Potential splitting approach to e-H and e-He${}^+$ scattering with zero total angular momentum

TL;DR

This paper introduces a novel potential splitting method for Coulombic scattering problems, reformulating the Schrödinger equation to improve numerical solutions for electron scattering on hydrogen and helium ions.

Contribution

The paper presents a new potential splitting approach combined with exterior complex scaling for Coulombic scattering, enabling more accurate and efficient calculations of resonant electron scattering.

Findings

Method successfully describes electron scattering on hydrogen and helium ions.

Numerical results demonstrate the approach's effectiveness in resonance regions.

Finite element method validates the proposed approach.

Abstract

An approach based on splitting the reaction potential into a finite range part and a long range tail part to describe few-body scattering in the case of a Coulombic interaction is proposed. The solution to the Schr\"odinger equation for the long range tail of the reaction potential is used as an incoming wave. This reformulation of the scattering problem into an inhomogeneous Schr\"odinger equation with asymptotic outgoing waves makes it suitable for solving with the exterior complex scaling technique. The validity of the approach is analyzed from a formal point of view and demonstrated numerically, where the calculations are performed with the finite element method. The method of splitting the potential in this way is illustrated with calculations of the electron scattering on the hydrogen atom and the positive helium ion in energy regions where resonances appear.