Debye-Waller factor in atom-surface scattering: Elastic and inelastic channels

Explicit expressions for the Debye-Waller factor for the elastic and one-phonon channels are presented to lowest order in the phonon displacement, using a hard wall model to represent the atom-surface interaction. The periodicity of the crystal is accounted for; thus we explicitly generalize to all elastic channels the reflectance result found by Garcia et al. within the plane-surface model, and we include the contribution of the umklapp processes to the inelastic channels. We show how for high incident energy of the atom all Debye-Waller factors reduce to the standard result.     

Debye-Waller factor through the glass transition temperature in a-selenium,by incoherent inelastic neutron scattering

We report, in this work, Incoherent Inelastic Neutron Scattering (IINS) measurements in amorphous bulk selenium. Taking into account the low frequency Vibrational Density-of-States(VDOS), we study the modification introduced in the Debye-Waller factor by increasing temperature through the glass transition temperature (T_g). The occurrence, in the vibrational density-of-states, of a ω² dependence in the acoustic region, allowed us to apply the Debye theory from which the variations of the Deybe-Waller factor are calculated in addition. It is shown that the main contribution to it is given by the acoustic region of the vibrational density of states and has a faster increase for temperatures above T_g.     

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.     

On the Debye-Waller factor for atom-surface scattering

The Debye-Waller factor in atom-surface scattering is considered. It is found that the equation suggested by Beeby is valid for soft potentials provided that (1) the attractive portion of the potential is stationary, (2) the repulsive portion of the potentials moves but does not distort, and (3) the effect of trajectories that reflect off the attractive well and multiply scatter from the repulsive wall is negligible.     

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.     

Debye-Waller factor of solid heavy methane

The temperature dependence of the Debye-Waller factor for crystalline (f.c.c. space-lattice) heavy methane obtained from direct Monte Carlo calculations appears to give reasonable indication of the orientational phase transitions observed at 22.2 K and 27.7 K.     

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.     

General approach to deep inelastic scattering

Due to preliminary indications of a possible scaling violation, it is interesting to clarify which of the parton light-cone results are indeed the consequences of a more general scheme. We consider the constraints imposed by the general ideas of duality (absence of exotics in the t-channel) applied to deep inelastic single-particle distributions. This provides a restrictive scheme, although it allows for a larger set of diagrams than that of the parton model. However, in a particular kinematical region where the diffractive component of the total deep inelastic cross section can be neglected, all the algebraic results of the parton model are recovered by this scheme.     

A non-local approach to the theory of inelastic dynamic light scattering from solid-state plasmas

The existing theory of inelastic dynamic light scattering from coupled systems of free carriers and lattice excitations in absorbing crystals is extended to include non-local electronic transport effects.     

A dynamical approach to the information content of collinear inelastic scattering

The information content of collinear inelastic scattering is discussed in terms of (a) the nature of the classical transformation in internal angle-action space induced by the collision, (b) the number of parameters required to characterize the transformation, and (c) the number and choice of trajectories required to determine the parameters. The constraints of time reversal symmetry, energy and flux conservation are embodied in the transformation equations. In a model application the full S matrix is successfully estimated in terms of a single information parameter deduced from knowledge of the purely elastic scattering trajectories.     

On the Debye-Waller factor in molecular beam scattering experiments

In the molecular beam scattering experiments against metal surfaces, one often obtains surface Debye temperatures larger than the bulk ones, in apparent contradiction to the larger thermal atomic motion at the surface. We point out that this is a consequence of that the thermal molecules scatter against the outer part of the electron distribution, and that the metal electrons do not follow the atomic motion rigidly. A self-consistent model calculation shows that this is a large enough effect to explain the experimental results.     

Quantum theory of atom-surface scattering: Debye-Waller factor

The Debye-Waller factor, introduced historically for X-rays, was used later for electrons, neutrons, and atoms as well. In this process of extension, however, the assumptions on which the Debye-Waller theory rested became more and more questionable until in the case of atoms (whose scattering from surfaces is both strong and slow) serious modifications are necessary. In the present article four models are discussed in order. In Model 1 a fast atom impinges on a surface whose atoms all vibrate deviating from their equilibrium positions by the same vector displacement ?. In Model 2 again the impinging atom is fast, but the atoms in the surface vibrate incoherently rather than coherently. It is shown that both Models 1 and 2 yield the conventional Debye-Waller result in the infinite crystal atom mass limit (for Model 2 Einstein oscillators have also to be assumed) and it is also shown how corrections to this result can be built. Turning then to slow impinging atoms, in Model 3 a slow atom impinges on a hard crystal surface, interacting with the rapidly varying potential of the vibrating solid. Model 3 is discussed in detail and it is shown that the Debye-Waller exponent can be written in terms of a time integral of the product of two correlations: the force correlation and the displacement correlation. The result is a dramatic increase of diffraction of relatively heavy atoms (with respect to the conventional theory). Finally, in Model 4 the impinging atom is again slow but the crystal is soft rather than hard. This case is more difficult to treat but a preliminary analysis again indicates a dramatic increase of diffraction since the soft solid adjusts itself to the instantaneous atom position leading to elastic scattering. The experimental implications of the present theory, especially for neon scattering from surfaces, are discussed.     

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.     

Modification of the Debye-Waller factor of solid Helium due to short-range correlations

Zeitschrift für Physik A Hadrons and nuclei - The Debye-Waller factor of solid3He and4He for both the bcc and the hcp phase is calculated using uncorrelated Gaussians multiplied with Jastrow...     

Multiphonon resonances in the Debye-Waller factor of atom surface scattering

He atom surface scattering by dispersionless phonons is treated employing coupled channel (CC) calculations. At low energies, they predict a behavior opposite to perturbative Born or "exponentiated" Born approximation: strong resonant phonon stimulated elastic and inhibited inelastic scattering. The corresponding resonances have not been observed in earlier CC results since these have considered only the temperature dependence of the Debye-Waller factor at higher energy or omitted the attractive well. The resonances can be interpreted in terms of bound states in the attractive well with several excited vibrational quanta. They may be observable for, e.g., He scattering by a cold Xe/Cu surface.     

DWBA approach to inelastic scattering at medium energies

Medium energy proton elastic and inelastic scattering to states of ⁵⁸Ni and ²⁰⁸Pb, and ⁴He elastic and inelastic scattering to states of ⁴⁰Ca, are analyzed using the partial wave approach, by solving the Schrödinger equation with relativistic kinematics and using the distorted wave Born approximation. Our results can be compared with results of several previous analyses of the nucleon inelastic data using the Glauber approximation. Our calculations are absolute, using nuclear collective parameters obtained from a survey of a large number of low-energy analyses of inelastic scattering of electrons, nucleons and nuclei from ⁴⁰Ca, ⁵⁸Ni and ²⁰⁸Pb.