The generalized two-center cluster model (GTCM), which can treat covalent and atomic configurations in general two-center systems, is applied to the light neutron-excess system ${}^{12}$Be $=$ $\alpha$ $+$ $\alpha$ $+$ 4$N$. The changes of the orbits of the neutrons are analyzed by calculating adiabatic energy surfaces with a variation of the $\alpha$-$\alpha$ distance. The smooth transition from covalent molecular orbits to atomic He-dimer states is realized in the adiabatic energy surfaces. According to this smooth transition, the adiabatic states are divided into two regions, the internal covalent region and the external He-dimer region, by introducing boundaries of the change in structure. The intrinsic structure of the excited energy levels is investigated. We found that, in an unbound region, the He dimers appear as the molecular resonances of $\alpha$ + ${}^8$He${}_{g.s.}$, ${}^6$He${}_{g.s.}$ + ${}^6$He${}_{g.s.}$, and ${}^5$He${}_{g.s.}$ + ${}^7$He${}_{g.s.}$. An exotic superdeformation, which has a hybrid configuration of both the covalent and He-dimer structures, is also realized in the same energy region. These unbound states can be classified into internal and external states, and the excitation degrees of freedom are assigned for the individual states. The level scheme of these unbound states reveals a strong degenerate feature with a considerable mixture of the different configurations. From the result of the level scheme, the “loose clusters” are introduced to characterize the unbound states in the neutron-excess system ${}^{12}$Be.

• Received 16 September 2011

DOI:https://doi.org/10.1103/PhysRevC.85.044308