Collision of an atom and a diatomic. A semiadiabatic approximation

Abstract

A semiadiabatic approximation is used to compute transition probabilities for vibrational excitation in the model problem of a collinear collision between a particle and a harmonic oscillator interacting via a repulsive exponential potential. The semiadiabatic approach differs from the previously studied adiabatic approach in that only part of the static interaction is included in the definition of the unperturbed Hamiltonian. The advantage is that the eigenfunctions of the semiadiabatic operator are more easily obtained than those of the adiabatic operator. The perturbation inducing transitions between the states of the semiadiabatic Hamiltonian is the kinetic energy operator and the remainder of the static potential. A rapid method is developed for estimating transition probabilities with an accuracy comparable to that obtained by using the corrected distorted wave approximation.