Solving the Coulomb scattering problem using the complex scaling method

TL;DR

This paper introduces a rigorous formalism using the complex scaling method to solve Coulomb scattering problems with long-range interactions, avoiding the need for exact asymptotic boundary conditions.

Contribution

It develops a novel formalism applying exterior complex scaling to long-range Coulomb and short-range potentials in scattering problems.

Findings

Formalism successfully applied to numerical examples

Transforms scattering problem into a boundary problem with zero boundary conditions

Provides new local and integral representations for scattering amplitudes

Abstract

Based on the work of Nuttall and Cohen [Phys. Rev. {\bf 188} (1969) 1542] and Resigno et al{} [Phys. Rev. A {\bf 55} (1997) 4253] we present a rigorous formalism for solving the scattering problem for long-range interactions without using exact asymptotic boundary conditions. The long-range interaction may contain both Coulomb and short-range potentials. The exterior complex scaling method, applied to a specially constructed inhomogeneous Schr\"odinger equation, transforms the scattering problem into a boundary problem with zero boundary conditions. The local and integral representations for the scattering amplitudes have been derived. The formalism is illustrated with numerical examples.