# Microsecond Isomer at the N=20 Island of Shape Inversion Observed at FRIB

## TL;DR

This paper reports the first observation of a microsecond isomer at the N=20 island of shape inversion at FRIB, providing insights into nuclear shape coexistence and the underlying structure of $^{32}$Na and $^{32}$Mg.

## Contribution

It presents the discovery of a unique microsecond isomer in $^{32}$Na, linking experimental data with shape coexistence and theoretical models of nuclear deformation.

## Key findings

- Observed a 24(2)-μs isomer in $^{32}$Na
- Identified the isomer as related to shape coexistence in $^{32}$Mg
- Supports deformation-dominated low-lying states in this region

## Abstract

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.