Transition probability functions for inelastic electron--electron scattering

TL;DR

This paper derives simple, accurate, and computationally efficient analytic expressions for transition matrix elements in inelastic electron-electron scattering, improving upon existing approximations.

Contribution

It introduces new analytic formulas for radial wave function overlaps in inelastic electron-electron scattering using Slater-type and hydrogen-like models.

Findings

Expressions are finite sums of polynomials and trigonometric functions.

The formulas are more accurate than traditional approximations.

They require minimal computational resources.

Abstract

In this work, the transition matrix elements for inelastic electron--electron scattering are investigated. The angular part is given by spherical harmonics. For the weighted radial wave function overlap, analytic expressions are derived in the Slater-type and the hydrogen-like orbital models. These expressions are shown to be composed of a finite sum of polynomials and elementary trigonometric functions. Hence, they are easy to use, require little computation time, and are significantly more accurate than commonly used approximations.