Elastic and inelastic diffraction of fast atoms, Debye-Waller factor, and Mössbauer-Lamb-Dicke regime

Abstract

The diffraction of fast atoms at crystal surfaces is ideal for a detailed investigation of the surface electronic density. However, instead of sharp diffraction spots, most experiments show elongated streaks characteristic of inelastic diffraction. This paper describes these inelastic profiles in terms of individual inelastic collisions with surface atoms taking place along the projectile trajectory and leading to vibrational excitation of the local Debye oscillator. A quasi-elastic regime where only one inelastic event contributes is identified as well as a mixed quantum-classical regime were several inelastic collision are involved. These regimes describe a smooth evolution of the scattering profiles from sharp spots to elongated streaks merging progressively into the classical diffusion regime.

Phonon contribution in grazing-incidence fast atom diffraction from insulator surfaces

“…In conclusion, present P0-SIVR results demonstrate that thermal vibrations affect the aspect of the GIFAD patterns from insulator surfaces, a finding that is especially relevant for the use of GIFAD as a surface analysis technique. But notice that there are other effects, like phonon excitations [22,23] or the presence of terraces in the crystal sample [37], not considered in this article, which can modify the interference structures too. Therefore, further experimental and theoretical work to investigate the different decoherence mechanisms in GIFAD would be valuable.…”

“…From the theoretical point of view, in spite of the above mentioned features, most of the GIFAD models [18][19][20][21] consider an ideal and static crystal surface, with atoms or ions at rest at their equilibrium positions. On the other hand, few articles deal with the decoherence introduced in GIFAD by lattice vibrations [6,7,16,22,23], so this issue represents a problem not fully understood yet.…”

Approach to coherent interference fringes in helium-surface scattering

“…This is perhaps more surprising when we consider the classical force vs time that the scatterer experiences, shown in Fig. 7 (note the similarity to the force shown in the work by Roncin and Debiossac [23]): f y (t ) ≈ 0. Zugarramurdi and Borisov [46] note that for typical experimental fast atom diffraction conditions, there is very little diffraction into reciprocal lattice vectors parallel to the beam direction; this analysis shows very little inelastic scattering in that direction as well.…”

“…To cast the previous discussion in a more physically intuitive picture, if the scatterer disturbs the lattice to produce a phonon of wavelength λ, the Kirchhoff sum of emitted waves will produce an outgoing beam pattern with elastic diffraction peaks corresponding to the static interaction, plus a contribution to each peak of a momentum k ∼ π λ to a phonon depending on the strength of the interaction. Roncin and Debiossac [23] describe a complementary picture to the decoherence scheme we have discussed; they note that the scattering atom acts to measure the surface atoms and induces decoherence via either position measurement (local measurements of thermal motion that is the traditional source of the Debye-Waller factor in diffraction) or momentum transfer (analogous to the surface particles undergoing emission with recoil). Toennies and co-workers [24,25] postanalyzed the scattered beam for specific energy loss, recovering Bragg peak coherence and measuring properties of surface phonons.…”

Coherent diffraction of hydrogen through the 246 pm lattice of graphene

“…After a momentum transfer of Δp, the wave function of the C atom χ (R) becomes e −iΔpR/ÿ χ(R) [46]. For a 1D harmonic oscillator the elastic diffraction probability P e is then described by the Debye-Waller factor (DWF) [47] …”