About the standard methodology in electron-molecule collision physics

TL;DR

This paper critically examines the assumptions in electron-molecule collision physics, showing that traditional spherical symmetry-based methods are inadequate for non-spherical potentials and proposing alternative approaches for accurate scattering analysis.

Contribution

It demonstrates the limitations of spherical symmetry assumptions in molecular scattering and introduces general formulas and methods for non-spherical potential analysis.

Findings

Spherical symmetry assumptions are invalid for non-spherical molecular potentials.

Wave functions at large distances can be expanded in non-spherical orthonormal functions.

New formulas for scattering phases and S-matrix for non-spherical potentials are derived.

Abstract

The article discusses the correctness of the assumption about the similarity of molecular continuum electron functions with wave functions in electron-atom scattering. 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, generated by the scattering centers. The asymptotic of this function determines in closed form the amplitude of elastic particle scattering. It is shown that this amplitude of scattering on a nonspherical target cannot be correctly represented as an expansion into a series of spherical functions , as is the case for scattering on an atom. Therefore, methods of the scattering phase calculation based on the assumption of spherical symmetry of the molecular potential field beyond the molecular sphere cannot be considered as justified and reliable. So is the representation outside this sphere of the wave function as a linear combination of the regular and irregular solutions of the Schr\"odinger equation. It has been shown that asymptotically at great distances from the molecule the continuum wave functions can be presented as an expansion in a set of other, than spherical, orthonormal functions . General formulas for these functions are obtained. The coefficients of the scattering amplitude expansion to a series of these functions determine the scattering phases for the molecular system under consideration. The special features of the S-matrix method for the case of arbitrary non-spherical potentials are discussed.