There is significant evidence supporting the existence of deformed ground states within the neutron-rich $N\approx 20$ neon, sodium, and magnesium isotopes that make up what is commonly called the “island of inversion.” However, the rotational band structures, which are a characteristic fingerprint of a rigid nonspherical shape, have yet to be observed. In this work, we report on a measurement and analysis of the yrast (lowest lying) rotational band in ${}^{32}\mathrm{Mg}$ up to spin $I=6^{+}$ produced in a two-step projectile fragmentation reaction and observed using the state-of-the-art $\gamma$-ray tracking detector array, GRETINA ($\gamma$-ray energy tracking in-beam nuclear array). Large-scale shell-model calculations using the SDPF-U-MIX effective interaction show excellent agreement with the new data. Moreover, a theoretical analysis of the spectrum of rotational states as a function of the pairing gap, together with cranked-shell-model calculations, provides intriguing evidence for a reduction in pairing correlations with increased angular momentum, also in line with the shell-model results.

• Received 7 January 2016

DOI:https://doi.org/10.1103/PhysRevC.93.031303