Application of complex transition density to nuclear reaction and effect of phase factor

Complex transition density can be constructed by a nuclear structure model with a complex basis and/or complex coefficient. In general, the complex transition density is converted to the real one with phase factor. In this study, we apply the complex transition density directly to the microscopic reaction model. We compare with scattering cross sections calculated with the real and complex transition densities in the frameworks of the optical model, the distorted wave Born approximation, and the coupled-channel (CC) calculation, respectively. In addition, we investigate the dependence of the phase factor for the transition density in the elastic and inelastic cross sections. The effect of the phase factor on the elastic and inelastic cross sections can be seen in the CC calculation. Finally, we found an important role of the phase factor in the nuclear elastic and inelastic scatterings.Comment: I found a mistake. The sign of the phase depends on the direction of the transition. However, the calculation and formulation in this manuscript do not incorporate that dependence. Since the results and conclusions change, this manuscript is withdraw