Rotational rainbows: An IOS study of rotational excitation of hard-shell molecules

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Abstract
The hard-shell model for rotationally inelastic scattering is studied within the infinite-order-sudden (IOS) approximation. In addition to the rotational rainbow oscillations of the differential cross sections for j = 0→j′ transitions, a pronounced diffraction structure for small j′ (j′≊0, 2, 4, and 6) and small scattering angles is observed. A classical and semiclassical IOS approximation developed recently is compared with the quantal results for hard-shell He–Na2 collisions at 0.1 eV. The semiclassical IOS approximation leads to a simple (almost closed form) formula for the inelastic differential cross sections. Very good agreement with the quantal results is obtained with the exception of the small angle region for low Δj transitions, which is dominated by diffraction structures. The validity of the IOS approximation for hard-shell molecules is discussed. The model results for He–Na2 are compared with IOS calculations using a soft ab initio potential surface. The results differ drastically with the exception of the region of backward scattering, where the rotational rainbow oscillations are in good agreement. The integral cross sections show the same disagreement—again with the exception of high j′ excitation, which is dominated by wide-angle scattering.