Regge Poles and Branch Cuts for Potential Scattering

Abstract

The analytic properties of partial wave amplitudes are studied for complex energy and angular momentum. The properties of the wavefunctions are first obtained by standard methods in the theory of differential equations for general classes of potentials, and the effects of the dominant singular term in the potential near the origin are investigated. These include the appearance of branch cuts in the angular‐momentum variable for potentials which are singular like z⁻², and the location of Regge poles for more singular potentials. The trajectories of Regge poles are also studied with particular reference to their behavior in the angular‐momentum plane as the energy tends to infinity. An example is given of a singular potential in which the trajectories move to infinity in a complex direction, contrary to the normal behavior for which they tend to negative integers. The real sections of Regge surfaces are also briefly discussed.