Classical Binary Collision Model Research Articles

Quantum versus classical approach of dechanneling and incoherent electromagnetic processes in aligned crystals (draft)

Particles traveling in aligned crystals at small angles w.r.t. crystallographic axes or planes are principally steered by the continuous Lindhard potential. This interaction conserves the energy E, the longitudinal momentum p∥, the transverse energy of the particle E⊥ and is elastic concerning the crystal quantum state. At high enough energy the particle motion is quasi-classical. The time-dependent fluctuations of the positions of the atoms or of the electrons of the crystal create a residual potential, on which the particle can scatter. This interaction does not conserve the previous quantities and is inelastic for the crystal. We compare its treatments with the classical binary collision model and with a phenomenological quantum model. The classical dechanneling rate is estimated to be several ten per cent larger than the quantum one. The influence of correlated vibrations of neighboring atoms is discussed.

Hyperfine coupling of the hydrogen atom in high temperature water

The hyperfine coupling constant of the hydrogen atom has been measured in pressurized liquid water up to 300 °C. The reduced constant A(water)∕A(vacuum) is 0.9939 at room temperature, and decreases to a minimum of 0.9918 at 240 °C. The reduced constant then increases at higher temperature. The g-factor is 2.002244(10) at room temperature and decreases to 2.00221(1) at 240 °C. The change in g-factor is proportional to the change in hyperfine coupling. The behavior below 110 °C is in excellent agreement with a previously proposed model in which the H atom is confined to a harmonic solvent cage, and vibrations within the cage mix "p-type" character into the wavefunction, resulting inA(water)∕A(vacuum) < 1. The harmonic model breaks down above 130 °C. We demonstrate that a classical binary collision model using approximate partial molar volume information can recover the observed minima near 240 °C.

A Monte Carlo investigation of secondary electron emission from solid targets: Spherical symmetry versus momentum conservation within the classical binary collision model

A Monte Carlo scheme is described where the secondary electron generation has been incorporated. The initial position of a secondary electron due to Fermi sea excitation is assumed to be where the inelastic collision took place, while the polar and azimuth angles of secondary electrons can be calculated in two different ways. The first one assumes a random direction of the secondary electrons, corresponding to the idea that slow secondary electrons should be generated with spherical symmetry. Such an approach violates momentum conservation. The second way of calculating the polar and azimuth angles of the secondary electrons takes into account the momentum conservation rules within the classical binary collision model. The aim of this paper is to compare the results of these two different approaches for the determination of the energy distribution of the secondary electrons emitted by solid targets.

Inelastic scattering process of H2O on Pt(1 1 1) studied by supersonic molecular beam techniques

Abstract In order to understand the inelastic scattering process, the incident kinetic energy dependence of the angular intensity distribution is measured of H2O scattered from Pt(1 1 1) at 500 K. The comparisons of H2O scattering with Ne scattering from Pt(1 1 1) and with the prediction of the simple classical binary collision model reveal that not only phonon creation in the surface but also a large amount of H2O rotational mode excitation and/or chattering scattering takes place during collision, especially for the high incident kinetic energy conditions.

Molecular Beam Study of H2O Interaction with Pt(111)

We have developed a highly stable supersonic H2O molecular beam and examined its properties by time-of-flight technique. A wide range of incident kinetic energy Ei of 340–730 meV with ΔE/E of 0.2–0.3 and 77–163 meV with ΔE/E of 0.4–0.6 is achieved by seeding He and He+Ar, respectively. The incident kinetic energy dependence of the angular intensity distributions of H2O scattered from Pt(111) at 500 K is measured in order to understand the inelastic scattering process of H2O on Pt(111). The comparisons of H2O scattering with Ne scattering from Pt(111) and with the prediction of the simple classical binary collision model reveal that not only phonon creation in the surface but also a large amount of H2O rotational mode excitation and/or chattering scattering takes place during collision, particularly for high incident kinetic energy conditions.

