SIMPLIFIED ANALYSIS OF HELIUM SCATTERING - SUPERNUMERARY RAINBOWS FROM A SOFT, CORRUGATED POTENTIAL

This paper presents a simple, but quantitative approach to the analysi s of helium diffraction from surfaces. Instead of calculating the inte nsities of helium diffraction beams, we analyze the locations of the s upernumerary rainbows, or oscillations in the intensity envelope of th e diffraction beams. Within a semiclassical framework, we interpret th e supernumerary rainbows in terms of the phase integrals associated wi th the different classical scattering trajectories. Using a perturbati on theory to calculate the classical trajectories, we obtain a simple, closed formula which predicts the locations of the supernumerary rain bows as a function of the scattering angle. This formula includes a co rrection for the softness of the scattering potential. Since the soft- potential effect depends strongly on the angle between the incoming an d outgoing trajectories, our scattering formula can be used to extract both the corrugation and the decay length of the scattering potential from a series of diffraction patterns taken at various angles of inci dence. The results of our perturbative semiclassical analysis are in g ood agreement with those of exact quantum-mechanical calculations.