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

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.

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Cited by in corpus (8)

• Shape coexistence in even-even nuclei: A theoretical overview
• The structure of ${}^{36}$Ca under the Coulomb magnifying glass
• Isospin symmetry breaking in the mirror pair ${}^{73}$Sr-${}^{73}$Br
• Evaluation of the ${}^{35}$K($p$,$\gamma$)${}^{36}$Ca reaction rate using the ${}^{37}$Ca($p$,$d$)${}^{36}$Ca transfer reaction
• Probing proton cross-shell excitations through the two-neutron removal from 38Ca
• Puzzling $B(E2;0^{+}\to 2^{+})$ strength in the proton dripline nucleus ${}^{36}$Ca
• Search for the $1/2^{+}$ intruder state in ${}^{35}$P
• In-beam $\gamma$-ray spectroscopy of negative-parity states of ${}^{37}$K populated in dissipative reactions