Quantum scattering of fast atoms and molecules on surfaces

Elastic and inelastic diffraction of fast neon atoms on a LiF surface

Grazing incidence fast atom diffraction has mainly been investigated with helium atoms, considered as the best possible choice for surface analysis. This article presents experimental diffraction profiles recorded with neon projectile, between 300 eV and 4 keV kinetic energy with incidence angles θi between 0.3 and 1.5° along three different directions of a LiF(001) crystal surface. These correspond to perpendicular energy ranging from a few meV up to almost 1 eV. A careful analysis of the scattering profile allows us to extract the diffracted intensities even when inelastic effects become so large that most quantum signatures have disappeared. The relevance of this approach is discussed in terms of surface topology.

A setup for grazing incidence fast atom diffraction

We describe a UHV setup for grazing incidence fast atom diffraction (GIFAD) experiments. The overall geometry is simply a source of keV atoms facing an imaging detector. Therefore, it is very similar to the geometry of reflection high energy electron diffraction experiments used to monitor growth at surfaces. Several custom instrumental developments are described making GIFAD operation efficient and straightforward. The difficulties associated with accurately measuring the small scattering angle and the related calibration are carefully analyzed.

Stereodynamics effects in grazing-incidence fast-molecule diffraction

Grazing-incidence fast-projectile diffraction has been proposed both as a complement and an alternative to thermal-energy projectile scattering, which explains the interest that this technique has received in recent years, especially in the case of atomic projectiles. On the other hand, despite the richer physics involved, molecular projectiles have received much less attention. In this work, we present a theoretical study of grazing-incidence fast-molecule diffraction of H₂ from KCl(001) using a six-dimensional density functional theory based potential energy surface and a time-dependent wavepacket propagation method. The analysis of the computed diffraction patterns as a function of the molecular alignment, and their comparison with the available experimental data, where the initial distribution of rotational states in the molecule is not known, reveals a puzzling stereodynamics effect of the diffracted projectiles: diffracted molecules aligned perpendicular, or quasi perpendicular, to the surface reproduce rather well the experimental diffraction pattern, whereas those molecules aligned parallel to or tilted with respect to the surface do not behave as in the experiments. These results call for more detailed investigations of the molecular beam generation process.

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.

Grazing incidence fast atom and molecule diffraction: theoretical challenges

This perspective article reviews the state-of-the-art of grazing incidence fast atom and molecule diffraction (GIFAD and GIFMD) simulations and addresses the main challenges that theorists, aiming to provide useful inputs in this topic, are facing. We first discuss briefly the methods used to build accurate potential energy surfaces describing the interaction between the projectile and the surface. Subsequently, we focus on the dynamics simulation methods for GIFAD, a phenomenon that has received a lot of experimental attention since 2007, when the first measurements were published. Following this experimental effort, theorists have developed and adapted a bunch of methods able to simulate, analyze and extract information from the experimental outputs. We review these methods, from the very simple ones based on classical dynamics to the full quantum ones, paying special attention to more versatile semiclassical approaches, which include quantum ingredients in the dynamics at a computational cost only slightly higher than that required in classical dynamics. Within the semiclassical framework it is possible, for example, to include in the dynamics the surface phonons and the projectile coherence, two factors that may have a relevant influence on the experimental measurements, at a reasonable computational cost. Finally, we address GIFMD, a phenomenon that has received much less attention and for which there is still a lot of room for research. We review the few examples of GIFMD available in the literature, and we discuss new phenomena associated with the molecular internal degrees of freedom, which may have some impact in other closely related fields, such as molecular reactivity on metal surfaces. Finally, we point out opened questions, raised from the comparisons between theoretical and experimental results, which claim for further experimental efforts.

Temperature dependence in fast-atom diffraction at surfaces

Grazing incidence fast atom diffraction at crystal surfaces (GIFAD or FAD) has demonstrated coherent diffraction both at effective energies close to one eV (λ_⊥ ≈ 14 pm for He) and at elevated surface temperatures offering high topological resolution and real time monitoring of growth processes. This is explained by a favorable Debye-Waller factor specific to the multiple collision regime of grazing incidence. This paper presents the first extensive evaluation of the temperature behavior between 177 and 1017 K on a LiF surface. Similarly to diffraction at thermal energies (TEAS), an exponential attenuation of the elastic intensity is observed but, contrarily to TEAS, the maximum coherence is not directly reduced by the attraction forces that increase the effective impact energy. It is more influenced by the surface stiffness and appears very sensitive to surface defects.

