A Markovian approach to atomic scattering from rough surfaces

Atomic scattering intensities from surfaces in a rough state are calculated, in the hard wall model, separating a form (or geometrical) factor from a statistical factor and neglecting all the edge effects. Attention has been paid more to the statistics than to the scattering problem. In principle only incoherent scattering occurs from a rough surface. This incoherent line shape is calculated for square and hexagonal lattices under the basic assumption that the surface level is a Markov process in two dimensions.     

Li+ neutralization as a probe of the local electronic potential in Li+-alkali covered metal surface collisions

A theoretical study of Li⁺ neutralization by collision on an alkali covered Al surface is presented. The neutralization probability is computed for Li atoms back scattered from Al sites and from alkali sites on the surface. The calculations are performed with a model representation using lithium as a representative for alkali adsorption. The results reproduce the very large difference in neutralization probability for Li scattered from substrate and adsorbate sites experimentally observed by Weare and Yarmoff [Surf. Sci. 348 (1996) 359] and thus confirm the importance of local effects in atom-surface charge transfer. For scattering from adsorbate sites, the neutralization is shown to be associated with a very large excitation probability of the scattered Li atom.     

Inelastic scattering of He atoms from a Cu(110) surface

A He beam has been used to measure inelastic scattering from a Cu(110) surface. The scattering was a result of predominantly single phonon events and both energy gain and loss processes were observed. This was in contrast to Cu(001) where only energy loss was observed. For Cu(110), aligned in the [001] azimuth, partial dispersion relations have been measured which meant that phonons with ΔQ values up to the zone boundary value have not been detected under the present experimental conditions. The elastic incoherent component varied with azimuthal angle for Cu(110).     

Coadsorption of NO and D2 on Rh(100)

The question addressed in the title was investigated experimentally for low coverage CO and H on Pt(111). The consistent result of two kinds of experiments is that the scattering cross section is in general not influenced by the surface temperature, except for H on Pt(111) in the limit of small changes of the normal component of the He wave vector, Δ k_z. The result simplifies substantially the use of He scattering as an analytical technique for surface dynamics investigations. Semi-classical arguments indicate that the lack of influence of the surface temperature at low coverages is related to two circumstances: (1) the small contribution to the specular He beam of the scattering from adsorbate induced disturbances of the repulsive potential and (2) the absence of long range modifications of the vibrational properties of Pt induced by adsorbed CO or H.     

Quantum theory of atom-surface scattering: Incommensurate and fluid adsorbates

The problem of atomic scattering from adsorbate-covered surfaces, treated earlier for the case of commensurate overlayers, is considered again in the eikonal approximation for incommensurate lattice phases and for fluid phases. Stochastic methods are employed and for a specific model (hard bosses on a plane) it is shown how the statistical and geometric problems can be separately solved. In order to explain the meaning of the coherent and incoherent scattering contributions a time-dependent theory is introduced and it is shown that the incoherent “elastic” scattering is in fact weakly inelastic and (for classical diffusion with diffusion coefficient D) has an energy width of the order ?DQ², where Q is the parallel momentum transfer. The problem of the decay of substrate diffraction intensities when the coverage of random impurities is increased is also discussed.     

X-ray scattering from a randomly rough surface

Abstract

On the basis of the method of reduced Rayleigh equations we present a simple and reciprocal theory of the coherent and incoherent scattering of x-rays from one- and two-dimensional randomly rough surfaces, that appears to be free from the limitations of earlier theories of such scattering based on the Born and distorted-wave Born approximations. In our approach, the reduced Rayleigh equation for the scattering amplitude(s) is solved perturbatively, with the small parameter of the theory η(ω) = 1 - ε(ω), where ε(ω) is the dielectric function of the scattering medium. The magnitude of η(ω) for x-rays is in the range from 10^?6 to 10^?3, depending on the wavelength of the x-rays. The contributions to the mean differential reflection coefficient from the coherent and incoherent components of the scattered x-rays are calculated through terms of second order in η(ω). The resulting expressions are valid to all orders in the surface profile function. The results for the incoherent scattering display a Yoneda peak when the scattering angle equals the critical angle for total internal reflection from the vacuum-scattering medium interface for a fixed angle of incidence, and when the angle of incidence equals the critical angle for total internal reflection for a fixed scattering angle. The approach used here may also be useful in theoretical studies of the scattering of electromagnetic waves from randomly rough dielectric-dielectric interfaces, when the difference between the dielectric constants on the two sides of the interface is small.     

