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

TL;DR

This paper investigates the breakdown of mirror symmetry in the excitation energies of $^{36}$S and $^{36}$Ca due to Coulomb effects, predicting a colossal mirror energy difference and exploring implications for nuclear structure near the Island of Inversion.

Contribution

It provides the first detailed theoretical analysis of Coulomb-induced mirror symmetry breaking in $^{36}$S and $^{36}$Ca, predicting a colossal mirror energy difference and new excited state configurations.

Findings

Reproduces the known large MED of -246 keV for 2+ states.

Predicts a 0+ excited state in $^{36}$Ca at 2.7 MeV, below the first 2+ state.

Forecasts a colossal MED of -720 keV, termed 'Colossal' Mirror Energy Difference (CMED).

Abstract

Shape coexistence is an 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 behaviour for their mirrors and the existence of a proton-rich IoI around $Z=20$, centred in the (surely unbound) nucleus $^{32}$Ca. In this article we show that in $^{36}$Ca and $^{36}$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 -246 keV. We reproduce this value and predict the first excited state in $^{36}$Ca to be a 0$^+$ at 2.7 MeV, 250 keV below the first 2$^+$. In its mirror $^{36}$S the 0$^+$ lies at 55 keV above the 2$^+$ measured at 3.291 MeV. Our calculations predict a huge MED of -720 keV, that we dub "Colossal" Mirror Energy Difference (CMED). A possible reaction mechanism to access the 0$^+_2$ in $^{36}$Ca will be discussed. In addition, we theoretically address the MED's of the $A=34$ $T=3$ and $A=32$ $T=4$ mirrors.