A puzzle in the inelastic scattering of atoms from surfaces

The insensitivity of helium atoms to possible inelastic scattering involving bulk phonons that terminate at the surface is explained in terms of the experimental parameters that need to be incorporated into the scattering theory.     

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.     

Multiphonon atomic scattering by solid surfaces

A multiphonon solution for the problem of atom-surface scattering at thermal energies is proposed. The scattering equations are solved using the assumption of low inelastic scattering intensities, and the theoretical formalism is basically an improvement of a previous work on one-phonon scattering. Present results reduce to the one-phonon expression of the previous work when the appropriate limit is taken.     

The thermal attenuation of elastic scattering of helium from copper single crystal surfaces

The dependence of diffraction peak intensities upon temperature for the scattering of helium from various copper surfaces: Cu (111), (100), (110), (113), (115) and (117), has been experimentally determined for two incident energies (21–63 meV) and a large range of incidence angles. For the close-packed faces (111) and (100), the data are consistent with a Debye-Waller formalism involving an effective surface mean square displacement <u²_eff〉. The quantitative fit with the data is good if anharmonic effects are properly taken into account. This result establishes that a generalized Debye-Waller formalism is, at least as a first approximation, relevant to the helium-surface diffraction. For the rougher surfaces the agreement remains good up to a threshold temperature above which the intensities are always lower than predicted by the model. It is proposed that this may be due to some kind of thermal roughening of the surface.     

Getting the elastic scattering length by observing inelastic collisions in ultracold metastable helium atoms

We report an experiment measuring simultaneously the temperature and the flux of ions produced by a cloud of triplet metastable helium atoms at the Bose-Einstein critical temperature. The onset of condensation is revealed by a sharp increase of the ion flux during evaporative cooling. Combining our measurements with previous measurements of ionization in a pure Bose-Einstein condensate, we extract an improved value of the scattering length a=11.3(+2.5)(-1.0) nm. The analysis includes corrections that take into account the effect of atomic interactions on the critical temperature, and thus an independent measurement of the scattering length would allow a new test of these calculations.     

Focussed inelastic resonances in particle scattering from surfaces

Particles, such as atoms or electrons, inelastically scattered from a crystal surface in resonance with a bound state are predicted to focus around a discrete set of final angles with a defined energy for each angle. The final angle and energy of such focussed inelastic resonances (FIR) are shown to be independent of the initial state. A calculation of the FIR amplitude indicates favorable conditions for the observation of the so far elusive bound states of He on low-index metal surfaces and of image states on stepped metal surfaces.     

Elastic and inelastic positron-helium scattering

Elastic and inelastic positron--helium scatterings have been investigated with the coupled-channel optical method (CCO). Ionization continuum and positronium formation channels are included via a complex equivalent-local optical potential. Calculations are reported of cross sections of elastic scattering, total excitation and n=2, 3, and 4 excitations of ground-state helium for incident energies from 30~eV to 400~eV. The present calculation shows that the ionization and Ps-formation channels significantly affect the cross sections of elastic and inelastic positron--helium scatterings.     

Compton profiles of heavy atoms by inelastic proton-electron scattering

So-called ion Compton profiles can be obtained if the recoiling electron after an inelastic ion-electron encounter is observed and energy analyzed. Electron recoil spectra induced by 21 MeV protons passing through thin Ag and Au foils are measured. It is demonstrated that the method is accurate enough to extract valence Compton profiles of Ag and Au from the data. The advantages and disadvantages compared to inelastic - or electron-electron scattering are discussed. It turns out that this new method for the measurement of Compton profiles is especially suitable for heavy elements and very thin or small targets (e.g. clusters).     

Differential cross sections for elastic and inelastic positron scattering from alkali atoms

We have investigated positron scattering from the alkali atoms lithium, sodium, potassium and rubidium, focusing on the calculation of differential cross sections for elastic scattering and impact excitation. The results obtained with the two-state and five-state close-coupling method as well as the first-order distorted wave Born approximation are compared with each other and with some selected results for electron scattering. Numerical problems due to lack of, or numerically inaccurate, calculation of partial waves with large angular momenta are solved through semi-empirical fitting/extrapolation procedures.     

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.     

Elastic diffuse and inelastic electron scattering from surfaces with disordered overlayers

The elastic diffuse scattering of electrons can be used for structure analysis of disordered species on surfaces. Effective data acquisition is achieved with instruments which do not resolve between elastic diffuse scattering and inelastic scattering due to phonons. With a newly designed high resolution spectrometer it is shown that the inelastic intensity is of the same magnitude or larger than the elastic diffuse scattering. It is also shown however, that the total inelastic intensity changes little when a lattice gas of adsorbates is present on the surface, whereas the elastic diffuse intensity increases linearly with coverage. Thus instruments with low energy resolution may be used for the analysis of local structure of disordered adsorbates provided one measures the difference between the total diffuse scattering of the adsorbate covered and the clean surface.     