Grazing incidence fast atom diffraction, similarities and differences with thermal energy atom scattering (TEAS)

Grazing incidence fast atom diffraction (GIFAD) at surfaces has made rapid progress and has established itself as a surface analysis tool where effective energy E_⊥ of the motion towards the surface is in the same range as that in thermal energy atom scattering (TEAS). To better compare the properties of both techniques, we use the diffraction patterns of helium and neon atoms impinging on a LiF (001) surface as a model system. E-Scan, θ-scan, and φ-scan are presented where the primary beam energy E is varied between a few hundred eV up to five keV, the angle of incidence θ_i between 0.2 and 2° and the azimuthal angle φ_i around 360°. The resulting diffraction charts are analyzed in terms of high and low values of effective energy E_⊥. The former provides high resolution at the positions of the surface atoms and the attached repulsive interaction potentials while the second is sensitive to the attractive forces towards the surface. The recent progress of inelastic diffraction is briefly presented.

Anomalous KCl(001) Surface Corrugation from Fast He Diffraction at Very Grazing Incidence

We present theoretical and experimental evidence of an anomalous surface corrugation behavior in He-KCl(001) for incidence along ⟨110⟩. When the He normal energy decreases below 100 meV, i.e., He-surface distances Z>2  Å, the corrugation unexpectedly increases up to an impressive ≳85%. This is not due to van der Waals interactions but to the combination of soft potential effects and the evolution of He-cation and He-anion interactions with Z. This feature, not previously analyzed on alkali-halide surfaces, may favor the alignment properties of weakly interacting overlayers.

Refraction of Fast Ne Atoms in the Attractive Well of a LiF(001) Surface

Ne atoms with energies of ≤3 keV are diffracted under grazing angles of incidence from a LiF(001) surface. For a small momentum component of the incident beam perpendicular to the surface, we observe an increase in the elastic rainbow angle together with a broadening of the inelastic scattering profile. We interpret these two effects as the refraction of the atomic wave in the attractive part of the surface potential. We use a fast, rigorous dynamical diffraction calculation to find a projectile-surface potential model that enables a quantitative reproduction of the experimental data for ≤10 diffraction orders. This allows us to extract an attractive potential well depth of 10.4 meV. Our results set a benchmark for more refined surface potential models that include the weak van der Waals region, a long-standing challenge in the study of atom-surface interactions.

Coherence-Length Effects in Fast Atom Diffraction at Grazing Incidence

Coherence properties of projectiles, found relevant in ion-atom collisions, are investigated by analyzing the influence of the degree of coherence of the atomic beam on interference patterns produced by grazing-incidence fast-atom diffraction (GIFAD or FAD). The transverse coherence length of the projectiles, which depends on the incidence conditions and the collimating setup, determines the overall characteristics of GIFAD distributions. We show that for atoms scattered from a LiF(001) surface after a given collimation, we can modify the interference signatures of the angular spectra by varying the total impact energy, while keeping the normal energy as a constant. Also, the role played by the geometry of the collimating aperture is analyzed, comparing results for square and circular openings. Furthermore, we study the spot-beam effect, which is due to different focus points of the impinging particles. We show that when a region narrower than a single crystallographic channel is coherently illuminated by the atomic beam, the spot-beam contribution strongly affects the visibility of the interference structures, contributing to the gradual quantum-classical transition of the projectile distributions.

Spot-beam effect in grazing atom-surface collisions: from quantum to classical

Grazing incidence fast atom diffraction (GIFAD) is a sensitive tool for surface analysis, which strongly relies on the quantum coherence of the incident beam. In this article we study the spot-beam effect, due to contributions coming from different positions of the focus point of the incident particles, which affects the coherence of GIFAD spectra. We show that the influence of the spot-beam effect on GIFAD patterns depends on the width of the surface area that is coherently lighted by the atomic beam. While for extended illuminations the spot-beam contribution plays a minor role, when a narrow surface area is coherently lighted, the spot-beam effect allows projectiles to explore different zones of a single crystallographic channel, bringing to light intra-channel interference structures. In this last case the spot-beam effect gives also rise to a non-coherent background, which deteriorates the visibility of the interference structures. We found that by varying the impact energy, while keeping the same collimating setup, it is possible to switch gradually from quantum to classical projectile distributions. Present results are compared with available experimental data, making evident that the inclusion of focusing effects is necessary for the proper theoretical description of the experimental spectra.

