Second order classical perturbation theory for atom surface scattering: Analysis of asymmetry in the angular distribution

Abstract

A second order classical perturbation theory is developed and applied to elastic atom corrugated surface scattering. The resulting theory accounts for experimentally observed asymmetry in the final angular distributions. These include qualitative features, such as reduction of the asymmetry in the intensity of the rainbow peaks with increased incidence energy as well as the asymmetry in the location of the rainbow peaks with respect to the specular scattering angle. The theory is especially applicable to "soft" corrugated potentials. Expressions for the angular distribution are derived for the exponential repulsive and Morse potential models. The theory is implemented numerically to a simplified model of the scattering of an Ar atom from a LiF(100) surface.

Reply to the ‘Comment on “Perturbation theory of scattering for grazing-incidence fast-atom diffraction”’ by G. A. Bocan, H. Breiss, S. Szilasi, A. Momeni, E. M. S. Casagrande, E. A. Sánchez, M. S. Gravielle and H. Khemliche, Phys. Chem. Chem. Phys., 2023, 25, DOI: 10.1039/D3CP02486E

“…In the case of non-normal incidence the presence of an attractive well will generally result in a rainbow angle that decreases as the incident energy increases. 14,20,23 The effect is evident from, for example, eqn (3.15) and (4.14) of Zhou et al 20 Fig. 2(a) shows the effect calculated to first order in perturbation theory.…”

“…The classical and semi-classical analysis by Pollak and Miret-Artés 14,20,21 offered a more quantitative approach than considered previously. They used a Morse potential where both terms in eqn (1) are modulated, in z , with the same function and reproduced the effects achieved with quantum calculations and an ab initio potential, 22 as well as describing the phenomenology observed in low-energy experiments.…”

“…2 Energy dependence of the rainbow angle in first-order perturbation theory with a corrugated Morse potential. (a) Shows the behaviour as the angle of incidence changes, calculated using eqn (3.15) and (4.14) of Zhou et al20 Here, y i is measured from the surface normal so that GIFAD scattering corresponds to y i = 01. (b) Shows the effect of modulating the well-depth across the GIFAD scattering channel, calculated using eqn (4), h a /h r o 1, red line, corresponds to a deeper well in the centre of the scattering channel, as observed on alkali halide (001) surfaces; h a /h r 4 1, blue line, has the deeper well on the top site 4.…”

Microscopic modeling of gas-surface scattering: II. Application to argon atom adsorption on a platinum (111) surface

“…The nature of sticking of heavy atoms to clean surfaces has been intensively investigated using semiclassical perturbation theory [9,[25][26][27][28][29]. Hubbard and Miller [25] calculated the sticking probability for the HeW(110) and NeW(110) systems in the regime when the energy transfer from the surface is small.…”

“…Pollak [26] derived an expression for the sticking probability in the limit of weak surface corrugation, and by assuming weak coupling to the harmonic surface phonon modes. Later, an improved theory has been presented in [27], which included the second order corrections to the angular distribution of the scattered particles. In their recent work, Sahoo and Pollak [28] employed a one-dimensional generalized Langevin equation and derived an analytic expression for the temperature-dependent energy loss.…”