Rainbows in rotationally inelastic scattering: A comparative study of different model potential surfaces and dynamical approximations

Abstract

Rainbow structures in rotationally elastic and inelastic differential cross sections in atom–diatom collisions are investigated by comparison of three model potential energy surfaces labeled I, II, and III which are represented by V(R,γ)=V0(R)+V2(R)P2(cos γ). The cross sections are calculated within the quantal infinite-order-sudden (IOS) approximation. The anisotropic part V2 is the same for all potentials and purely repulsive. The isotropic part V0 for potential I is also repulsive and the differential cross sections show the well-studied rotational rainbow structures. Structural changes occur for collisions in potential II and III which have V0 terms being attractive at intermediate and large atom–molecule separations and having well depths of 10% and 25% of the collision energy, respectively. For example, the elastic cross section has no classical rainbow in the case of potential I but three in the case of potential III. The rainbow structures are analyzed within the classical and semiclassical versions of the IOS approximation and interpreted in terms of catastrophe theory. The quantitative comparison of the classical with the quantal IOS cross sections manifests possible quantum effects, i.e., tunneling into nonclassical regions and interference effects due to the superposition of several contributions (up to six in the present study). They can be very prominent and thus we conclude that much caution is needed if experimental data are compared with classical calculations. The accuracy of the IOS approximation is tested by comparison of classical IOS cross sections with cross sections obtained from exact classical trajectory calculations. The agreement is generally good with the exemption of the rainbow region and small angle, rotationally elastic scattering.