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

Abstract: 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, $3/2^-_1$, is predominantly composed of the intruder prolate one-quasiparticle (1qp) configuration $\nu1/2^-[321]$. In contrast, the $7/2^-_1$ state is identified as a high-$K$ isomer, primarily built on the prolate 1qp configuration $\nu7/2^-[303]$. Additionally, the $3/2^-_2$ state is found to be an admixture dominated by an oblate configuration with $K^\pi = 1/2^-$, along with a small contribution from a prolate configuration with $K^\pi = 3/2^-$. 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 $N = 28$.