1/2${}^{-}$ $\alpha$ cluster resonances of ${}^{13}$C studied by the analytic continuation in the coupling constant

Abstract

The 1/2${}^{-}$ resonant states in ${}^{13}\mathrm{C}$ are investigated to search for the Hoyle-analog state. In order to treat the resonance states located around the 3$\alpha +n$ threshold, the analytic continuation in the coupling constant (ACCC) has been combined with the real-time evolution method (REM). The properties of the 1/2${}^{-}$ resonance states such as the radii and monopole transition probabilities are calculated. We show the 1/2${}_3^{-}$ and 1/2${}_4^{-}$ states are well-developed $\alpha$ cluster states, and the 1/2${}_4^{-}$ state is a candidate of the Hoyle-analog state.