Ab initio study of island of inversion in odd-$A$ nuclei: Structure of $^{31,33}$Mg

Abstract: We study the $N=20$ island of inversion region in the odd-$A$ Ne and Mg isotopes from the fundamental nuclear forces based on chiral two- and three-nucleon potentials. The state-of-the-art \textit{ab initio} valence space in medium similarity renormalization method was used for this purpose. Our study focuses on the evolution of single-particle states and discusses their transition into the island of inversion through particle-hole excitations across the $N=20$ shell gap. The computed low-lying states and magnetic moments are in good agreement with the experimental data. We presented the rotational band structures, established via $E2$ transitions, in $^{31}$Mg and $^{33}$Mg, which emerge from both normal and intruder configurations at low excitation energies. Our results suggest the presence of weak, moderate, and strongly prolate-deformed configurations at low energy in both isotopes. The present work offers valuable insights into the configurations and shapes of low-lying states in nuclei within the island of inversion, enhancing our understanding of the structures of exotic nuclei from first principles.