Be-$\alpha$ correlations in the linear-chain structure of C isotopes

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 $^{10}$Be+$\alpha$ correlation in the linear-chain state of $^{14}$C. To clarify the origin of the $^{10}$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.