Selective adsorption resonances at rainbow conditions in the scattering of atoms by stepped surfaces: application to the He/Cu(117) system

For stepped surfaces, dynamics is not parity reversal invariant with respect to the step configuration and the way the atomic beam approaches the surface, downstairs or upstairs scattering, should dramatically change rainbow patterns. We show that only one close-coupling calculation provides us information of the two possible scatterings at once. Furthermore, it is possible to find some incident conditions where surface rainbow is displayed for both configurations. At the same time, if resonances are analysed at rainbow conditions, we could enhance resonant features in the diffraction channel displaying rainbow. An application to the study of diffraction of ⁴He atoms by the Cu(117) surface is presented.     

Multiphonon atom-surface scattering from corrugated surfaces: derivation of the inelastic scattering spectrum for diffraction states

A strictly quantum mechanical derivation of the energy and parallel momentum resolved scattering spectrum formula that combines the effects of the diffraction of atoms from corrugated surfaces and multiple inelastic scattering by dispersive phonons is presented. The final result is expressed in the compact and numerically tractable form of a Fourier transform of a cumulant expansion in which each term embodies an interplay between the processes of projectile diffraction and multiphonon scattering to all orders in the respective interaction potentials. The Debye-Waller reduction of the intensities of diffraction peaks is explicitly formulated.     

Classical theory of atom–surface scattering: The rainbow effect

The scattering of heavy atoms and molecules from surfaces is oftentimes dominated by classical mechanics. A large body of experiments have gathered data on the angular distributions of the scattered species, their energy loss distribution, sticking probability, dependence on surface temperature and more. For many years these phenomena have been considered theoretically in the framework of the “washboard model” in which the interaction of the incident particle with the surface is described in terms of hard wall potentials. Although this class of models has helped in elucidating some of the features it left open many questions such as: true potentials are clearly not hard wall potentials, it does not provide a realistic framework for phonon scattering, and it cannot explain the incident angle and incident energy dependence of rainbow scattering, nor can it provide a consistent theory for sticking. In recent years we have been developing a classical perturbation theory approach which has provided new insight into the dynamics of atom–surface scattering. The theory includes both surface corrugation as well as interaction with surface phonons in terms of harmonic baths which are linearly coupled to the system coordinates. This model has been successful in elucidating many new features of rainbow scattering in terms of frictions and bath fluctuations or noise. It has also given new insight into the origins of asymmetry in atomic scattering from surfaces. New phenomena deduced from the theory include friction induced rainbows, energy loss rainbows, a theory of super-rainbows, and more. In this review we present the classical theory of atom–surface scattering as well as extensions and implications for semiclassical scattering and the further development of a quantum theory of surface scattering. Special emphasis is given to the inversion of scattering data into information on the particle–surface interactions.     

Influence of the quantum size effect for grazing electrons on the electronic conductivity of metal films

The thickness dependence of the electronic conductivity of thin (5–150 nm) single-crystal (100) films of refractory metals is investigated at different temperatures ranging from 4.2 K to room temperature. Regions of square-root, quasilinear, and quadratic dependences are observed. The quasilinear thickness dependence is explained by the influence of quantum effects on the transverse motion of electrons in the case when electron scattering by the film surfaces dominates. For macroscopic film thicknesses 30–50 nm, much greater than the Fermi wavelength of an electron, quantum corrections to the electronic conductivity reach values of the order of 50%. This is a consequence of the quantum size effect for grazing electrons, which leads to an anomaly in electron scattering by the film surfaces. The region of the quadratic thickness dependence corresponds to the quantum limit, and the square-root region corresponds to the classical limit. The effect is explained in a quasiclassical two-parameter model (the effective angle α* for small-angle electrons and the parameter γ, equal to the ratio of this angle to the diffraction angle) that takes into account the diffraction angular limits for grazing electrons. The effect occurs for parameters α*≪1 and γ∼1 and differs from the “ordinary” quantum size effect. Pis’ma Zh. éksp. Teor. Fiz. 66, No. 11, 693–698 (10 December 1997)     

Rainbow Interferometry with Wire Diffraction for Simultaneous Measurement of Droplet Temperature,Size and Velocity

A rainbow measurement technique is presented which measures simultaneously the size, temperature and velocity of individual droplets in a spray. The technique is based on rainbow interferometry in combination with diffraction by a wire placed in the spatial filter of the scattered-light detector. A photomultiplier detects the wire diffraction pattern superimposed on the rainbow interference pattern created by a droplet scattering laser light. The velocity is determined from the equivalent geometric wire shadow. The necessary sphericity validation is performed by comparing the Airy and the ripple droplet diameters, resulting from the respective interference structures. The temperature is recovered from the position of the wire diffraction pattern relative to the main rainbow maximum. The technique was applied to a water spray at ambient temperature. The results showed the importance of nonsphericity detection.     

