Extension of the Integral Formulation of Scattering Theory to Coulomb Interactions

Abstract

The integral formulation of scattering theory is extended to the treatment of a residual interaction with a Coulomb tail. The approach involves expanding the Green's function in a basis set and then finding the proper analytical treatment of the familiar pole as well as of other singularities in the kernel which are peculiar to long-range interactions. The pure Coulomb case is given as an example of the formulation. Methods of reducing the integral equations to an algebraic set are given for a residual interaction with arbitrary short-range form and a Coulomb tail. Finally, the extension of this procedure to many channels is described.