Studying resonance in the complex charge plane

Abstract

Potential resonances are usually investigated either directly in the complex energy plane or indirectly in the complex angular momentum plane. Another formulation complementing these two is presented in this work. It is an indirect method which studies resonances in a complex charge plane (Z-plane). The complex scaling (rotation) method is employed in the development of this formulation. Bound states spectrum and resonance energies are mapped onto a discrete set of poles of a resolvent operator on the real line of the Z-plane. These poles move along trajectories as we vary the energy. A finite L2 basis is used in the numerical implementation of the method. Stability of poles and trajectories against variations in all computational parameters is demonstrated. Resonances for a given potential example are calculated and compared with those obtained elsewhere. In this presentation, modest effort will be devoted to mathematical rigor.