Diffraction of H from LiF(001): From slow normal incidence to fast grazing incidence

Abstract

International audienceDescribing diffraction of atomic and molecular projectiles at fast grazing incidence presents a realchallenge for quantum theoretical simulations due to the high incidence energy (100 eV–1 keV) usedin experiments. This is one of the main reasons why most theoretical simulations performed to dateare based on reduced dimensional models. Here we analyze two alternatives to reduce the computationaleffort, while preserving the real dimensionality of the system. First, we show that grazing incidenceconditions are already fulfilled for incidence angles 6 5 degrees, i.e., incidence angles higher than those typicallyused in experiments. Thus, accurate comparisons with experiment can be performed considering diffrac-tion at grazing incidence, but with smaller total incidence energies, whilst keeping the same experimen-tal normal energy in the calculations. Second, we show that diffraction probabilities obtained at fastgrazing incidence are fairly well reproduced by simulations performed at slow normal incidence. Thislatter approach would allow one to simulate several experimental spectra, measured at the same normalincidence energy for several incidence crystallographic directions, with only one calculation. Thisapproach requires to keep the full dimensionality of the system

H2/LiF(001) diffractive scattering under fast grazing incidence using a DFT-based potential energy surface

“…7(a)], the agreement between theory and experiment is remarkable, supporting the accuracy of our DFT-based 6D PES. The good agreement between the MCTDH simulations, the TDWP ones, and the experimental results further support our previous conclusions for H/LiF(001) [16], according to which fast grazing incidence conditions are reached for θ i values higher (E i lower) than the typical ones used in experiments. On the other hand, for incidence along the [110] direction, although the agreement between 5D-MCTDH and 6D-TDWP simulations is once again excellent, the comparison between experiment and theory is rather poor.…”

“…Spectra measured for molecular projectiles are richer than for atomic projectiles due to the internal molecular degrees of freedom (DOFs) [7], and therefore they are in principle a more sensitive tool for surface analysis. From a theoretical point of view, the diffraction of atomic projectiles has been widely studied [4,6,[8][9][10][11][12][13][14][15][16]. However, little attention has been devoted to molecular projectiles, beyond some classical scattering studies [17][18][19], although in this case theory can play a key role in understanding experimental results.…”

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

“…The range of validity of this axial channeling approximation has been investigated in detail [19,20,39]. With this energy landscape, several techniques have successfully described the diffraction patterns such as exact wave packet [8,14,21], close coupling [15] or multi configuration time-dependent Hartree [20]. Other approaches based on Bohmian trajectories [23] or even classical trajectories and semi classical approaches [24,25] including specific correction of the rainbow divergence [25] have shown good agreement with experimental results.…”

“…The specificity of grazing angles is accounted for by averaging the actual 3D potential energy surface V 3D (x, y, z) along the direction of the fast movement (here x as in Fig.1) producing a 2D landscape V 2D (y, z) where a particle with energy E ⊥ diffracts just as in standard thermal energy atom scattering [8,18]. The range of validity of this axial channeling approximation has been investigated in detail [19,20,39]. With this energy landscape, several techniques have successfully described the diffraction patterns such as exact wave packet [8,14,21], close coupling [15] or multi configuration time-dependent Hartree [20].…”

Energy loss and inelastic diffraction of fast atoms at grazing incidence

“…Here x is taken along the low index crystal axis as depicted in Fig.1 and d x is the period along x. This axial channeling approximation (ASCA) was established with quantitative criterion well satisfied for grazing incidence keV projectile and small lattice units [14,15]. Experimentally this is evidenced by the presence of only one Laue circle.…”