Huygens-Fresnel Picture for Electron-Molecule Elastic Scattering

TL;DR

This paper introduces a Huygens-Fresnel based model for calculating elastic scattering cross sections of slow electrons by molecules, incorporating multiple scattering and diffraction effects with a novel wave function approach.

Contribution

It presents a new wave function representation based on the Huygens-Fresnel principle for electron-molecule scattering, enabling closed-form calculation of scattering amplitudes.

Findings

Calculated differential and total cross sections for C2 and H2 molecules.

Demonstrated the effectiveness of the model in capturing diffraction patterns.

Discussed the application of the S-matrix method to non-spherical potentials.

Abstract

The elastic scattering cross sections for a slow electron by C2 and H2 molecules have been calculated within the framework of the non-overlapping atomic potential model. For the amplitudes of the multiple electron scattering by a target the wave function of the molecular continuum is represented as a combination of a plane wave and two spherical waves generated by the centers of atomic spheres. This wave function obeys the Huygens-Fresnel principle according to which the electron wave scattering by a system of two centers is accompanied by generation of two spherical waves; their interaction creates a diffraction pattern far from the target. Each of the Huygens waves, in turn, is a superposition of the partial spherical waves with different orbital angular momenta l and their projections m. The amplitudes of these partial waves are defined by the corresponding phases of electron elastic scattering by an isolated atomic potential. In numerical calculations the s- and p-phase shifts are taken into account. So the number of interfering electron waves is equal to eight: two of which are the s-type waves and the remaining six waves are of the p-type with different m values. The calculation of the scattering amplitudes in closed form (rather than in the form of S-matrix expansion) is reduced to solving a system of eight inhomogeneous algebraic equations. The differential and total cross sections of electron scattering by fixed-in-space molecules and randomly oriented ones have been calculated as well. We conclude by discussing the special features of the S-matrix method for the case of arbitrary non-spherical potentials.