Variational approach to the scattering of charged particles by a many-electron system

TL;DR

This paper introduces a variational method based on a modified Schwinger principle to calculate nonlinear scattering cross-sections of charged particles interacting with many-electron systems, validated by comparisons with Hartree calculations.

Contribution

It develops a nonperturbative variational approach using linear and quadratic density-response functions for scattering in many-electron systems, extending beyond low-velocity regimes.

Findings

Good agreement with Hartree calculations for energy loss of antiprotons

Applicable to nonlinear screening in various particle interactions

Extends theoretical tools for high-velocity projectile scattering

Abstract

We report a variational approach to the nonlinearly screened interaction of charged particles with a many-electron system. This approach has been developed by introducing a modification of the Schwinger variational principle of scattering theory, which allows to obtain nonperturbative scattering cross-sections of moving projectiles from the knowledge of the linear and quadratic density-response functions of the target. Our theory is illustrated with a calculation of the energy loss per unit path length of slow antiprotons moving in a uniform electron gas, which shows good agreement with a fully nonlinear self-consistent Hartree calculation. Since available self-consistent calculations are restricted to low heavy-projectile velocities, we expect our theory to have novel applications to a variety of processes where nonlinear screening plays an important role.