Explanation of the nature of the island of inversion exhibited by ³²Mg at the Hartree-Fock-Bogoliubov level and beyond*

Abstract This study presents an explanation of the nature of the island of inversion exhibited by the unstable nucleus 32 Mg through the application of the axially deformed relativistic Hartree-Fock-Bogoliubov (D-RHFB) and configuration-interaction relativistic Hartree-Fock (CI-RHF) models, which correspond to the Hartree-Fock-Bogoliubov level and beyond, respectively. Using the same Lagrangian PKA1, the D-RHFB and CI-RHF models demonstrate an excellent agreement with experimental data for the ground-state deformation and the low-lying excitation energies of 32 Mg. Furthermore, a new insight into the nature of the island of inversion is implemented from the breaking of the pseudo-spin symmetry (PSS) in addition to the cross-shell excitation, both of which are essential to obtaining a stable deformation and rotational collectivity for 32 Mg. In particular, the exchange degrees of freedom, such as the ρ -tensor coupling in PKA1, are shown to be essential in determining the configuration interactions and binding of the nucleus.