Solving close-coupling equations in momentum space without singularities for charged targets

TL;DR

This paper extends the convergent close-coupling method to charged targets, enabling singularity-free calculations of scattering cross sections at zero energy and thresholds, demonstrated on electron-H and electron-He+ systems.

Contribution

It introduces an analytical Greens function treatment for charged targets within the close-coupling framework, allowing calculations at zero energy and thresholds without singularities.

Findings

Accurate scattering length for neutral targets at zero energy.

Cross sections at thresholds for charged targets computed directly.

Method validated on electron-H and electron-He+ scattering.

Abstract

The analytical treatment of the Greens function in the convergent close-coupling method [Bray et al. Comp. Phys. Comm. 203 147 (2016)] has been extended to charged targets. Furthermore, we show that this approach allows for calculation of cross sections at zero channel energy. For neutral targets this means the electron scattering length may be obtained from a single calculation with zero incident energy. For charged targets the non-zero excitation cross sections at thresholds can also be calculated by simply setting the incident energy to the exact threshold value. These features are demonstrated by considering electron scattering on H and He+.