Broken mirror symmetry in $^{36}$S and $^{36}$Ca

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 Ca-32. In this article we show that in Ca-36 and S-36, 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 - 246 keV. We reproduce this value and predict the first excited state in Ca-36 to be a 0(+) at 2.7 MeV, 250 keV below the first 2(+). In its mirror S-36 the 0(+) lies at 55keV above the 2(+) measured at 3.291 MeV. Our calculations predict a huge MED of -720 keV, that we dub the "colossal" mirror energy difference. A possible reaction mechanism to access the O-2(+) in Ca-36 will be discussed. In addition, we theoretically address the MEDs of the A = 34, T = 3 and A = 32, T = 4 mirrors.