We investigate the linear-chain structures in highly excited states of ${}^{14}$C using a generalized molecular-orbital model, by which we incorporate an asymmetric configuration of three $\alpha$ clusters in the linear-chain states. By applying this model to the ${}^{14}$C system, we study the ${}^{10}\text{Be}+\alpha$ correlation in the linear-chain state of ${}^{14}$C. To clarify the origin of the ${}^{10}\text{Be}+\alpha$ correlation in the ${}^{14}$C linear-chain state, we analyze linear $3\alpha$ and $3\alpha +n$ systems in a similar way. We find that a linear $3\alpha$ system prefers the asymmetric $2\alpha +\alpha$ configuration, whose origin is the many-body correlation incorporated by the parity projection. This configuration causes an asymmetric mean field for two valence neutrons, which induces the concentration of valence neutron wave functions around the correlating 2$\alpha$. A linear-chain structure of ${}^{16}$C is also discussed.

• Received 7 March 2011

DOI:https://doi.org/10.1103/PhysRevC.84.024328