Continuum states from time-dependent density functional theory

TL;DR

This paper develops methods within time-dependent density functional theory to analyze low-lying continuum states and scattering properties of electron-target systems, providing more accurate phase shift approximations than previous static exchange methods.

Contribution

It derives exact formulas for scattering amplitudes from susceptibility in one dimension and introduces a single-pole approximation for phase shifts in three dimensions.

Findings

Single-pole approximation outperforms static exchange in accuracy.

Exact formulas for scattering amplitudes are derived in one dimension.

Method enhances understanding of electron scattering in continuum states.

Abstract

Linear response time-dependent density functional theory is used to study low-lying electronic continuum states of targets that can bind an extra electron. Exact formulas to extract scattering amplitudes from the susceptibility are derived in one dimension. A single-pole approximation for scattering phase shifts in three dimensions is shown to be more accurate than static exchange for singlet electron-He$^+$ scattering.