Two-body Coulomb scattering and complex scaling

TL;DR

This paper introduces a new partial wave level splitting method for solving the two-body Coulomb scattering problem using complex scaling, simplifying numerical solutions and applicable with short-range interactions.

Contribution

A novel splitting approach at the partial wave level is proposed, improving the numerical solution of Coulomb scattering with complex scaling.

Findings

The scattered wave function tends to zero at large distances.

The new method simplifies numerical solutions by allowing expansion on bound-state basis.

Applicable to Coulomb potential with additional short-range interactions.

Abstract

The two-body Coulomb scattering problem is solved using the standard complex scaling method. The explicit enforcement of the scattering boundary condition is avoided. Splitting of the scattering wave function based on the Coulomb modified plane wave is considered. This decomposition leads a three-dimensional Schr\"odinger equation with source term. Partial wave expansion is carried out and the asymptotic form of the solution is determined. This splitting does not lead to simplification of the scattering boundary condition if complex scaling is invoked. A new splitting carried out only on partial wave level is introduced and this method is proved to be very useful. The scattered part of the wave function tends to zero at large inter-particle distance. This property permits of easy numerical solution: the scattered part of the wave function can be expanded on bound-state type basis. The new method can be applied not only for pure Coulomb potential butin the presence of short range interaction too.