Ultrafast Crystallization Dynamics at an Organic-Inorganic Interface Revealed in Real Time by Grazing Incidence Fast Atom Diffraction

The poor structural properties of organic-inorganic interfaces and their variability represent the main cause of device under-performance. Understanding and controlling the development of these properties in real time has been a difficult experimental challenge. Using a recent technique based on grazing incidence fast atom diffraction (GIFAD), we were able to directly observe during deposition structural transitions in a perylene monolayer on Ag(110). Crystallization from the liquid phase occurs into two distinct structures with drastically different dynamics. Transition to the most compact packing occurs by self-organization only after a second layer has started to build up; subsequent incorporation of molecules from second to first layer triggers an ultrafast crystallization on a macroscopic sale. The final compact crystalline structure shows a long-range order and superior stability, which opens good perspectives for producing in a controlled manner highly ordered hybrid interfaces for photovoltaics and molecular electronics.

Exploring surface landscapes with molecules: rotationally induced diffraction of H2 on LiF(001) under fast grazing incidence conditions

Atomic diffraction by surfaces under fast grazing incidence conditions has been used for almost a decade to characterize surface properties with more accuracy than with more traditional atomic diffraction methods. From six-dimensional solutions of the time-dependent Schrödinger equation, we show that diffraction of H₂ molecules under fast grazing incidence conditions could be even more informative for the characterization of ionic surfaces, due to the large anisotropic electrostatic interaction between the quadrupole moment of the molecule and the electric field created by the ionic crystal. Using the LiF(001) surface as a benchmark, we show that fast grazing incidence diffraction of H₂ strongly depends on the initial rotational state of the molecule, while rotationally inelastic processes are irrelevant. We demonstrate that, as a result of the anisotropy of the impinging projectile, initial rotational excitation leads to an increase in intensity of high-order diffraction peaks at incidence directions that satisfy precise symmetry constraints, thus providing a more detailed information on the surface characteristics than that obtained from low-order atomic diffraction peaks under fast grazing incidence conditions. As quadrupole-ion surface potentials are expected to accurately represent the interaction between H₂ and any surface with a marked ionic character, our analysis should be of general applicability to any of such surfaces. Finally, we show that a density functional theory description of the molecule-ion surface potential catches the main features observed experimentally.

Quantum and classical dynamics of reactive scattering of H2 from metal surfaces

State-of-the-art theoretical models allow nowadays an accurate description of H₂/metal surface systems and phenomena relative to heterogeneous catalysis. Here we review the most relevant ones investigated during the last 10 years.

Transient quantum trapping of fast atoms at surfaces

We report on the experimental observation and theoretical study of the bound state resonances in fast atom diffraction at surfaces. In our studies, the 4He atom beam has been scattered from a high-quality LiF(001) surface at very small grazing incidence angles. In this regime, the reciprocal lattice vector exchange with the surface allows transient trapping of the 0.3-0.5 keV projectiles into the quasistationary states bound by the attractive atom-surface potential well which is only 10 meV deep. Analysis of the linewidths of the calculated and measured resonances reveals that prior to their release, the trapped projectiles preserve their coherence over travel distances along the surface as large as 0.2  μm, while being in average only at some angstroms in front of the last atomic plane.

Diffraction of helium on MgO(100) surface calculated from first-principles

In this work we simulate the diffraction peak intensities of He beams scattered on the MgO(100) surface using hierarchical protocol, based on periodic and finite-cluster quantum-chemical calculations.

Surface structure of alanine on Cu(110) studied by fast atom diffraction

We demonstrate that quantum scattering of fast atoms and molecules under grazing angles of incidence can be exploited to study the structure of organic molecules on metal surfaces. Making use of keV H and He atoms as well as H2 molecules, the surface structures of the chiral amino acid alanine adsorbed on a Cu(110) surface is studied. We present a detailed investigation on the (3×2) phase of a monolayer of enantiopure and racemic alanine on Cu(110), revealing the formation of an elongated surface unit cell of c(n×2) symmetry with n=3.16±0.04 for the sticking out methyl groups of the alanine molecules.

