}, Phys. Rev. Lett {\bf 89} 142502 (2002). \\ [3] M. Bentley and S. M. Lenzi, PPNP {\bf 59} 497 (2007).