Shape coexistence and superdeformation in ${}^{28}$Si

We study the shape coexistence of differently deformed states within ${}^{28}$Si using shell-model and beyond-mean-field techniques. Experimentally, ${}^{28}$Si exhibits shape coexistence between an oblate ground state and an excited prolate structure. The oblate rotational band is described well within the $sd$ shell using the USDB interaction. However, for the prolate band, a modification of this interaction is required, lowering the single-particle energy of the $1d_{3\mathrm{/}2}$ orbit. Furthermore, we explore the possibility of a superdeformed configuration in ${}^{28}$Si. Our calculations, spanning both the $sd$ and $pf$ shells, rule out the existence of a superdeformed $0^{+}$ bandhead within an excitation energy range of 10-20 MeV.