Theory of electronic transitions in slow atomic collisions

Abstract

This review deals with quantitative descriptions of electronic transitions in atom-atom and ion-atom collisions. In one type of description, the nuclear motion is treated classically or semiclassically, and a wave function for the electrons satisfies a time-dependent Schr\"odinger equation. Expansion of this wave function in a suitable basis leads to time-dependent coupled equations. The role played by electron-translation factors in this expansion is noted, and their effects upon transition amplitudes are discussed. In a fully quantum-mechanical framework there is a wave function describing the motion of electrons and nuclei. Expansion of this wave function in a basis which spans the space of electron variables leads to quantum-mechanical close-coupled equations. In the conventional formulation, known as perturbed-stationary-states theory, certain difficulties arise because scattering boundary conditions cannot be exactly satisfied within a finite basis. These difficulties are examined, and a theory is developed which surmounts them. This theory is based upon an intersecting-curved-wave picture. The use of rotating or space-fixed electronic basis sets is discussed. Various bases are classified by Hund's cases (a)-(e). For rotating basis sets, the angular motion of the nuclei is best described using symmetric-top eigenfunctions, and an example of partial-wave analysis in such functions is developed. Definitions of adiabatic and diabatic representations are given, and rules for choosing a good representation are presented. Finally, representations and excitation mechanisms for specific systems are reviewed. Processes discussed include spin-flip transitions, rotational coupling transitions, inner-shell excitations, covalent-ionic transitions, resonant and near-resonant charge exchange, fine-structure transitions, and collisional autoionization and electron detachment.