Semiclassical description of inelastic atom scattering by surfaces

Inelastic scattering of atoms of moderate energies (say<5 eV) by solid surfaces is almost entirely due to energy exchange with lattice vibrations. It can give valuable information about the atom-surface interaction potential and the vibrational dynamics at surfaces. Theoretically this process represents a challenging many-body problem, calling for suitable approximation methods. Work in progress (K. Burke, L. D. Chang, and W. Kohn) is described. (1) We have solved a simple model problem in which the normal modes of the lattice are schematized by a single one-dimensional harmonic oscillator, initially in its ground state (T=0). The classical solution gives a unique energy loss. We have calculated the leading quantum correction and find a Gaussian final energy distribution whose width is proportional toh ^1/2. Our exact results are in general different from the so-called trajectory approximation. (2) We are about to propose a new type of atom-surface scattering experiment, which will provide a direct measure of the quantum corrections to classical scattering.     

Elastic scattering of electrons by helium and neon atoms

Summary  Partial and total cross-sections of electrons scattering by helium and neon atoms are calculated at eleven values of incident energy ranging from 0.1 a.u. to 1.1 a.u. The calculations are carried out via model potential (describing the electron target interaction). The iterative Green’s function partial-wave expansion technique was used. The comparison between our results and those obtained by other authors show significant agreement and supports our simple model scattering process.     

Crystallographic determination of metal surfaces with helium scattering

Helium-surface diffraction data has been used to construct the interaction potential between a Helium atom and a metal surface. The constructed potential fits experimental data for all beam energies and angles of incidence and more importantly is independent of beam energy. Such a potential essentially consists of two parts: a short range repulsive corrugated potential due to electronic overlap, and a long range attractive potential due to dispersion forces. We have generated potentials for He scattering for Ni, Cu and Au and in all cases found excellent agreement with experiments. We also report that the repulsive part of the He scattering potential can be obtained rather simply from first principles without adjustable parameters. This suggests that one can determine surface crystallography from first principles without adjustable parameters.     

Advances in crystal analyzers for inelastic X-ray scattering

The realization of spherical crystal analyzers for inelastic X-ray scattering experiments (IXS) is an ongoing project at the ESRF since 1992. We developed reliable techniques to routinely produce silicon spherical analyzers with very high (ΔE=1÷10 meV) and high energy resolution (ΔE=0.2÷1.5 eV), and with very good focal properties and efficiency. In this article we report the state of the art of the analyzer construction and the main improvements made during the last years.     

The conditions for total reflection of low-energy atoms from crystal surfaces

A single-mode dye laser is described in which a “double Michelson” mode selector is used instead of intracavity Fabry-Perot systems. This simple device gives a lower threshold, a high single-mode power (≳250 mW), and a good geometrical quality of the laser beam. Synchronous pressure scanning of the cavity and the mode selector frequencies makes it possible to continuously sweep the optical frequency over 40 GHz without any difficulty. Another version, in which one mirror of the “double Michelson” has been replaced by a retroreflecting optical grating, is also reported. In this case, no selective element (Lyot filter, wedge, ...) has to be inserted in the laser cavity.     

Multiphonon Raman scattering from individual single-walled carbon nanotubes

Combinations of up to 6 zone-edge and zone-center optical phonons are observed in the Raman spectra of individual single-walled carbon nanotubes (SWNTs). These multiphonon Raman modes exhibit distinct signatures of the one-dimensional nature of SWNTs and provide information on the phonon structure, exciton-phonon coupling, and excitonic transitions in nanotubes.     

Resonant inelastic contact scattering of X-ray photons on atoms and ions

The existence of an extended resonance structure outside the X-ray emission regions is theoretically predicted in the total double differential cross section for the scattering of linearly polarized photons on free atoms (ions). This structure is almost entirely determined by inelastic photon scattering of the contact type. The amplitude of the inelastic contact scattering probability is described using an analytical expression for a non-relativistic transition operator, which was previously obtained by the author outside the dipole and momentum approximations. The resonant inelastic contact scattering of X-ray photons on a neon atom and neonlike ions of argon, titanium, and iron has been studied. Calculations were performed in a nonrelativistic approximation for the wave functions of the scattering states, with allowance for many-body effects of the radial relaxation of one-electron orbitals in the Hartree-Fock field of a deep 1s vacancy and (for neon atom) the double excitation/ionization of the ground atomic state.