Semiclassical multi-phonon theory for atom-surface scattering: Application to the Cu(111) system.

The semiclassical perturbation theory of Hubbard and Miller [J. Chem. Phys. 80, 5827 (1984)] is further developed to include the full multi-phonon transitions in atom-surface scattering. A practically applicable expression is developed for the angular scattering distribution by utilising a discretized bath of oscillators, instead of the continuum limit. At sufficiently low surface temperature good agreement is found between the present multi-phonon theory and the previous one-, and two-phonon theory derived in the continuum limit in our previous study [Daon, Pollak, and Miret-Artés, J. Chem. Phys. 137, 201103 (2012)]. The theory is applied to the measured angular distributions of Ne, Ar, and Kr scattered from a Cu(111) surface. We find that the present multi-phonon theory substantially improves the agreement between experiment and theory, especially at the higher surface temperatures. This provides evidence for the importance of multi-phonon transitions in determining the angular distribution as the surface temperature is increased.

Communication: Semiclassical perturbation theory for the quantum diffractive scattering of atoms on thermal surfaces.

Inspired by the semiclassical perturbation theory of Hubbard and Miller [J. Chem. Phys. 80, 5827 (1984)], we derive explicit expressions for the angular distribution of particles scattered from thermal surfaces. At very low surface temperature, the observed experimental background scattering is proportional to the spectral density of the phonons. The angular distribution is a sum of diffraction peaks and a broad background reflecting the spectral density. The theory is applied to measured angular distributions of Ne, Ar, and Kr scattered from a Cu(111) surface.

Semiclassical perturbation theory for diffraction in heavy atom surface scattering.

The semiclassical perturbation theory formalism of Hubbard and Miller [J. Chem. Phys. 78, 1801 (1983)] for atom surface scattering is used to explore the possibility of observation of heavy atom diffractive scattering. In the limit of vanishing ℏ the semiclassical theory is shown to reduce to the classical perturbation theory. The quantum diffraction pattern is sensitive to the characteristics of the beam of incoming particles. Necessary conditions for observation of quantum diffraction are derived for the angular width of the incoming beam. An analytic expression for the angular distribution as a function of the angular and momentum variance of the incoming beam is obtained. We show both analytically and through some numerical results that increasing the angular width of the incident beam leads to decoherence of the quantum diffraction peaks and one approaches the classical limit. However, the incoherence of the beam in the parallel direction does not destroy the diffraction pattern. We consider the specific example of Ar atoms scattered from a rigid LiF(100) surface.