Broken mirror symmetry in S36 and Ca36

Shape coexistence is a ubiquitous phenomenon in the neutron-rich nuclei belonging to (or sitting at the shores of) the $N=20$ island of inversion (IoI). Exact isospin symmetry predicts the same behavior for their mirrors and the existence of a proton-rich IoI around $Z=20$, centered in the (surely unbound) nucleus $^{32}\mathrm{Ca}$. In this article we show that in $^{36}\mathrm{Ca}$ and $^{36}\mathrm{S}$, Coulomb effects break dramatically the mirror symmetry in the excitation energies due to the different structures of the intruder and normal states. The mirror energy difference (MED) of their ${2}^{+}$ states is known to be very large at $\ensuremath{-}246$ keV. We reproduce this value and predict the first excited state in $^{36}\mathrm{Ca}$ to be a ${0}^{+}$ at 2.7 MeV, 250 keV below the first ${2}^{+}$. In its mirror $^{36}\mathrm{S}$ the ${0}^{+}$ lies at 55 keV above the ${2}^{+}$ measured at 3.291 MeV. Our calculations predict a huge MED of $\ensuremath{-}720$ keV, that we dub the ``colossal'' mirror energy difference. A possible reaction mechanism to access the ${0}_{2}^{+}$ in $^{36}\mathrm{Ca}$ will be discussed. In addition, we theoretically address the MEDs of the $A=34,\phantom{\rule{4pt}{0ex}}T=3$ and $A=32,\phantom{\rule{4pt}{0ex}}T=4$ mirrors.