A critical analysis of the two-dimensional atom ellipsoid model to study rotational collisions

Abstract

The two-dimensional (2D) hard ellipsoid model is criticized and the calculations are compared with the 2D classical trajectory results. The scattering angle θ and the final j for a set of initial conditions (α and b) have been analyzed and it was concluded that the contribution of ∂j/ ∂α is the leading term in the Jacobian function. Moreover, the rainbow trajectory calculated by the hard ellipsoid model turned out to be highly accurate for low scattering angles and semi-quantative for the maximum rotational rainbow. For the latter, a relative error of about 10% has been found compared with classical trajectory results. Finally, an inversion procedure based on such a model has also been re-analyzed and better information on the anisotropy of the interaction potential was found using an exact equation rather than an approximate formula for the hard ellipsoid model.