Spectroscopy of 12C within the boundary condition for three-body resonant states

Abstract

The 3 α-cluster structure of excited states in 12C is investigated by taking into account the correct boundary condition for three-body resonant states. In this study, we adopt the Complex Scaling Method (CSM), which enables us to obtain the resonant states that can be described as square integrable states with the same boundary conditions as those of the bound states, and calculate not only resonance energies but also the total decay widths of the 3 α system. We compare the calculated resonance parameters to the experimental data and also to the previous 3 α model results obtained with a bound state approximation. Our results well explain the many observed levels and give an assurance for the presence of the second 2 + state, which is expected by the 3 α model calculations with the approximations of bound state or two-body scattering. As for the negative-parity states, it is considered that the calculated 4 − state is assigned to the observed E x = 13.4 MeV state. Through the calculation of channel amplitudes, the obtained third 0 + state is found to have a s-wave dominant and a more dilute structure compared to the second 0 + state.