Crystallographic effects in low energy ion scattering due to local ion-atom neutralisation

New experiments on 1 keV ₄He⁺ ion scattering from Ni {100} and Ni {100} (√2 × √2)R45°?O surfaces show azimuthal anisotropies attributable to variations in ion neutralisation probability for different ion trajectories relative to the position of the surface atoms. These effects are shown to be compatible with a simple localised ion-atom neutralisation mechanism. The results indicate that local neutralization is an important process in substrate shadowing in low energy ion scattering studies of adsorbate structures.     

The electric conductivity of a laminated metal system (alternating magnetic and nonmagnetic layers)

A set of kinetic equations for the distribution functions of carriers differing both by the energy spectrum and by the spin projection is used to investigate the conductivity of a multilayer sample (alternating layers of magnetic (m) and nonmagnetic (_n) metals). The boundary conditions on the interlayer surfaces are derived in an approximation in which the surface scattering is divided into “specular” and “diffuse” scattering and is characterized by scattering parameters (reflection and transmission) which are related to each other by relations dependent on spin projections and on the type of spectrum. The problem on the longitudinal (with respect to the layers) current is treated; situations are analyzed in which the variation in conductivity due to the change of mutual orientation of magnetization in successive m layers from antiparallel to parallel may be of the order of the values of the conductivity proper (the so-called giant magnetoresistance effect). This is possible only in the case of thin (compared with the free path) n layers (in m layers, the ratios of the characteristic dimensions may be arbitrary) and in the mandatory presence of specular surface scattering. Results are given for different possible ratios of Fermi momenta of electron groups and for different fractions of specular and diffuse scattering. The possibility of realizing the effects of both signs is demonstrated.     

Statistical scattering of waves in disordered waveguides: Universal properties

The statistical theory of certain complex wave interference phenomena, like the statistical fluctuations of transmission and reflection of waves, is of considerable interest in many fields of physics. In this article, we shall be mainly interested in those situations where the complexity derives from the quenched randomness of scattering potentials, as in the case of disordered conductors, or, more in general, disordered waveguides.In studies performed in such systems one has found remarkable statistical regularities, in the sense that the probability distribution for various macroscopic quantities involves a rather small number of relevant physical parameters, while the rest of the microscopic details serves as mere “scaffolding”. We shall review past work in which this feature was captured following a maximum-entropy approach, as well as later studies in which the existence of a limiting distribution, in the sense of a generalized central-limit theorem, has been actually demonstrated. We then describe a microscopic potential model that was developed recently, which gives rise to a further generalization of the central-limit theorem and thus to a limiting macroscopic statistics.     

Spin-flip probability for 7.6 MeV neutrons scattered inelastically (Q = −2.23 MeV) by a sulfur target

The spin-flip probability for 7.6 MeV (ΔE = 0.250 MeV) neutrons scattered inelastically (Q = ?2.23 MeV) from naturally occuring sulfur has been measured at scattering angles between 40° and 160° using a γ-correlated neutron time-of-flight method. The scattering by the natural sulfur target was assumed to be characteristic of ³²S. The results of the measurement were compared with an incoherent sum of statistical compound-nucleus (CN) and direct-interaction (DI) contributions. The DI contributions were obtained using either a DWBA calculation or the coupled-channel (CC) formalism. Neither combination of CN plus DI contributions reproduced the experimental spin-flip probability angular distribution which was peaked near 110° with a maximum value of 0.33 ± 0.08.     

Simple and multiple scattering in disordered one-dimensional media: Renormalisation group approach

The exact characteristic penetration length associated with both simple and multiple incoherent elastic scattering in semi-infinite one-dimensional disordered media is established as a function ofp (concentration of scattering centers) andf ₀ (transmission coefficient of a single center). Then we exhibit how these phenomena can be seen as critical ones, and the corresponding are reobtained within convenient real space renormalisation group frameworks. Finally we discuss a generalized model where the single center transmission coefficientf can randomly take two different valuesf ₁ andf ₂.     

Diffuse LEED intensities of disordered crystal surfaces: II. Multiple scattering on disordered overlayers

The diffraction of low energy electrons from disordered overlayers adsorbed on ordered substrates is treated theoretically by an extension of Beeby's multiple scattering method. A lattice gas model is assumed for the disordered adsorbate layer. Multiple scattering within a certain area around each atom — each atom of the overlayer and within the ordered substrate — is treated self-consistently, the remaining contributions to the total scattering amplitude being averaged. The theory can be used in the limiting cases of random distribution and of long range order within the adsorbate layer.     

