Cluster structures and monopole transitions of $^{14}$C

TL;DR

This paper investigates the cluster structures and monopole excitations of $^{14}$C using AMD and cluster models, identifying vibrational and linear-chain configurations, and proposing experimental observation methods.

Contribution

It introduces a combined AMD and cluster model approach to analyze $^{14}$C structures, revealing new vibrational and linear-chain states and their decay properties.

Findings

Identification of a vibrational $0^+_3$ state with strong monopole transition

Prediction of a linear-chain $3eta$ band in $^{14}$C

Evaluation of $^{10}$Be$+ ext{alpha}$ decay widths

Abstract

Cluster structures of $^{14}$C were investigated with a method of antisymmetrized molecular dynamics (AMD) combined with a $3\alpha+nn$ cluster model while focusing on the monopole excitations and linear-chain $3\alpha$ band. Variation after parity and angular momentum projections was performed in the AMD framework, and the generator coordinate method was applied to take into account various $3\alpha+nn$ cluster configurations. Energy spectra and monopole and $E2$ transition strengths of $0^+$, $2^+$, and $4^+$ states were calculated to assign band structures. The $0^+_3$ state with remarkable monopole transition was obtained as a vibrational mode of the triangle $3\alpha$ configuration. In addition, the linear-chain $3\alpha$ band from the band-head $0^+_4$ state was obtained. $^{10}$Be$+\alpha$ decay widths of $0^+$, $2^+$, and $4^+$ states were evaluated. $\alpha$ inelastic scattering off $^{14}$C was also investigated by the microscopic coupled-channel calculation with the $g$-matrix folding model to propose possible observation of the $0^+_3$ state via $\alpha$ scattering experiments.