Analysis of the methods proposed for computing the scattering of atoms from a hard corrugated surface model of He/LiF (001)

Abstract

It appears that the scattering of atoms on crystal surfaces is accounted for by a corrugated infinite wall model of the surface. To determine the “corrugation function” which represents best the experimental scattering intensities, it is necessary to choose among many possible versions, the simplest and most effective computational method of the theoretical scattering amplitudes. It is the purpose of this paper to analyze the relative merits of three particular versions which we call HDM, NHM and GR, and which are described in section 3. This comparison is carried out on the He/LiF(001) system for variable incident wave vector ( k) and orientation (θ i) as well as a number of Fourier components (ζ G ) used to describe the “corrugation function”. We conclude that the GR method presents advantages over the other two: (i) it reduces the computer time necessary for the HDM and NHM methods, (ii) converges and computes to within 10 −4 in unitarity the scattering amplitudes in a larger range of energies as well as angular and corrugation parameters, and (iii) it presents a great simplicity and the corrugation is very handy. The size of that range depends on the computer facilities used. In our case, the GR method works for any calculation in which kC 0 < 9 and C 0 < 0.35 A ̊ (where k is the incident wave vector and C 0 twice the amplitude of the corrugation). These characteristics prove to make the GR method a good tool for the study of surface crystallography by parametrization of the surface corrugation.