Enhanced scattering from a thin film with one-dimensional disorder

This paper deals with a TE plane wave scattering from a thin film with one-dimensional disorder by means of the stochastic functional approach. The thin film is one-dimensionally inhomogeneous in the horizontal direction with infinite extent, and is homogeneous in the vertical direction with finite thickness. Based on an approximate wavefield representation in terms of a Wiener–Hermite expansion in a preceding paper (Tamura et al., 2004, Waves in Random Media, 14, 435–465), the first- and second-order incoherent scattering cross-sections are presented in explicit forms and scattering properties are discussed. The scattering properties vary entirely with the film thickness. In a case where the thickness is smaller than a few wavelengths in the thin film, enhanced scattering and associated enhanced scattering may appear as sharp peaks or dips on the second-order incoherent scattering distribution if the thin film has guided wave modes. When the thickness becomes sufficiently larger than the wavelength inside the film, a new enhanced scattering phenomenon appears as gentle peaks on the second-order incoherent scattering distribution in four special directions. Such four directions are the directions of forward scattering, specular reflection, backscattering, and the symmetrical direction of forward scattering with respect to the normal of the film surface.The first-order incoherent scattering occurs distinctly in four such directions. Such enhanced scattering is independent of the existence of the guided wave modes inside the thin film, and deeply relates to the structure of the thin film with one-dimensional disorder that has infinite correlation in the vertical direction. For SiC and glass thin films having one-dimensional disorder with a Gaussian correlation and three types of exponential correlation, the first- and second-order incoherent scattering cross-sections are illustrated in figures. The narrow enhanced scattering peaks appear for the glass film in a thin case. The gentle enhanced peaks turn up for both the SiC and glass films in a thick case. Furthermore, the optical theorem is calculated for several cases. It is then found that the error of the optical theorem decreases and the performance of the wavefield is improved by taking into account the second-order incoherent scattering.     

Analysis of reflection electron energy loss spectra (REELS) for determination of the dielectric function of solids: Fe, Co, Ni

A simple procedure is developed to simultaneously eliminate multiple scattering contributions from two reflection electron energy-loss spectra (REELS) measured at different energies or for different experimental geometrical configurations. The procedure provides the differential inverse inelastic mean free path (DIIMFP) and the differential surface excitation probability (DSEP). The only required input parameters are the differential cross section for elastic scattering and a reasonable estimate for the inelastic mean free path (IMFP). No prior information on surface excitations is required for the deconvolution. The retrieved DIIMFP and DSEP can be used to determine the dielectric function of a solid by fitting the DSEP and DIIMFP to theory. Eventually, the optical data can be used to calculate the (differential and total) inelastic mean free path and the surface excitation probability. The procedure is applied to Fe, Co and Ni and the retrieved optical data as well as the inelastic mean free paths and surface excitation parameters derived from it are compared to values reported earlier in the literature. In all cases, reasonable agreement is found between the present data and the earlier results, supporting the validity of the procedure.     

Excitation of states of medium-mass nuclei in the region of giant resonances in inelastic deuteron scattering

Results are presented that were obtained by measuring a continuum in the inelastic scattering of 37-MeV deuterons on ¹²C, ⁴⁸Ti, and ^58,64Ni nuclei in the angular range 16° ≤ θ ≤ 61°. Broad excitation maxima are found for deuteron scattering angles in the range θ ≤ 21°. The region of a broad maximum includes giant resonances of target nuclei, whose levels are excited quite readily at E _d = 37 MeV. Summation of the inelastic-scattering cross sections over all final states of the excited| nucleus and the use of completeness of the wave functions for these states make it possible to express the total cross section for inelastic (incoherent) deuteron scattering only in terms of the wave functions for the ground state of the target nucleus. The corresponding quasielastic-scattering amplitude is taken in the diffraction approximation. Nucleon correlations in the target nucleus are disregarded. Upon disregarding a small contribution of multiple quasielastic scattering at small scattering angles, the cross section for incoherent deuteron scattering is represented approximately as the product of known factors—the square of the absolute value of the amplitude for diffractive quasielastic scattering and the effective number of target nucleons scattering deuterons. The results of these calculations agree qualitatively with experimental data.     