Rotational state distribution of NO molecules scattered from surfaces

Quantum mechanical calculations of final rotational state distributions are carried out for a simple model of the scattering of NO from surfaces. The dependence of the results on parameters of the potential such as sign and size of the anisotropy and asymmetry, the well depth etc. is discussed. Certain difficulties in explaining experimental results for NO scattered from Ag (111) are pointed out. The dependence of the results on an initial rotational temperature is discussed also. Its main effect — which is well known from the literature — is to average out the quantum oscillations of the cross sections around the rainbow structures. The oscillations may become visible at rotational temperatures slightly lower than used up to now.Dedicated to B. Mühlschlegel on the occasion of his 60th birthday     

Intensity of intersubband electron scattering by polar optical phonons in semiconductor quantum wires with account of energy level broadening

An approach describing the effect of energy level broadening in semiconductor quantum wires on the intensity of intersubband electron scattering by polar optical phonons is suggested. As a broadening mechanism, scattering by atomic thermal vibrations and by the roughness of the confining surfaces of a quantum system is considered. It is shown that in this case the dependence of the intensity of intersubband scattering of electrons on their kinetic energy has no singularities.     

Classical scattering of Atoms by a model surface

A classical model of atom/surface scattering is presented in which the gas-surface interaction consists of a corrugated hard wall plus attractive square well. New analytic solutions for the scattering intensity for monoenergetic beams are given for both one- and two-dimensional surfaces. Explicit formulae for trapping probabilities and rainbow angles are obtained. An oven beam velocity distribution is incorporated into the model, and calculated results are presented both for in-plane and out-of-plane scattering. Comparisons are made with the Ne/LiF data of Smith, O'Keefe, and Palmer and with the classical calculations of McClure. Objections to the classical rainbow scattering interpretation are discussed.     

Simple approach to refraction effects in atom-surface scattering

A simple method of calculating low energy atom-surface diffraction intensities is presented for the case in which the scattering is dominated by a single rainbow pattern. Good agreement is obtained when these calculations are compared with recent results for the scattering of He by a Pt(997) surface.     

The Aharonov–Bohm effect in scattering theory

The Aharonov–Bohm effect is considered as a scattering event with nonrelativistic charged particles of the wavelength which is less than the transverse size of an impenetrable magnetic vortex. The quasiclassical WKB method is shown to be efficient in solving this scattering problem. We find that the scattering cross section consists of two terms, one describing the classical phenomenon of elastic reflection and another one describing the quantum phenomenon of diffraction; the Aharonov–Bohm effect is manifested as a fringe shift in the diffraction pattern. Both the classical and the quantum phenomena are independent of the choice of a boundary condition at the vortex edge, providing that probability is conserved. We show that a propagation of charged particles can be controlled by altering the flux of a magnetic vortex placed on their way.     

Interaction of neutral hydrogen atoms with KCl(OO1)

Neutral hydrogen atoms with velocity selected thermal energies, have been scattered from KCl(001) cleavage planes in UHV. For cold crystal surfaces (T_SF ? 170 K) even a small residual pressure of water resulted in an ordered monolayer coverage of the (001) plane. From this surface, diffraction has been observed with diffracted beams up to third order and characteristically varying intensities were observed and analysed in terms of a quantum mechanical rainbow scattering theory. Resonant transitions of atoms to bound states at the surface (“selective adsorption”) were observed and used to determine the interaction potential of hydrogen atoms with this water covered surface: first in terms of a Morse potential, second in terms of a $\text{C}{}_3\text{z}{}^3$-dependent attractive potential. The surface Debye-Waller factor has been measured for clean KCl(001), for the water covered (001) plane as well as for partially covered surfaces. The results are interpreted within a simple model.     

