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

Cluster structures of $^{14}$C were investigated with a method of antisymmetrized molecular dynamics (AMD) combined with a $3α+nn$ cluster model while focusing on the monopole excitations and linear-chain $3α$ 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 $3α+nn$ 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 $3α$ configuration. In addition, the linear-chain $3α$ band from the band-head $0^+_4$ state was obtained. $^{10}$Be$+α$ decay widths of $0^+$, $2^+$, and $4^+$ states were evaluated. $α$ 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 $α$ scattering experiments.

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