Experimental methods of molecular matter-wave optics

We describe the state of the art in preparing, manipulating and detecting coherent molecular matter. We focus on experimental methods for handling the quantum motion of compound systems from diatomic molecules to clusters or biomolecules.Molecular quantum optics offers many challenges and innovative prospects: already the combination of two atoms into one molecule takes several well-established methods from atomic physics, such as for instance laser cooling, to their limits. The enormous internal complexity that arises when hundreds or thousands of atoms are bound in a single organic molecule, cluster or nanocrystal provides a richness that can only be tackled by combining methods from atomic physics, chemistry, cluster physics, nanotechnology and the life sciences.We review various molecular beam sources and their suitability for matter-wave experiments. We discuss numerous molecular detection schemes and give an overview over diffraction and interference experiments that have already been performed with molecules or clusters.Applications of de Broglie studies with composite systems range from fundamental tests of physics up to quantum-enhanced metrology in physical chemistry, biophysics and the surface sciences.Nanoparticle quantum optics is a growing field, which will intrigue researchers still for many years to come. This review can, therefore, only be a snapshot of a very dynamical process.

High resolution imaging of superficial mosaicity in single crystals using grazing incidence fast atom diffraction

A new table top technique is used to simultaneously analyze the local morphology of crystalline surfaces as well as the misalignment of large scale domains at the topmost surface layer. The approach is based on fast atom diffraction at grazing incidence (GIFAD); the diffraction pattern yields the structural characteristics and the topology of the surface electronic density with atomic resolution. If superficial mosaicity is present, diffraction patterns arising from each mosaic domain can be distinguished, providing high sensitivity to the properties of each of the domains. Taking NaCl(001) as an example, we observe a discrete tilt angle distribution of the mosaic domains following an arithmetic progression with a 0.025° ± 0.005° difference; a twist mosaic angle of 0.09° ± 0.01° is also observed.

Helium mediated deposition: modeling the He-TiO2(110)-(1×1) interaction potential and application to the collision of a helium droplet from density functional calculations

This paper is the first of a two-part series dealing with quantum-mechanical (density-functional-based) studies of helium-mediated deposition of catalytic species on the rutile TiO(2)(110)-(1×1) surface. The interaction of helium with the TiO(2)(110)-(1×1) surface is first evaluated using the Perdew-Burke-Ernzerhof functional at a numerical grid dense enough to build an analytical three-dimensional potential energy surface. Three (two prototype) potential models for the He-surface interaction in helium scattering calculations are analyzed to build the analytical potential energy surface: (1) the hard-corrugated-wall potential model; (2) the corrugated-Morse potential model; and (3) the three-dimensional Morse potential model. Different model potentials are then used to study the dynamics upon collision of a (4)He(300) cluster with the TiO(2)(110) surface at zero temperature within the framework of a time-dependent density-functional approach for the quantum fluid [D. Mateo, D. Jin, M. Barranco, and M. Pi, J. Chem. Phys. 134, 044507 (2011)] and classical dynamics calculations. The laterally averaged density functional theory-based potential with an added long-range dispersion interaction term is further applied. At variance with classical dynamics calculations, showing helium droplet splashing out of the surface at impact, the time evolution of the macroscopic helium wave-function predicts that the helium droplet spreads on the rutile surface and leads to the formation of a thin film above the substrate. This work thus provides a basis for simulating helium mediated deposition of metallic clusters embedded within helium nanodroplets.

Semiclassical perturbation theory for diffraction in heavy atom surface scattering

The semiclassical perturbation theory formalism of Hubbard and Miller [J. Chem. Phys. 78, 1801 (1983)] for atom surface scattering is used to explore the possibility of observation of heavy atom diffractive scattering. In the limit of vanishing ℏ the semiclassical theory is shown to reduce to the classical perturbation theory. The quantum diffraction pattern is sensitive to the characteristics of the beam of incoming particles. Necessary conditions for observation of quantum diffraction are derived for the angular width of the incoming beam. An analytic expression for the angular distribution as a function of the angular and momentum variance of the incoming beam is obtained. We show both analytically and through some numerical results that increasing the angular width of the incident beam leads to decoherence of the quantum diffraction peaks and one approaches the classical limit. However, the incoherence of the beam in the parallel direction does not destroy the diffraction pattern. We consider the specific example of Ar atoms scattered from a rigid LiF(100) surface.

