On the order of accuracy of the Born—Oppenheimer approximation for molecular collision states

Abstract
The accuracy of the approximation separating nuclear and electronic motions in molecular systems, is examined for atom-atom collisions. As in the study of Born & Oppenheimer of the analogous problem for bound molecular states, the parameter λ = ( m / M ) 1/2 ( m , M are respectively the electronic mass and the mean mass of the nuclei) is used for the classification of the order of magnitude of the various quantities involved. The fundamental observables of collision theory, whose accuracy is therefore of central interest in the present context, are the transition probabilities. By developing the integral equation for the transition matrix in powers of λ, and using an asymptotic expansion for the electronic Hamiltonian and energy in terms of the inverse of the internuclear distance, it is shown that the adiabatic approximation yields a T -matrix (hence also transition amplitudes) correct up to the order of λ 3 . A similar treatment is applied to the Lippmann-Schwinger equation for the total wavefunction and leads to the conclusion that the adiabatic approximation for the latter is correct up to the order of λ 2 . These results are subject to the condition that the electronic energy is not degenerate. The conclusions of the present study can be generalized to cover collisions between two groups of atoms.

This publication has 4 references indexed in Scilit: