Scattering of thermal He beams by crossed atomic and molecular beams. I. Sensitivity of the elastic differential cross section to the interatomic potential

The ability of diffraction oscillations in atomic beam scattering experiments to uniquely determine interatomic potentials for highly quantal systems is examined. Assumed but realistic potentials are used to generate, by scattering calculations and incorporation of random errors, differential cross sections which are then treated as if they were "experimental" data. From these, attempts are made to recover the initial potential by varying the parameters of assumed mathematical forms different from the original one, until a best fit to the "experimental" results is obtained. It is found that the region of the interaction potential around the van der Waals minimum is accurately determined by the "measured" differential cross sections over a range of interatomic separations significantly wider than would be expected classically. It is also found, for collision energies at which the weakly repulsive wall is appreciably sampled, that the SPF-Dunham and double Morse-van der Waals types of potentials lead to accurate determinations of the interatomic potential, whereas many other mathematical forms do not. Analytical parameterizations most appropriate for obtaining accurate interatomic potentials from thermal DCS experiments, for a given highly quantal system, may depend on the collision energy used.