Three-body decay of linear-chain states in $^{14}$C

The decay properties of the linear-chain states in $^{14}$C are investigated by using the antisymmetrized molecular dynamics. The calculation predicts two rotational bands with linear-chain configurations having the $\pi$-bond and $\sigma$-bond valence neutrons. For the $\pi$-bond linear-chain, the calculated excitation energies and the widths of $\alpha$-decay to the ground state of $^{10}{\rm Be}$ reasonably agree with the experimental candidates observed by the $\alpha+{}^{10}{\rm Be}$ resonant scattering. On the other hand, the $\sigma$-bond linear-chain is the candidate of the higher-lying resonant states reported by the break-up reaction. As the evidence of the $\sigma$-bond linear-chain, we discuss its decay pattern. It is found that the $\sigma$-bond linear-chain not only decays to the excited band of $^{10}{\rm Be}$ but also decays to the three-body channel of $^{6}{\rm He}+\alpha+\alpha$, and the branching ratio of these decays are comparable. Hence, we suggest that this characteristic decay pattern is a strong signature of the linear-chain formation and a key observable to distinguish two different linear-chains.