Direct inversion method for obtaining anisotropic potentials from rotationally inelastic and elastic cross sections

A method is given for the direct inversion of rotationally elastic and inelastic differential scattering cross sections, to yield the underlying intermolecular anisotropic potential surface. The scheme presented applies to molecules of large rotational spacings, for which the inelastic transitions are relatively weak. Semiclassical considerations and the exponential distorted-wave approximation are used in developing the method. Employed also is a peeling transform that, in effect, determines the interaction at each distance range from a different angular range of the data. The method is tested by application to simulated data, calculated for Ne + D₂ from a known potential at 0.07 eV collision energy. The inversion procedure recovered the anisotropic part of the interaction to within a few percent error.