Hoyle-analogue state in 13C studied with Antisymmetrized Molecular Dynamics

Abstract

The cluster states in ${}^{13}\mathrm{C}$ are investigated by antisymmetrized molecular dynamics. By investigating the spectroscopic factors, the cluster configurations of the excited states are discussed. It is found that the $1/2_2^{+}$ state is dominantly composed of the ${}^{12}\mathrm{C}(0_2^{+})\otimes s_{1/2}$ configuration and can be regarded as a Hoyle analogue state. On the other hand, the p-wave states ($3/2^{-}$ and $1/2^{-}$) do not have such structure, because of the coupling with other configurations. The isoscalar monopole and dipole transition strengths from the ground to the excited states are also studied. It is shown that the excited $1/2^{-}$ states have strong isoscalar monopole transition strengths consistent with the observation. On the other hand, the excited $1/2^{+}$ states unexpectedly have weak isoscalar dipole transitions except for the $1/2_1^{+}$ state. It is discussed that the suppression of the dipole transition is attributed to the property of the dipole operator.