A new amplitude-phase method for analyzing scattering solutions of the radial Dirac equation

Abstract

A novel amplitude-phase method for analyzing radial Dirac solutions is presented. This approach addresses the original coupled radial Dirac equations without first transforming them to decoupled second-order differential equations. As a reference test, the method is applied to the scattering problem of a Dirac particle (electron) in a long-range Coulomb 4-vector potential with zero space components. Numerical results for the partial-wave S-matrix are compared with those from an exact analytic S-matrix formula.