The scattering of He atoms from a hard corrugated surface model using the GR method. I

Extensive computations on the scattering of atoms from a hard corrugated surface model (HCS) under the Rayleigh hypothesis by using the GR numerical method are presented. The computational applicability, the limits of convergence, as well as the sensitivity of the method are studied as a function of the scattering and corrugation parameters. We also calculate a set of curves, called topographic curves, of constant diffraction probabilities versus the incident angle and the corrugation parameters for a square unit cell. The effect of the strength and number of the Fourier coefficients of the corrugation function are analyzed obtaining rainbow disappearance when these coefficients increase in strength and number. A tentative analysis of the crystallography of the LiF(001) surface by using monoenergetic thermal helium beams is given in terms of the hard sphere and ’’contact’’ hard sphere model proposed here. The agreement with the experimental data on He/LiF(001) is excellent. We also discuss an empirical method for determining Debye–Waller factors by fitting the calculated peaks to the observed ones. We calculate the mean square displacement of the atoms vibrating at the surface for different directions on the He/LiF (001) system. These displacements and consequently the Debye–Waller factors are different than if the incident particles were electrons. Finally, several proposals for future experimental work are made.