In-beam γ -ray spectroscopy of Mg32 via direct reactions

Background: The nucleus $^{32}\mathrm{Mg}$ ($N=20$ and $Z=12$) plays a central role in the so-called ``island of inversion,'' where in the ground states $sd$-shell neutrons are promoted to the $fp$-shell orbitals across the shell gap, resulting in the disappearance of the canonical neutron magic number $N=20$.Purpose: The primary goals of this work are to extend the level scheme of $^{32}\mathrm{Mg}$, provide spin-parity assignments to excited states, and discuss the microscopic structure of each state through comparisons with theoretical calculations.Method: In-beam $\ensuremath{\gamma}$-ray spectroscopy of $^{32}\mathrm{Mg}$ was performed using two direct-reaction probes: one-neutron (two-proton) knockout reactions on $^{33}\mathrm{Mg}$ ($^{34}\mathrm{Si}$). Final-state exclusive cross sections and parallel momentum distributions were extracted from the experimental data and compared with eikonal-based reaction model calculations combined with shell-model overlap functions.Results: Owing to the remarkable selectivity of the one-neutron and two-proton knockout reactions, a significantly updated level scheme for $^{32}\mathrm{Mg}$, which exhibits negative-parity intruder and positive-parity normal states, was constructed. The experimental results were confronted with four different nuclear structure models.Conclusions: In some of these models, different aspects of $^{32}\mathrm{Mg}$ and the transition into the island of inversion are well described. However, unexplained discrepancies remain, and, even with the help of these state-of-the-art theoretical approaches, the structure of this key nucleus is not yet fully captured.