Calculation of intermediate-energy electron-impact ionization of molecular hydrogen and nitrogen using the paraxial approximation

TL;DR

This paper introduces a computational approach combining the paraxial approximation and time-dependent Hartree-Fock to efficiently calculate electron-impact ionization cross sections for molecules, showing promising results for helium and hydrogen but less accuracy for nitrogen.

Contribution

The study develops a novel computational method that simplifies the scattering problem for molecular ionization, enabling more efficient calculations at intermediate energies.

Findings

Results closely match experimental data for helium and hydrogen.

Discrepancies observed for nitrogen due to frozen core approximation limitations.

Method reduces complex scattering problems to a five-dimensional Schrödinger equation.

Abstract

We have implemented the paraxial approximation followed by the time-dependent Hartree-Fock method with frozen core for the single impact ionization of atoms and two-atomic molecules. It reduces the original scattering problem to the five-dimensional time-dependent Schr\"odinger equation solution. By using this method we calculated the multi-fold differential cross section of the impact single ionization of the helium atom, the hydrogen molecule and the nitrogen molecule by the intermediate energy electrons. Our results for the helium and the hydrogen are quite close to experimental data, but for N$_2$ the agreement is worse apparently because of the insufficiency of the frozen core approximation.