|m| Partial wave treatment for two-dimensional Coulomb-scattering and Regge pole

Abstract

The symmetry and |m| partial-wave analysis for two-dimensional (2D) Coulomb-scattering is investigated. As a function of energyE, the |m| partial-wave scattering amplitudef |m|(θ) is analytically continuated to the, negativeE (complexk) plane, and it is found that the bound state energy eigenvalues (E<0) are just located at the poles off |m|(θ) on the positive imaginaryk axis as is expected. In addition, as a function of |m|,f |m|(θ) is analytically continuated to the complex |m| plane, the bound state energy eigenvalues are just located at the poles off |m|(θ) on the positive real |m| axis.