Inelastic scattering of vortex electrons beyond the Born approximation

TL;DR

This paper develops a theoretical framework for inelastic scattering of vortex electrons by hydrogen atoms, emphasizing Coulomb interaction effects beyond the Born approximation, and analyzes specific atomic transitions at low electron energies.

Contribution

It introduces vortex electron wave functions from both free and distorted solutions, extending scattering theory beyond the first Born approximation for inelastic processes.

Findings

Coulomb interaction significantly alters vortex electron phase and density.

Pronounced effects observed for specific atomic sublevel excitations.

Large scattering angles show the most substantial Coulomb effects.

Abstract

We present a theoretical study of the inelastic scattering of vortex electrons by a hydrogen atom. In our study, special emphasis is placed on the effects of the Coulomb interaction between a projectile electron and a target atom. To understand these effects, we construct vortex electron wave functions both from free space and distorted solutions of the Schr\"odinger equation. These wave functions give rise to the first Born and distorted wave scattering amplitudes, respectively. The derived theory has been employed to investigate the $1s \rightarrow 2p$ transition of a hydrogen atom induced by electrons with the kinetic energies in the range from 20 to 100 eV. The results of the calculations have clearly indicated that the Coulomb interaction can significantly affect the phase pattern and probability density of a vortex electron beam as well as the squared transition amplitudes. For the latter, the most pronounced effect was found for the excitation to the $\ket{2p\, m_f=0}$ sublevel and large scattering angles.