Application of the Magnus approximation to inelastic collinear scattering of an atom from a diatomic molecule

Abstract

Approximate quantum-mechanical vibrational transition probabilities are calculated for a collinear collision of an atom and a diatomic molecule. The approach consists of solving the time-dependent Schrodinger equation with the help of the first term of the Magnus expansion in an interaction picture which includes the elastic channel distortions exactly. It is shown that in this approach the transition probabilities are obtained after exponentiation of the distorted-wave approximation to the transition matrix. For collisions with harmonic and Morse oscillators, the results are compared with those of close-coupling calculations. A substantial improvement on the distorted-wave approximation has been found even in cases where the scaled mass of the incident atom is large.