Slow Heavy-Particle Collision Theory Based on a Quasiadiabatic Representation of the Electronic States of Molecules

Abstract

Collisions between heavy particles which entail a change in electronic state (such as changes in ionization or excitation) are considered in the low-velocity ($v\ensuremath{\ll}1$ a.u.) region. The electronic part of the problem is treated in a way which is both exact and at the same time lends itself most directly to the solution of the collision problem. This is done by introducing a representation of the electronic Hamiltonian ${H}_{\mathrm{el}}$ for the molecular system which is exact but nondiagonal. The basis states, which are a generalization of the resonant and potential scattering states of resonance theory, are not constrained by the noncrossing rule. Using these states as an expansion basis, the full Schr\"odinger equation for the collision is reduced to an effectively finite set of coupled two-body equations for the heavy-particle motion. The only approximation made, aside from small velocity, is the Born-Oppenheimer approximation. Therefore, both the electronic problem and the resultant problem of coupled heavy-particle motions may be treated with an accuracy that should be comparable with that of the corresponding molecular-stationary-state calculations.