Semiclassical theory of inelastic molecular collisions: Rotational transitions in small-angle dipole–dipole scattering

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Abstract
The angular distribution of small‐angle scattering is calculated for collisions of polar molecules. As found in previous calculations of the total cross section, the magnitude and form of the scattering vary drastically with the amount of inelastic energy transfer between rotation and translation. Collisions with various orientations of the increments Δj1 and Δj2 in the rotational momenta of the two molecules also give markedly different contributions. A semiclassical treatment of the inelastic scattering amplitude is used, with a random phase approximation for the strong‐coupling realm at small impact parameters and the Born approximation for the weak‐coupling realm at very large impact parameters. A classical time‐dependent perturbation calculation is also carried out using a ’’flywheel’’ approximation which averages over the unperturbed rotational motion of the molecules during the collision. These small‐angle scattering calculations give good agreement with the angular distribution measurements on CsCl+SbCl3 made by Helbing and Pauly. The resolution correction for total cross section measurements is also derived from these calculations and is found to bring theoretical and experimental cross sections into reasonable correspondence for several systems. The main results are given as simple, closed formulas in terms of reduced variables and are compared with those for the spherically symmetric r−3 and r−6 potentials.