Young-type interference for scattering of fast helium atoms from an oxygen covered Mo(112) surface

In studies on two structures of oxygen adsorbates on Mo(112), we demonstrate the potential of fast atom diffraction to derive the surface unit cell size and its symmetry. Helium atoms with energies of 1-2 keV are scattered from an adsorbate covered Mo(112) surface along low indexed surface directions under grazing angles of incidence. From the observed diffraction patterns, the lateral periodicity of the surface structures is derived. In addition to the periodic lattice, information on the structure within the unit cell can be obtained from double slit type of interference.

Coherence during scattering of fast H atoms from a LiF(001) surface

The coherence for diffraction effects during grazing scattering of fast hydrogen and helium atoms from a LiF(001) surface with energies up to some keV is investigated via the coincident detection of two-dimensional angular distributions for scattered projectiles with their energy loss. For keV H atoms, we identify electronic excitations of the target surface as the dominant mechanism for decoherence, whereas for He atoms this contribution is small. The suppression of electronic excitations owing to the band gap of insulators plays an essential role for preserving quantum coherence and thus for the application of fast atom diffraction as a surface analytical tool.

Nearly resonant multidimensional systems under a transient perturbative interaction

We analyze the response of a classical system with N>or=2 internal degrees of freedom satisfying R<or=(N-1) approximated resonance conditions to an external perturbative transient interaction. Under certain assumptions on the system internal frequencies and on the coupling interaction, we show the precise N-R adiabatic invariants and obtain an estimate of the span of the domain defined by the intersecting resonances. The results are illustrated considering a system of three anharmonic oscillators transiently coupled by an explicitly time-dependent interaction, and applied to the low energy vibro-rotationally inelastic collisions between two diatomic molecules.

Cyclic Sommerfeld resonances in nanorods at grazing incidences

We investigate electromagnetic scattering from nanoscale wires and reveal the emergence of a family of exotic resonances for source waves close to grazing incidence. These grazing resonances have a much higher Q-bandwidth product and thus, a much higher Q factor and broader bandwidth than the pure plasmonic resonances found in metal nanowires. Furthermore, these grazing resonances are much less susceptible to material losses than surface plasmon resonances. Contrary to the process of exciting surface plasmon resonances, these grazing resonances can arise in both dielectric and metallic nanowires and appear near to the cutoff wavelength of the circular waveguide. This peculiar resonance effect originates from the excitation of long range guided surface waves through the interplay of coherently scattered continuum modes coupled with first-order azimuthal propagating modes of the cylindrical nanowire. These first-order cyclic Sommerfeld waves and associated cyclic Sommerfeld resonances revealed here opens up the possibility of an alternative scheme of enhanced fields with a better merit (higher Q-bandwidth product and lower loss) than conventional surface plasmon resonances in the nano-regime. This nanowire resonance phenomenon can be utilized in broad scientific areas, including: metamaterial designs, nanophotonic integration, nanoantennas, and nanosensors.

Return to coherence via Debye-Waller factor quenching

A number of scattering situations can naively be expected to show essentially classical features, because of a (generalized) Debye-Waller factor causing decoherence and destroying interference and diffraction phenomena. It is shown, however, that such decoherence may be quenched in several ways: A-the momentum transfer to a large system may be separated into subtransfers to individual atoms, each subtransfer being too small to cause a strong Debye-Waller effect; B-(more significantly) the high-frequency vibrations may be ineffective in causing strong decoherence, because the corresponding correlation functions remain non-vanishing for too short a time. When this Debye-Waller factor quenching takes place, coherence is restored and typical quantum wave-like phenomena reappear.

Molecular effects in H2 scattering from metal surfaces at grazing incidence

Collisions of fast atoms with surfaces at grazing incidence have been recently proposed as a promising new tool to determine surface parameters with unprecedented accuracy. Here we show, by means of classical dynamics calculations performed with first-principles six-dimensional potential energy surfaces for H2/NiAl(110) and H2/Pd(111) that, under grazing incidence conditions, fast light molecular projectiles are also useful to determine sticking probabilities at thermal energies, from the threshold up to the saturation limit. Thus they are the ideal complement to traditional experiments at thermal energies to determine sticking curves up to the saturation limit.

