A uniform semiclassical sudden approximation for rotationally inelastic scattering

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Abstract
The infinite‐order‐sudden (IOS) approximation is investigated in the semiclassical limit. A simplified IOS formula for rotationally inelastic differential cross sections is derived involving a uniform stationary phase approximation for two‐dimensional oscillatory integrals with two stationary points. The semiclassical analysis provides a quantitative description of the rotational rainbow structure in the differential cross section. The numerical calculation of semiclassical IOS cross sections is extremely fast compared to numerically exact IOS methods, especially if high Δjtransitions are involved. Rigid rotor results for He–Na2 collisions with Δj≲26 and for K–CO collisions with Δj≲70 show satisfactory agreement with quantal IOS calculations.