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

Excited-state spectroscopy from the first experiment at the Facility for Rare Isotope Beams (FRIB) is reported. A $24(2)\text{−}\mathrm{\mu }\mathrm{s}$ isomer was observed with the FRIB Decay Station initiator (FDSi) through a cascade of 224- and 401-keV $\gamma$ rays in coincidence with ${}^{32}\mathrm{Na}$ nuclei. This is the only known microsecond isomer ($1\mathrm{\mu }\mathrm{s}\le T_{1/2}<1\mathrm{ms}$) in the region. This nucleus is at the heart of the $N=20$ island of shape inversion and is at the crossroads of the 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 ${}^{32}\mathrm{Mg}$, ${}^{32}\mathrm{Mg}+{\pi }^{-1}+{\nu }^{+1}$. This odd-odd coupling and isomer formation provides a sensitive measure of the underlying shape degrees of freedom of ${}^{32}\mathrm{Mg}$, 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 ${}^{32}\mathrm{Na}$: 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.

Figure 1

(a): $\gamma$-ray spectrum following implanted ${}^{32}\mathrm{Na}$ ions (black), and $\gamma$-ray spectrum in coincidence with 401-keV $\gamma$ rays and following implanted ${}^{32}\mathrm{Na}$ ions (red). (b): $\gamma$-ray energy versus time difference of $\gamma$ ray and ${}^{32}\mathrm{Na}$ implant.

Figure 2

The $\gamma$-implant time distribution formed by the sum of 224- and 401-keV $\gamma$ gates. An exponential maximum-likelihood fit is shown with the solid red line. The dashed red line shows the constant baseline.

Figure 3

Schematic representation of (a) $6^{-}$ spherical shape isomer and (b) $0^{+}$ deformed spin isomer.

Figure 4

Comparison of calculated and proposed experimental level schemes. Deformed $0^{-}$, $3^{-}$, and $0^{+}$ band heads are present with associated rotational bands. The “m$p$-n$h$” language refers to the number of neutron particles above and neutron holes below the $N=20$ shell closure, where mixing of the cross-shell excitations is predicted.

Figure 5

Single-particle occupancies from Nilsson, SDPF-U-MIX, and VS-IMSRG calculations: (a) Occupancies for the $0^{+}$ state, (b) Occupancies for the $0^{-}$ state, and (c) Difference between occupancies of the $0^{+}$ and $0^{-}$ states, highlighting the strong $\nu f_{7/2}\to \nu d_{3/2}$ nature of the $M2$ transition. The occupancies of the $2^{-}$ and $0^{-}$ states are near identical in all three calculations, where the former is a rotation built upon the latter.