Semiclassical perturbation theory for diffraction in heavy atom surface scattering

Grazing incidence fast atom diffraction: general considerations, semiclassical perturbation theory and experimental implications

Using semiclassical methods, an analytical approach to describe grazing incidence scattering of fast atoms (GIFAD) from surfaces is described. First, we consider a model with a surface corrugated in the scattering plane, which includes the surface normal and the incidence direction. The treatment uses a realistic, Morse potential, within a perturbation approach, and correctly reproduces the basic GIFAD phenomenology, whereby the scattering is directed primarily in the specular direction. Second, we treat the more general case of scattering from a surface corrugated in two-dimensions. Using time averaging along the direction of fast motion in the incidence direction, we derive a time dependent potential for the GIFAD scattering away from a low index direction. The results correctly describe the observation that diffraction is seen only when the scattering plane is aligned close to a low-index direction in the surface plane. For the case of helium scattering from LiF(001) we demonstrate that the resulting theoretical predictions agree well with experiment and show that the analysis provides new information on the scattering time and the length scale of the interaction. The analysis also gives insights into the validity of the axial surface channeling approximation (ASCA) and shows that within first order perturbation theory, along a low-index direction, the full 3-dimensional problem can be represented accurately by an equivalent 2-dimensional problem with a potential averaged along the third dimension. In contrast, away from low-index directions, the effective 2-dimensional potential in the projectile frame is time-dependent.

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

Recent grazing-incidence, fast atom diffraction (GIFAD) experiments have highlighted the well known observation that the distance between classical rainbow angles depends on the incident energy. The GIFAD experiments imply an incident vertical scattering angle, facilitating an analytic analysis using classical perturbation theory, which leads to the conclusion that the so called "dynamic corrugation" amplitude, as defined by Bocan et al., Phys. Rev. Lett., 2020 125, 096101 is, within first-order perturbation theory, proportional to the tangent of the rainbow angle. Therefore it provides no further information about the interaction than is gleaned from the rainbow angle and its energy dependence. Perhaps more importantly, the resulting analytic theory reveals how the energy dependence of rainbow angles may be inverted into information on the force field governing the interaction of the incident projectile with the surface.

Quantum Markovian master equation for scattering from surfaces

We propose a semi-phenomenological Markovian Master equation for describing the quantum dynamics of atom-surface scattering. It embodies the Lindblad-like structure and can describe both damping and pumping of energy between the system and the bath. It preserves positivity and correctly accounts for the vanishing of the interaction of the particle with the surface when the particle is distant from the surface. As a numerical test, we apply it to a model of an Ar atom scattered from a LiF surface, allowing for interaction only in the vertical direction. At low temperatures, we find that the quantum mechanical average energy loss is smaller than the classical energy loss. The numerical results obtained from the space dependent friction master equation are compared with numerical simulations for a discretized bath, using the multi-configurational time dependent Hartree methodology. The agreement between the two simulations is quantitative.