Interference phenomenon in electron-molecule collisions

TL;DR

This paper investigates the interference effects in electron scattering by a pair of atomic spheres, challenging standard assumptions and deriving new formulas for scattering amplitudes using the S-matrix method.

Contribution

It introduces a novel approach to analyze electron-molecule collisions without assuming atomic-like wave functions outside the molecular sphere.

Findings

Derived closed-form expressions for scattering amplitudes.

Presented a new expansion basis for the continuum wave function.

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

Abstract

The article discusses how the pattern of elastic scattering of an electron on a pair of identical atomic spheres will look if we abandon the standard in the molecular physics assumption that, outside the molecular sphere, in the external region, the wave function of the molecular continuum is atomic-like and is a linear combination of regular and irregular solutions of the wave equations. To do this, the elastic scattering of slow particles by pair of non-overlapping short-range potentials has been studied. The continuum wave function of particle is represented as a combination of a plane wave and two spherical s-waves that propagated freely throughout space. The asymptotic of this function determines in closed form the amplitude of elastic particle scattering. It has been shown that this amplitude can be presented as a partial expansion in a set of ortho-normal functions other, than spherical harmonics . General formulas for these functions are obtained. The coefficients of the scattering amplitude expansion to a series of functions determine the scattering phases for the two-atomic target under consideration. The special features of the S-matrix method for the case of arbitrary non-spherical potentials are discussed.