Theory of Electron-Molecule Collisions by Frame Transformations

Abstract

Laboratory-frame and body-frame treatments are combined using the $l$-uncoupling transformation which had served to interpret the absorption spectrum of ${\mathrm{H}}_2$. Application of a phase-amplitude procedure converts the Schrödinger equation to a Volterra-type integral form, which reduces to a Born-like approximation when the long-range interactions are weak. Attention is directed to features of low-energy collisions that must be considered by a realistic theory. This paper develops a formalism that can take advantage of different simplifying factors in different ranges of the electron-molecule distance. Detailed developments and applications are deferred.