Time-dependent density-functional theory approach to nonlinear particle-solid interactions in comparison with scattering theory

TL;DR

This paper develops a time-dependent density-functional theory method to analyze nonlinear particle-solid interactions, specifically evaluating the quadratic stopping power of an electron gas for slow ions, and compares it with scattering theory results.

Contribution

It provides an explicit expression for the quadratic density-response function within TDDFT and demonstrates its equivalence to scattering theory for slow ions, including numerical validation.

Findings

Quadratic response theory matches scattering theory results for slow ions.

Numerical calculations validate the range of quadratic-response theory.

Explicit expressions facilitate analysis of nonlinear particle-solid interactions.

Abstract

An explicit expression for the quadratic density-response function of a many-electron system is obtained in the framework of the time-dependent density-functional theory, in terms of the linear and quadratic density-response functions of noninteracting Kohn-Sham electrons and functional derivatives of the time-dependent exchange-correlation potential. This is used to evaluate the quadratic stopping power of a homogeneous electron gas for slow ions, which is demonstrated to be equivalent to that obtained up to second order in the ion charge in the framework of a fully nonlinear scattering approach. Numerical calculations are reported, thereby exploring the range of validity of quadratic-response theory.