On the applicability of the Exterior Complex Scaling method for scattering problems including Coulombic potentials

We study some formal aspects of the exterior complex scaling approach when implemented for both short and long-range potentials. The method requires an artificial cut-off of the potential in order to avoid exponential divergencies. Preserving the cut-off strategy, we propose alternative proposals to the ECS recipe which lead to a well-defined scattering problem. For a Coulombic long-range two-body potential we carefully analyze the use of a free wave function as asymptotic term, and then propose two variants of distorted--wave reformulation. A numerical illustration is provided. We then study in detail the cut-off procedure and identify some inconsistencies. To avoid them a proposal is put forward and its efficiency is demonstrated with analytical solutions for the pure Coulomb potential.