Discovery of the Shape Coexisting $0^{+}$ State in ${}^{32}\mathrm{Mg}$ by a Two Neutron Transfer Reaction

The “island of inversion” nucleus ${}^{32}\mathrm{Mg}$ has been studied by a ($t$, $p$) two neutron transfer reaction in inverse kinematics at REX-ISOLDE. The shape coexistent excited $0^{+}$ state in ${}^{32}\mathrm{Mg}$ has been identified by the characteristic angular distribution of the protons of the $\Delta L=0$ transfer. The excitation energy of 1058 keV is much lower than predicted by any theoretical model. The low $\gamma$-ray intensity observed for the decay of this $0^{+}$ state indicates a lifetime of more than 10 ns. Deduced spectroscopic amplitudes are compared with occupation numbers from shell-model calculations.

Figure 1

Energy versus ${\vartheta }_{\mathrm{lab}}$ spectrum for ${}^{30}\mathrm{Mg}$ on the tritium target for unambiguously identified protons. The two lines show the kinematic curves for the ground state (solid) and an excited state at 1.1 MeV (dashed).

Figure 2

Excitation energy of the ejectile ${}^{32}\mathrm{Mg}$ reconstructed from the measured energy of protons in T-REX. The excitation energy of the observed state amounts to 1083(33) keV.

Figure 3

$\gamma$-ray energy spectrum in coincidence with protons from transfer to the excited state. The inset shows the suggested partial level scheme of ${}^{32}\mathrm{Mg}$.

Figure 4

Proton angular distributions for the reaction $t({}^{30}\mathrm{Mg},p){}^{32}\mathrm{Mg}$ populating the ground state (a) and the 1058 keV state (b). The curves in panel a) are from DWBA calculations with fitted (solid) and global (dashed) optical model parameters [34]. Panel b) includes DWBA calculations for $\Delta L=0$ (solid), $\Delta L=1$ (dashed) and $\Delta L=2$ (dotted) transfer. The angle range around ${\vartheta }_{\mathrm{cm}}=50°$ corresponds to ${\vartheta }_{\mathrm{lab}}=90°$ which is not covered by the T-REX detector.