Theoretical investigation of rotational rainbow structures in X–Na2 collisions using CI potential surfaces. II. Combined rotational–vibrational excitation for X = He scattering

Abstract

Combined rotational–vibrational excitaton cross sections for He–Na2 scattering are reported for collision energies of 0.05?E?0.15 eV. The infinite-order-sudden (IOS) approximation is used to decouple the rotational and the orbital angular momenta, whereas the vibrational degree of freedom is treated exactly by solving vibrationally coupled radial equations. An analytical potential energy surface obtained from 160 ab initio CI energies is used in these scattering calculations. The cross sections for vibrational excitation or de-excitation are extremely small compared to the vibrationally elastic cross sections but increase rapidly with the collision energy. The influence of the target vibration on pure rotational excitation processes is negligibly small for energies considered in this study, such that the rigid-rotor approximation applied previously for the same system is confirmed to be reasonable. Furthermore, the rotational rainbow structures which are characteristic for the He–Na2 system depend only very slightly on whether the molecule is initially in the ground n = 0 or the first vibrationally excited state n = 1. This was in contradiction to the experimental finding of Bergmann et al. [J. Chem. Phys. 72, 4777 (1980)], who reported a dramatic enhancement of the rotational energy transfer for scattering within the n = 1 vibrational state. The rotational rainbow maxima occur at almost equal positions independent of whether the transition is vibrationally elastic or inelastic. A small shift to wider scattering angles in the case of Δn = 1 is observed at lower energies.