A stationary phase study of m rainbows in molecule-corrugated surface scattering

Using the stationary phase limit of the quantum mechanical full sudden S matrix for diatom-corrugated rigid surface scattering of Proctor, Kouri, and Gerber [J. Chem. Phys. 80, 3845 (1984)] we obtain expressions for the rotational actions j and m of an inelastically scattered diatom. By integrating over all points on the lattice, we reduce these to functions of the polar angles θ and φ only. It is found that j is a strong function of θ, but almost independent of φ, whereas the reverse is true for m . Both j(θ) and m(φ) are continuous plots which exhibit extrema known to produce rainbow behavior in inelastic gas-phase scattering theory. We propose that this implies the existence of rainbows in the m distribution, and show the dependence of these rainbows on various potential parameters, including corrugation, potential repulsion parameter, and lattice constant. The results explain earlier trajectory studies. © 1988 American Institute of Physics.