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

## TL;DR

This paper investigates the decay properties of linear-chain states in carbon-14 using antisymmetrized molecular dynamics, predicting two rotational bands with distinct neutron bonding configurations and analyzing their decay patterns to identify signatures of linear-chain formation.

## Contribution

It introduces a theoretical prediction of two different linear-chain configurations in $^{14}$C and analyzes their decay patterns, providing key observables to distinguish these configurations from experimental data.

## Key findings

- Predicted two rotational bands with $ ext{pi}$-bond and $ ext{sigma}$-bond configurations.
- The $ ext{pi}$-bond band agrees with experimental $ ext{alpha}$-decay data.
- The $ ext{sigma}$-bond band decays to excited $^{10}$Be$^*$ and $^{6}$He+$ ext{alpha}$+$ ext{alpha}$ channels.

## Abstract

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.