Cluster correlations for low-lying intruder states of12Be

Abstract

The formation of intruder states in the low-lying states of ${}^{12}\mathrm{Be}=\ensuremath{\alpha}+\ensuremath{\alpha}+4N$ is studied by applying the generalized two-center cluster model, which can optimize the excess neutrons' orbits depending on the $\ensuremath{\alpha}\ensuremath{-}\ensuremath{\alpha}$ distance. The correlation energy for the intruder states is analyzed from the viewpoint of two different pictures based on the cluster structure: the covalent picture around two $\ensuremath{\alpha}$ clusters and the binary He-cluster picture. In the covalent picture, the binding energy of ${({\ensuremath{\pi}}_{32}^{\ensuremath{-}})}^{2}{({\ensuremath{\sigma}}_{12}^{+})}^{2}$, corresponding to $\ensuremath{\nu}{(0p)}^{4}{(1s0d)}^{2}$ in a naive shell model, gains largely owing to the spin-triplet pairing of the $0d$-wave neutrons, which is induced by the two-body spin-orbit interaction. The spin-triplet pairing gives rise to the reduction of the kinetic energy and the increase of the attractive spin-orbit interaction for the excess neutrons. As a result of these correlation energies, the $\ensuremath{\nu}{(0p)}^{4}{(1s0d)}^{2}$ configuration becomes dominant in the ground state. In the binary cluster picture, the correlation energy is investigated from the coupled channels among $\ensuremath{\alpha}+{}^{8}\mathrm{He}$, ${}^{6}\mathrm{He}+{}^{6}\mathrm{He}$, and ${}^{5}\mathrm{He}+{}^{7}\mathrm{He}$. The coupling to ${}^{5}\mathrm{He}+{}^{7}\mathrm{He}$, which is neglected in usual binary-cluster models, plays an important role for a large reduction of kinetic energy and the formation of a pair of the low-lying 0${}^{+}$ states with a close energy spacing recently observed in experiment. The rotational bands are also discussed from the viewpoint of these two cluster pictures.