Atom scattering from an augmented corrugated hard wall surface

Abstract

Atom scattering from a potential of the form V0+VHw, where V0 is a one-dimensional potential and VHw is a hard wall potential, is considered. The formalism is quite standard; the only difficulty comes in finding a Green’s function for [h/2∇2/2M+E−V0]−1. It is argued that the Green’s function used in CCGM and elsewhere is incorrect; the expansion of all scattering states that decay as Z→−∞ is not complete for potentials characteristic of atom–surface scattering. A new Green’s function is derived using a plane wave basis set. Calculations show that the effect of V0 is to make the surface seem flatter, but it makes little difference to the qualitative features of the scattering profile except near a resonance. If one had data at a single energy for scattering from a potential that approximates an augmented hard wall, one could fit them using a simple hard wall (i.e., V0 = 0) but when one does so, one calculates the wrong surface shape. As a result, if one wants to use atom–surface scattering to determine surface morphology, one has to take data at a wide range of incident energies, something that is not being done by most experimentalists.