Excited-state spectroscopy from the first Facility for Rare Isotope Beams (FRIB) experiment is reported. A 24(2)-$\mu$s isomer was observed with the FRIB Decay Station initiator (FDSi) through a cascade of 224- and 401-keV $\gamma$ rays in coincidence with $^{ 32}\textrm{ Na}$ nuclei. This is the only known microsecond isomer ($1{ \text{ }\mu\text{ s}}\leq T_{ 1/2} < 1\text{ ms}$) in the region. This nucleus is at the heart of the $N=20$ island of shape inversion and is at the crossroads of spherical shell-model, deformed shell-model, and ab initio theories. It can be represented as the coupling of a proton hole and neutron particle to $^{ 32}\textrm{ Mg}$, $^{ 32}\textrm{ Mg}+\pi^{ -1} + \nu^{ +1}$. This odd-odd coupling and isomer formation provides a sensitive measure of the underlying shape degrees of freedom of $^{ 32}\textrm{ Mg}$, where the onset of spherical-to-deformed shape inversion begins with a low-lying deformed $2^+$ state at 885 keV and a low-lying shape-coexisting $0_2^+$ state at 1058 keV. We suggest two possible explanations for the 625-keV isomer in $^{ 32}$Na: a $6^-$ spherical shape isomer that decays by $E2$ or a $0^+$ deformed spin isomer that decays by $M2$. The present results and calculations are most consistent with the latter, indicating that the low-lying states are dominated by deformation.
Categories: nucl-ex