Quantum Correlation Properties Between Two Spatially Separated Atoms in Free Space Reinforced by Incoherent Pumping

Quantum correlation dynamics between two identical and spatially separated atoms in free space is investigated by the use of concurrence C and quantum discord (QD). The behaviors of QD differs in many unexpected ways from the entanglement in this system. Firstly, it shows the situations which the concurrence and QD can behave very differently with a “sudden birth” phenomenon of the former but not of the latter, and QD is only oscillating decays with time and the interqubit distance. We also verify the cases which QD is always greater than the concurrence and the region where the concurrence is vanished but with nonzero values for QD. Meanwhile an unexpected situation which the concurrence is greater than QD under the initial state |eg〉 is analyzed. It is revealed that the quantum correlation based only on QD is expected to be more robust than entanglement which is not suitable for all the initial states under the decoherence environment. Then, by introducing the incoherent pumping, we also study the different properties of the steady-state entanglement and QD about this atomic subsystem. It is shown that the incoherent pumping can overcome the decay of the atoms and the influences about the interqubit distance r ₁₂/λ on the steady-state correlation can make the decay of the concurrence obviously quicker than QD, the life of the steady-state QD is evidently larger than the steady-state entanglement.     

N-point functions and low-energy scattering by N centres

The scattering of a low-energy particle by a potential of a small range is known to be described satisfactorily by the s-wave alone. In the present paper we give a method of describing low-energy scattering by N potentials with the aid of N waves. For this purpose, a special system of Laplacian eigenfunctions is suggested. The scattering amplitude depends on only N parameters, irrespective of overlapping of potentials. The physical significance of these parameters δ_λ, λ=1,2,…N, is shown by exp (2iδ_λ)=S_λ where S_λ is the eigenvalue of the S matrix. The parameters δ_λ may be obtained by direct methods and perturbation theory.The low-energy scattering by an arbitrary configuration of N centres is discussed. The differential cross-section is averaged over all orientations of the configuration and radially about the direct beam, giving it as a function of the scattering angle. This formula may be used for the phase shift analysis.     

Electronic excitations on clean and adsorbate covered Pd(111) by angle resolved electron energy loss spectroscopy

Electronic excitations on clean and adsorbate covered Pd(111) have been investigated by angle resolved electron energy loss spectroscopy. Primary energies in the range of 50–1000 eV were chosen for strong specular reflection to emphasize elastic diffraction-before-loss processes. The clean Pd spectra are compared with optical data, and good correspondence is found for the optical limit (q ? 0). The loss features are interpreted in terms of plasmon resonances and interband transitions within the framework of a recent band structure calculation. Virtually no dispersion is observed for the intrinsic Pd losses, but vertical interband transitions decay fast in the dispersive (q ≠ 0) spectra. Two adsorbate systems are investigated in this study: CO in a disordered adsorbate layer and bromine in a well-ordered $\text{(}\text{3×}\text{3 )R30°}$ structure. Adsorbate derived loss features are generally prominent in the nonspecular (q ≠ 0) spectra. While no dispersion is seen for the intramolecular 13.5 eV excitation of adsorbed CO, dispersion up to 1 eV is found for the Br 4p derived loss feature of the ordered overlayer. This is discussed in terms of a two-dimensional adsorbate band structure of bromine.     

Ion survival probabilities for 3 keV Ar+ scattering from La,Yb, and chemisorbed H2, O2, and H2O on La surfaces

TOF spectra of scattered primary and surface recoiled neutrals and ions for 3 keV Ar⁺ bombardment of clean La and Yb and H₂, O₂, and H₂O saturated La surfaces are presented. The spectra are analyzed in terms of single (SS) and multiple (MS) scattering of the primary ions and surface recoiling (SR) of adsorbate atoms. Measurement of spectra of neutrals + ions and neutrals alone allows determination of scattered ion fractions Y. The Y values for the SS event are high for clean La (37%) and lower for adsorbate covered La (32% for H₂, 13% for O₂, and 8% for H₂O); Yb exhibits a similar behavior, i.e. 16% for clean Yb and 5% for O₂ + H₂O covered Yb. Photon emission accompanying the scattering collision has been observed from clean La and Yb and adsorbate covered La. A preferential inelastic energy loss of 15 ± 3 eV for the SS event has been observed for scattered neutrals as opposed to ions for La and H₂ saturated La at 135°. These results are interpreted within the models for Auger and resonant electronic charge exchange transitions during approach or departure of an ion with a surface and the electron promotions occuring during close atomic encounters where the electron shells are interpenetrating.