Coherent and diffuse X-ray scattering from a multicomponent superlattice with quantum dots

GaAs-AlAs superlattices with InAs quantum dots grown by molecular beam epitaxy have been studied by high-resolution X-ray diffractometry. It has been experimentally revealed that the maxima of the superstructural diffuse scattering from the quantum dots do not coincide with the angular positions of the coherent superstructural satellites. A statistical theory of diffraction on the superlattice taking into account the spatial correlation of the quantum dots has been developed to explain this effect. It has been shown within this theory that the peak positions of the diffuse component can differ from the maxima of the coherent scattering. X-ray scattering by the multicomponent superlattice have been numerically simulated and the calculation results have been compared with the experimental data.     

Cutoffs and shadows in classical scattering of atoms from surfaces

A commonly used model for the scattering of atoms from crystalline surfaces is that of a classical hard sphere interacting with a hard, corrugated surface. This model is simple enough to permit the study of the effect on the scattering of variation of parameters of the model. We examine here how changes in the amplitude and symmetry of the corrugations, the size of the sphere, and the depth of an attractive well near the surface modify the scattering. We show, in particular, how edge effects due to shadowing of parts of the surface and second hits by the sphere distort the classical rainbow structure. We show the results as topological and intensity plots for special cases. The edge effects give new information on the structure of the surface. For suitable real systems, experimental measurement of the angular and energy dependence of the fraction of the scattering that is elastic may show some of the features described.     

Fast atom diffraction at metal surface

Fast atoms with energies from 300 eV up to 1.7 keV are scattered under a grazing angle of incidence from a clean and flat Ni(1 1 0) surface. For scattering under ”axial surface channeling” conditions, we observe – as reported recently for insulator and semiconductor surfaces – defined diffraction patterns in the angular intensity distributions for scattered fast ³He and ⁴He atoms. We have investigated the domain of scattering conditions where decoherence phenomena are sufficiently small in order to observe for metal targets quantum scattering of fast atomic projectiles. As a consequence, fast atom diffraction appears to be a general technique with a wide range of applicability in surface science.     

Quantum diffusion of H on Pt(111): step effects

Using a linear optical diffraction technique, we have systematically investigated the defect effects on quantum surface diffusion of hydrogen on Pt(111) surfaces. The quantum tunneling effect was clearly observed for hydrogen diffusion at low temperatures as manifested by a leveling off of the diffusion coefficient on flat surfaces. The strong influence of surface defects on the quantum diffusion is in good agreement with the creation of an inhomogeneous surface with adsorption sites of different binding energies.     

Quantum Zeno and anti-Zeno effects in surface diffusion of interacting adsorbates

Surface diffusion of interacting adsorbates is here analyzed within the context of two fundamental phenomena of quantum dynamics, namely the quantum Zeno effect and the anti-Zeno effect. The physical implications of these effects are introduced here in a rather simple and general manner within the framework of non-selective measurements and for two (surface) temperature regimes: high and very low (including zero temperature). The quantum intermediate scattering function describing the adsorbate diffusion process is then evaluated for flat surfaces, since it is fully analytical in this case. Finally, a generalization to corrugated surfaces is also discussed. In this regard, it is found that, considering a Markovian framework and high surface temperatures, the anti-Zeno effect has already been observed, though not recognized as such.     

Global rainbow thermometry for droplet-temperature measurement

Standard rainbow thermometry connects the scattering angle of the main rainbow maximum, generated by a single droplet, to the droplet's refractive index and thus to its temperature. Droplet nonsphericity influences the rainbow position and therefore degrades the quality of the droplet-temperature measurement. We propose global rainbow thermometry, which measures the average rainbow position that is created by multiple droplets and from which a mean temperature can be derived. The new technique aims at eliminating the nonsphericity effect. The principle of this method is presented, and a typical recorded image is discussed.     

Diffraction of electrons on the travelling electromagnetic wave

The quantum effect of diffraction scattering of the electron on the travelling electromagnetic wave in the presence of the third body has been found. As the third body, the refracting medium, the division bounds of different mediums or any inhomogenity of it, the atomic nucleus, screens, openings (giving diffraction emission) etc. may appear. The cause of this effect is physically connected with the real absorption and emission of non-vacuum quanta, the concrete mechanism of which is conditioned by the direct and inverse induced Cherenkov, transitional, bremsstrahlung, diffraction effects respectively. Owing to the real absorption-emission the scattering is inelastic, so the diffraction on the travelling wave is accompanied by the acceleration of electrons (one half decelerates).