Scattering theory for arbitrary potentials
  The fundamental quantities of potential scattering theory are generalized to accommodate long-range interactions. New definitions for the scattering amplitude and wave operators valid for arbitrary interactions including potentials with a Coulomb tail are presented. It is shown that for the Coulomb potential the generalized amplitude gives the physical on-shell amplitude without recourse to a renormalization procedure. 
A. S. Kadyrov, I. Bray, A. M. Mukhamedzhanov, A. T. Stelbovics