Multireference covariant density functional theory for shape coexistence and isomerism in ${}^{43}$S

We extend the multireference covariant density functional theory (MR-CDFT) to describe the low-lying states of the odd-mass nucleus ${}^{43}$S near the neutron magic number $N=28$ with shape coexistence. The wave functions of the low-lying states are constructed as superpositions of configurations with different intrinsic shapes and $K$ quantum numbers, projected onto good particle numbers and angular momenta. The MR-CDFT successfully reproduces the main features of the low-energy structure in ${}^{43}$S. Our results indicate that the ground state, $3\mathrm{/}{2}_1^{-}$, is predominantly composed of the intruder prolate one-quasiparticle (1qp) configuration $\nu 1\mathrm{/}{2}^{-}[321]$. In contrast, the $7\mathrm{/}{2}_1^{-}$ state is identified as a high-$K$ isomer, primarily built on the prolate 1qp configuration $\nu 7\mathrm{/}{2}^{-}[303]$. Additionally, the $3\mathrm{/}{2}_2^{-}$ state is found to be an admixture dominated by an oblate configuration with $K^{\pi }=1\mathrm{/}{2}^{-}$, along with a small contribution from a prolate configuration with $K^{\pi }=3\mathrm{/}{2}^{-}$. These results demonstrate the capability of MR-CDFT to capture the intricate interplay among shape coexistence, $K$-mixing, and isomerism in the low-energy structure of odd-mass nuclei around $N=28$.