Strongly coupled rotational band in ${}^{33}\mathrm{Mg}$

The “island of inversion” at $N\approx 20$ for the neon, sodium, and magnesium isotopes has long been an area of interest both experimentally and theoretically due to the subtle competition between 0p-0h and $n\mathrm{p}-n\mathrm{h}$ configurations leading to deformed shapes. However, the presence of rotational band structures, which are fingerprints of deformed shapes, have only recently been observed in this region. In this work, we report on a measurement of the low-lying level structure of ${}^{33}\mathrm{Mg}$ populated by a two-stage projectile fragmentation reaction and studied with the Gamma Ray Energy Tracking In-Beam Nuclear Array (GRETINA). The experimental level energies, ground-state magnetic moment, intrinsic quadrupole moment, and $\gamma$-ray intensities show good agreement with the strong-coupling limit of a rotational model.

Figure 1

The fragments were identified using energy loss and total kinetic energy measurements from the S800 focal plane detector suite. The magnesium isotopes at $Z$ = 12 are highlighted, with ${}^{33}\mathrm{Mg}$ highlighted with a black circle.

Figure 2

The Doppler reconstructed $\gamma$-ray spectrum of ${}^{33}\mathrm{Mg}$ (a) detected with GRETINA (using clustering) following the secondary fragmentation of the beam. Transitions in ${}^{33}\mathrm{Mg}$ are marked with their energies in black; the transition marked with a red circle corresponds to a $\gamma$ ray in the neighboring isotope, ${}^{32}\mathrm{Mg}$. The transition at 1175 keV corresponds to a weak, unplaced transition in ${}^{33}\mathrm{Mg}$. Panel (b) shows the background-subtracted, clustered $\gamma -\gamma$ projection of the 297-keV $\gamma$ ray. Clear coincidence can be seen with the 483-keV ground-state transition.

Figure 3

The level scheme of ${}^{33}\mathrm{Mg}$ based upon $\gamma$-ray singles, $\gamma -\gamma$ coincidence data, and literature placements. The width of the arrows is representative of the relative intensity of the transition. All $\gamma$-ray transitions were measured with 4-keV uncertainty.

Figure 4

The calculations for $\lambda , Q_0$, and $\mu$ are shown in the three panels. The measured values are denoted with dashed blue lines with shaded error bands. The error band on the experimental value of $\mu$ is sufficiently small and appears as a line instead of an error band. The vertical red error band denotes the agreement range for the calculated $\lambda$ and experimental value and the green vertical band denotes the range where the calculated $Q_0$ and the experimental value agree.