58 Surface Science 148 (1984) 5X-71 North-Holland, Amsterdam A CLASSICAL PATH APPROXIMATION FOR DIFFRACTIVE SURFACE SCATTERING Hans-Dieter MEYER Theoretische Chemre, Physiknlrsch -Chemisches Instrtut, Umc~ersrtiu Herdelherg. Im Neuenhetmer F&d 253, D -6900 Heidelberg, Fed. Rep. of Germon,: and J. Peter TOENNIES Max Plunck Instrtut ftir Strijmungsforschung, Btittmgerstrusse 6 8. D 3400 Giittittgen. Fed. Rep. of Germuny Received 2 April 1984; accepted for publication 28 May 1984 The well-known classical path approximation is applied to a calculation of diffraction mtensi- ttes in the scattering of atoms from a rigid crystal with a soft interaction potential. A general expression is derived for the diffraction intensities which can be applied to potentials with several higher-order terms in the Fourier series. For an uncorrugated Morse potential with a first-order exponential corrugation term an analytic solution is obtained which is compared with the infinite order suddent (10s) approximation calculations for Ne/W(llO) and He/LiF(lOO). Both ap- proximations are very accurate for the weakly corrugated Ne/W system. For He/LiF the present approximation is more accurate than the sudden (10s) approximation and has the added advantage of providing an analytic solution. Several improvements are suggested. 1. Introduction Diffraction of He atoms has been developed into a very sensitive probe of surface crystallography [l]. The interpretation of diffraction intensities in terms of the interaction potential requires a dynamical theory. The simplest approach based on the eikonal approximations assumes a simple corrugated hard repul- sive wall potential [2]. The attractive potential is accounted for only by an increase in the energy of impact. Despite its simplicity this theory works surprisingly well. Recent work has concentrated on understanding the softness of the repulsive potential [3-S]. At present the interpretation is possible only using an exact close-coupling calculation [6], which is time-consuming and does not provide much physical insight. A simpler approximation is the infinite order sudden (10s) approximation [7] adapted from studies of gas phase 0039-6028/84/$03.00 0 Elsevier Science Publishers B.V. (North-Holland Physics Publishing Division)