On the direct inversion of total scattering cross sections beyond the glory region

A method is described for directly inverting measurements of the total scattering cross section at velocities beyond the glory undulations to determine the intermolecular potential, without the use of specific mathematical models for the potential. The only parameter needed is a quantity describing the potential well area, which is accurately obtained from the spacing of the glory undulations. A second quantity obtained from the glory spacings allows the use of relative rather than absolute cross sections. The method is illustrated with simulated cross section data. The results of this paper and the preceding one show that virtually the entire potential curve can in principle be obtained from only relative measurements of the total cross section, without the use of specific models.