Low-lying states in $^{32}$Mg studied by proton inelastic scattering

Low-lying excited states in the neutron-rich nucleus $^{32}$Mg were studied by proton inelastic scattering in inverse kinematics via an in-beam $\gamma $-ray spectroscopy technique. Populated states were identified by measuring de-excitation $\gamma $ rays, in which five new states were found by $\gamma -\gamma $ coincidence analyses. The differential cross sections were analyzed by using coupled-channel calculations to determine the transferred angular momenta and the amplitudes of individual transitions. The spin and parity of the 2321-keV state was assigned as 4$^{+}$. The ratio between the energies of the 2$^{+}$ and 4$^{+}$ states indicates that $^{32}$Mg is a transitional nucleus rather than an axially deformed rigid rotor. A candidate for the 3$^{-}$ state was found at an excitation energy of 3115 keV, which is lower than the 3$^{-}$ energies in other N = 20 isotones. A small B(E3) value of 0.6 W.u. suggests a single-particle nature. The collectivities in the nucleus $^{32}$Mg with N = 20 are discussed based on the results obtained in the present experiment.