Intruder dominance in the $0_2^{+}$ state of ${}^{32}\mathrm{Mg}$ studied with a novel technique for in-flight decays

The development of advanced $\gamma$-ray tracking arrays allows for a sensitive new technique to investigate elusive states of exotic nuclei with fast rare-isotope beams. By taking advantage of the excellent energy and position resolution of the Gamma-Ray Energy Tracking In-beam Nuclear Array, we developed a novel technique to identify in-flight isomeric decays of the $0_2^{+}$ state in ${}^{32}\mathrm{Mg}$ populated in a two-proton removal reaction. We confirm the $0_2^{+}\to 2_1^{+}\gamma$-ray transition of ${}^{32}\mathrm{Mg}$ and constrain the $0_2^{+}$ decay lifetime, suggesting a large collectivity. The small partial cross section populating the $0_2^{+}$ state in this reaction provides experimental evidence for the reduced occupancy of the normal configuration of the $0_2^{+}$ state, indicating the intruder dominance of this state.

Figure 1

The present experimental setup. The ${}^9\mathrm{Be}({}^{34}\mathrm{Si},{}^{32}\mathrm{Mg})X$ reaction populates the $0_2^{+}$ isomer which emits a cascade of $\gamma$-rays ${\gamma }_1$ and ${\gamma }_2$ at angles ${\theta }_1$ and ${\theta }_2$ relative to the ion trajectory.

Figure 2

Doppler-corrected $\gamma$-ray energy spectra are shown for data (blue circles), background from the scaled response of beam products excluding the Mg isotopes (black lines), and the sums of the simulated and background responses (red lines). ${}^{31}\mathrm{Mg}$ is shown (a) in the upper spectra and the constraint that the 244-keV transition only interacts within $r=20\mathrm{mm}$ of its first interaction is included in the lower filled spectrum (scaled by 0.5). ${}^{32}\mathrm{Mg}$ is shown (b) with the $r=20-\mathrm{mm}$ gate applied to the coincident $\gamma$ ray in the upper spectrum (scaled by 0.6), and with additional gates requiring proper identification of the interaction points of the 885-keV $\gamma$ ray in the lower filled spectrum. The insets show the number of decays near (250–525 mm) at middistance (525–700 mm) and far from the target (700–1000 mm). The data (open circles) are compared to simulations assuming lifetimes of 5 ns (red solid line), 15 ns (blue dashed line), and 45 ns (black dotted line).

Figure 3

Possible values for partial cross section and lifetime of the $0_2^{+}$ state of ${}^{32}\mathrm{Mg}$ within $1\sigma$ are plotted (gray band). From the work of Ref. [38], the $1\sigma$ upper limit of the cross section at 0.10 mb is included (red line), and the overlap of that work and this Rapid Communication is highlighted (red hatched region).