Rotational rainbow oscillations in He–Na2 collisions: Comparison between coupled states and infinite order sudden approximations

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Abstract
Differential and integral cross sections for the rotational excitation of Na2 in collisions with He at 0.1 eV are calculated in the coupled states and the rotationally sudden approximation. The final rotational state distribution at fixed scattering angle exhibits an interference structure similar to the usual rainbow pattern in potential scattering, namely, a broad main rainbow maximum for high Δj transitions and ’’supernumerary’’ oscillations on the bright side of the rotational rainbow for lower Δj transitions. This rainbow effect is explained in the stationary phase limit of the sudden approximation by interferences between’’trajectories’’ from different atom–molecule orientations. It is shown that the oscillations in the rotational distribution at fixed angle are equivalent to the oscillations vs scattering angle for a single rotational transition as reported by Schinke [Chem. Phys. 34, 65 (1978)]. The sudden cross sections are in satisfactory accord with the coupled-states results, when the average rotational state ? is choosen to reflect energy conservation.