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

The decay properties of the linear-chain states in ${}^{14}\mathrm{C}$ are investigated by using 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 ${}^{10}\mathrm{Be}$ reasonably agree with the experimental candidates observed by the $\alpha +{}^{10}\mathrm{Be}$ resonant scattering. On the other hand, the $\sigma$-bond linear-chain is the candidate of the higher-lying resonant states reported by the breakup 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 ${}^{10}\mathrm{Be}$ but also decays to the three-body channel of ${}^6\mathrm{He}+\alpha +\alpha$, 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.

Figure 1

Schematic figure showing the Brink–Bloch wave function.

Figure 2

The density distribution of (a) ${}^8\mathrm{Be}$, the positive-parity states of ${}^{10}\mathrm{Be}$ with valence neutrons in a (b) $\pi$ orbit and (c) $\sigma$ orbit, and (d), (e) negative-parity states of ${}^{10}\mathrm{Be}$. The contour lines show the proton density distributions. The color plots in panels (b) and (c) show the single-particle orbits occupied by the most weakly bound neutron. In the negative-parity state, the color plots of panel (d) show the single-particle orbits occupied by the most weakly bound neutron, and those of panel (e) show the other valence neutron.

Figure 3

The positive-parity energy levels up to $J^{\pi }=8^{+}$. Filled circles show the resonances with the definite spin-parity assignments observed in the $\alpha +{}^{10}\mathrm{Be}$ resonant scattering [36, 37, 39]. Blue line shows the resonance at 22.5 MeV without spin-parity assignment observed in the breakup reaction [41]. Filled boxes show the calculated linear-chain bands, while lines show the other states. Only even angular momenta are shown.

Figure 4

The density distribution of the linear-chain configurations of ${}^{14}\mathrm{C}$, with valence neutrons in a (a) $\pi$ orbit and (b) $\sigma$ orbit. The contour lines show the proton density distributions. The color plots show the single-particle orbits occupied by the most weakly bound neutron.

Figure 5

Schematic figure showing the $\pi$ and $\sigma$ orbits around the linear chain. The combination of the $p$ orbits perpendicular to the symmetry axis generates $\pi$ orbits, while the combination of parallel orbits generates $\sigma$ orbit.

Figure 6

Calculated $\alpha$- and ${}^6\mathrm{He}$-decay reduced widths up to $J^{\pi }=8^{+}$. Panels (a) and (b) show the decay to the ground band of ${}^{10}\mathrm{Be}(\pi$-bonded ${}^{10}\mathrm{Be}$). Panels (c) and (d) show the decay to the excited band of ${}^{10}\mathrm{Be}$ ($\sigma$-bonded ${}^{10}\mathrm{Be}$). Panels (e) and (f) show the decay to the negative-parity states of ${}^{10}\mathrm{Be}$. Panels (g) and (h) show the decay to the ground band of ${}^8\mathrm{Be}$. The $l$ denotes the relative motion between $\mathrm{Be}\left(2^{+}\right)$ and $\alpha$ particle. The channel radius $a$ is 6.0 fm.