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

The two-dimensional (2D) hard ellipsoid model is criticized and the calculations are compared with the 2D classical trajectory results. The scattering angle theta and the final j for a set of initial conditions (alpha and b) have been analyzed and it was concluded that the contribution of partial derivative j/partial derivative alpha 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-quantitative 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.