Complex angular momentum analysis of rotationally inelastic diffraction scattering in sudden atom-homonuclear–molecule collisions

Abstract

A new complex angular momentum (CAM) theory of rotationally inelastic scattering has been developed for atom homonuclear–diatomic molecule collisions. The CAM theory is valid for sudden collisions, when the infinite-order-sudden (IOS) approximation for atom rigid-rotator scattering is appropriate. In the IOS/CAM theory, the inelastic scattering amplitude is written in terms of two subamplitudes: a background integral and a residue series. Physically the background integral corresponds to particles scattered by the repulsive potential core, while the residue series corresponds to short lived surface waves that propagate around the potential core. Diffraction effects arise from the interference of these two subamplitudes. The IOS/CAM theory is more general and accurate than the simple Drozdov–Blair theory of inelastic diffraction scattering. The weak coupling limit of the IOS/CAM equations has also been investigated and a new phase rule has been derived that is more general than the Blair phase rule. Approximate conditions for the validity of the new phase rule have been investigated using a model anisotropic potential of the form [g(γ)/r]n, n≥3. Numerical calculations of inelastic angular distributions using the IOS/CAM equations have been made for the strongly anisotropic He–N2 and weakly anisotropic Ne–D2 collision systems. Using a semiclassical approximation to the background integral and a single Regge pole term in the residue series, we obtain good agreement with conventional partial wave IOS angular distributions.