  Understanding the influence of phonon-mediated processes on grazing-incidence
fast atom diffraction (GIFAD) patterns is relevant for its use as a surface
analysis technique. In this work, we apply the Phonon-Surface Initial Value
Representation (P0-SIVR) approximation to study lattice vibration effects on
GIFAD patterns for the He-LiF(001) system at room temperature. The P0-SIVR
approach is a semiquantum method that describes the zero-phonon atom-surface
scattering including the contribution of intermediate phonon transitions. The
main features introduced by thermal lattice vibrations in the angular
distributions of the scattered helium atoms are investigated by considering
normal energies in the 0.1 -3 eV range. In all the cases, thermal fluctuations
introduce a wide polar spread that transforms the interference maxima into
elongated strips. We found that the polar width of these fringes does not
depend on the normal energy, as it was experimentally observed. In addition,
when the normal energy increases, not only the relative intensities of
interference peaks are affected by the crystal vibrations, but also the
visibility of the interference structures, which disappear completely for
normal energies approximately equal to or higher than 3 eV. These findings
agree fairly well with the experimental data reported in Phys. Chem. Chem.
Phys. 237615 (2021). However, it should be noticed that the simulated polar
widths underestimate the experimentally-derived limit, suggesting that there
are other mechanisms, such as inelastic phonon processes, that contribute to
the polar dispersion of the GIFAD patterns.
