The formation of intruder states in the low-lying states of ${}^{12}\mathrm{Be}=\alpha +\alpha +4N$ is studied by applying the generalized two-center cluster model, which can optimize the excess neutrons' orbits depending on the $\alpha -\alpha$ 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 $\alpha$ clusters and the binary He-cluster picture. In the covalent picture, the binding energy of ${\left({\pi }_{32}^{-}\right)}^2{\left({\sigma }_{12}^{+}\right)}^2$, corresponding to $\nu {\left(0p\right)}^4{\left(1s0d\right)}^2$ 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 $\nu {\left(0p\right)}^4{\left(1s0d\right)}^2$ configuration becomes dominant in the ground state. In the binary cluster picture, the correlation energy is investigated from the coupled channels among $\alpha +{}^8\mathrm{He}$, ${}^6\mathrm{He}+{}^6\mathrm{He}$, 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.

• Received 5 May 2011

DOI:https://doi.org/10.1103/PhysRevC.85.014302