Abstract
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 $\ensuremath{\alpha}$ clusters in the linear-chain states. By applying this model to the ${}^{14}$C system, we study the ${}^{10}\text{Be}+\ensuremath{\alpha}$ correlation in the linear-chain state of ${}^{14}$C. To clarify the origin of the ${}^{10}\text{Be}+\ensuremath{\alpha}$ correlation in the ${}^{14}$C linear-chain state, we analyze linear $3\phantom{\rule{0.16em}{0ex}}\ensuremath{\alpha}$ and $3\ensuremath{\alpha}\phantom{\rule{0.28em}{0ex}}+\phantom{\rule{0.28em}{0ex}}n$ systems in a similar way. We find that a linear $3\ensuremath{\alpha}$ system prefers the asymmetric $2\ensuremath{\alpha}\phantom{\rule{0.16em}{0ex}}+\phantom{\rule{0.16em}{0ex}}\ensuremath{\alpha}$ 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$\ensuremath{\alpha}$. A linear-chain structure of ${}^{16}$C is also discussed.
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