An expression for the total cross section for molecular scattering in the presence of an angle dependent potential

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Abstract
The intermolecular potential between an atom and a diatomic molecule is expanded in the spherical harmonics Ylm of the angle between the molecular axis and the interparticle axis. Using a perturbation expansion of the diagonal scattering matrix elements in powers of the coefficient ℋ of the Y 20 term in the potential, it is shown that the total cross section averaged over initial rotational quantum states mj contains a contribution O(ℋ2) arising predominantly from inelastic events. This contribution is found to have the same energy dependence as that arising from central forces, but is small and barely detectable even under extreme experimental conditions. It is concluded from a simple model for dispersion forces that for neutral molecules the long range part of the potential measured from the slope of the Massey-Mohr plot contains less than a 1 per cent contribution from an angle dependent term in the potential having P 2 symmetry. This conclusion is arrived at whether or not the angular momentum of relative motion is coupled to that of internal motion. An approximate coupling scheme of angular momentum is presented that may be useful in discussing other rotational effects accompanying collision. It is pointed out that inelastic events can dominate total cross sections for ion-molecule scattering.

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