A fredholm integral equation method for scattering phase shifts

Abstract

A method is presented for obtaining exact scattering phase shifts using an integral equation formulation. It is similar to recent work by Reinhardt and Szabo but differs in that in the integral equation used, no inherent singularities have to be avoided. The method has been applied to both the exponential and screened coulomb potentials, and has proved to be complementary to the method of numerically integrating the radial equation-this Fredholm integral method converges more quickly for non-zero angular momentum and/or high impact energies. It is, however, applicable to all angular momenta and at all energies, including the zero-energy limit. The main drawback is that knowledge of the second born off-shell matrix elements for the potential is required.