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

Abstract

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.

Perturbation theory of scattering for grazing-incidence fast-atom diffraction

“…Inelastic effects could been included, to first and second order, using classical and semi-classical perturbation theory methods. 20,29 These may also offer the opportunity to explore the role of surface temperature and frictional coupling in the scattering.…”

Unified quantum theory of elastic and inelastic atomic scattering from a physisorbed monolayer solid

“…The strong coupling is manifested in the relatively small fraction of the scattering that is in elastic channels and in symmetry-breaking effects such as the excitation of shear horizontal (SH) phonons for scattering near high-symmetry directions of a monolayer solid [5]. The applicability of the traditional Debye-Waller formulation of attenuation of elastic (diffraction) intensities by inelastic processes is rather limited [20] for a low energy atom probe, and for heavy inert gas atoms there has been major recent development of the theory [21,22]. The intensity of one-phonon creation events may even increase with temperature, contrary to the simple language of Debye-Waller attenuation [23].…”