Quantum scattering of neon from a nanotextured surface

Phonon exchange is the usual cause of decoherence in atom-surface scattering. By including quantum effects in the treatment of Debye-Waller scattering, we show that phonon exchange becomes ineffective when the relevant phonon frequencies are high. The result explains the surprising observation of strong elastic scattering of Ne from a Cu(100) surface nanotextured with a c(2 × 2) Li adsorbate structure. We extend a previous model to describe the phonon spectra by an Einstein oscillator component with an admixture of a Debye spectrum. The Einstein oscillator represents the dominant, high frequency vibration of the adsorbate, normal to the surface, while the Debye spectrum represents the substrate contribution. Neon scattering is so slow that exciting the adsorbate mode has a low probability and is impossible if the incident energy is below the threshold. Thus, adsorbate vibrations are averaged out. A theoretical discussion and calculation shows that under such circumstances the vibrations of a light adsorbate do not contribute to the Debye-Waller effect, with the result that Ne scattering at thermal energies is quantum mechanical and largely elastic, explaining the high reflectivity and the diffraction peaks observed experimentally.

Fast atom diffraction from superstructures on a Fe110 surface

Fast atoms with energies from 500 eV up to several keV are grazingly scattered from a Fe(110) surface covered with defined superstructures of sulfur or oxygen atoms. For scattering along low index azimuthal directions, we observe defined diffraction patterns in the angular distributions for scattered projectiles. From the analysis of those patterns, we derive the widths of low indexed axial channels and the corrugation of the interaction potential across these channels. This allows us to estimate the positions of adsorbed atoms on the Fe(110) surface. By demonstration, for adsorbate induced superstructures on a metal surface, we show that fast atom diffraction, first observed for insulators, can be applied to studies on surface structures for a wide range of materials.

Suppression of decoherence in fast-atom diffraction at surfaces

Scattering of fast neutral atoms with keV kinetic energies at alkali-halide surfaces under grazing angles displays intriguing diffraction patterns. The surprisingly strong persistence of quantum coherence despite the impulsive interaction with an environment at solid state density and elevated temperatures raises fundamental questions such as to the suppression of decoherence and of the quantum-to-classical crossover. We present an ab initio simulation of the quantum diffraction of fast helium beams at a LiF (100) surface in the 110 direction and compare with recent experimental diffraction data. From the quantitative reconstruction of diffraction images the vertical LiF-surface reconstruction, or buckling, can be determined.

Grazing incidence diffraction of keV helium atoms on a Ag(110) surface

Diffraction of fast atoms at grazing incidence has been recently demonstrated on the surface of alkali halides and wide band gap semiconductors, opening applications for the online monitoring of surface processes such as growth of ultrathin layers. This Letter reports energy resolved diffraction of helium on Ag(110) metal surface showing that a band gap is not mandatory to restrict the decoherence due to electron-hole pair excitations by the keV projectile. Measurement of the energy loss, which is in the eV range, sheds light on the scattering process.

Evidence of wave-particle duality for single fast hydrogen atoms

We report the direct observation of interference effects in a Young's double-slit experiment where the interfering waves are two spatially separated components of the de Broglie wave of single 1.3 MeV hydrogen atoms formed close to either target nucleus in H++H2 electron-transfer collisions. Quantum interference strongly influences the results even though the hydrogen atoms have a de Broglie wavelength, lambda_{dB}, as small as 25 fm.

Supernumerary rainbows in the angular distribution of scattered projectiles for grazing collisions of fast atoms with a LiF(001) surface

Fast atoms with keV energies are scattered under a grazing angle of incidence from a clean and flat LiF(001) surface. For scattering along low index azimuthal directions within the surface plane ("axial surface channeling") we observe pronounced peak structures in the angular distributions for scattered projectiles that are attributed to "supernumerary rainbows." This phenomenon can be understood in the framework of quantum scattering only and is observed here up to projectile energies of 20 keV. We demonstrate that the interaction potential and, in particular, its corrugation for fast atomic projectiles at surfaces can be derived with a high accuracy.

Diffraction of fast atomic projectiles during grazing scattering from a LiF(001) surface

Light atoms and molecules with energies from 300 eV to 25 keV are scattered under a grazing angle of incidence from a LiF(001) surface. For impact of neutral projectiles along low index directions for strings of atoms in the surface plane we observe a defined pattern of intensity spots in the angular distribution of reflected particles which is consistently described using concepts of diffraction theory and specific features of grazing scattering of atoms from insulator surfaces. Experimental results for scattering of H, D, 3He, and 4He atoms as well as H2 and D2 molecules can be unequivocally referred to atom diffraction with de Broglie wavelengths as low as about 0.001 Angstroms.