Inelastic Collision Processes of Methane and Ethane Molecules at a Pt(111) Surface Studied by Molecular Beam Scattering Techniques

Despite distinct differences in molecular structures and chemical bonds of various alkanes, the inelastic collision processes of CH4 and C2H6 on a Pt(111) surface have been found to be very similar. Both processes can be explained qualitatively by a simple classical binary collision model. Angular intensity distributions of reflected molecules of both species indicate that direct inelastic collision is primarily governed by the molecular mass, the incident kinetic energy of the molecule and the surface temperature of the Pt(111). Other factors such as the molecular structure and chemical bond play minor roles in the process. However, the degree of inelastic collision, that is, the energy transfer rate per collision, increases with the molecular mass. Helium atom scattering has revealed that the dissociation process on the surface is identical for both molecules depending on the incident energy and the surface temperature, as methyl moiety, ethylidyne moiety and complete decomposition into carbon and hydrogen atoms, successively. At elevated surface temperatures, however, thermally assisted hydrogen tunneling appears to dominate ethane dissociation.

Ripening Mechanisms in Ultrathin Metal Films

AbstractResults of recent experimental model studies on ripening of submonolayer films via Ostwald ripening and dynamic coalescence are described. The experiments have been performed on ensembles of Ag-adatom or vacancy islands on a Ag(111) surface using Scanning Tunneling Microscopy. For Ostwald ripening of adatom islands, deviations from the classical mean-field ripening behaviour are observed which show up as pronounced local correlations in island decay and growth rates. For ripening via dynamic coalescence which is studied for ensembles of vacancy islands, it is found that the increase of the average island size with time in the late-stage regime is correctly described by the classical binary collision model.

Heavy ion-surface interaction at low energy: scattering of 3–300 eV Cs +, Xe +, and Ar + from the Si surface

In order to understand the nature of a hyperthermal collision between a heavy projectile and a light atom surface, Cs +, Xe +, and Ar + ion beams are scattered from Si surfaces for collision energies of 3–300 eV. The scattered ions are analyzed for their mass and kinetic energy. The kinetic energy of the scattered ions is much higher than expected from a classical binary collision model, for example, the ratio of scattered to incident ion energy ( E s E i ) is 0.64 for a Cs +Si(111) collision at an incident energy of 3 eV and a scattering angle of 90°. The E s E i for Cs + decreases sharply with increasing energy up to 50 eV. For Xe + and Ar + scattering from Si(100), even higher E s E i values are measured at low collision energy, but this is attributed to preferential neutralization of the slow noble gas ions on the surface and the resulting upshift in their ionic energy distribution. Molecular dynamics classical trajectory simulation of heavy projectile-light atom surface collisions reveals that the lattice atoms collectively respond during a hyperthermal collision, resulting in a drastic E s E i increase compared to the collision of a light projectile. An important parameter that determines the E s E i ratio is the time scale of the collision relative to the energy propagation inside a solid.

Reconstruction of the sum-rule-constrained classical binary-collision model for inner-shell ionizations.

Tung has constructed a sum-rule-constrained classical binary-collision model for the estimation of generalized oscillator strengths (GOS's) of the 1s and 2s subshells of atoms. He applied three sum rules to determine the momentum-dependent parameters introduced in the GOS function based on the classical binary-collision model. Several deficiencies have then been found regarding these sum rules that adopted the less accurate hydrogenic model and included the unwanted contribution from discrete excitations. In the present work, we have reconstructed this model by employing improved sum rules obtained from Hartree-Fock-Slater matrix element calculations. The refined model has been successfully applied to estimate ionization generalized oscillator strengths of atomic K and L shells.

Stopping power of diamond for low energy electrons

Abstract Theoretical models used to describe the interaction of electrons with the valence band of insulators are discussed. Results for the application of these models to calculate stopping power and mean-free path of low-energy electrons (< 10 keV) in diamond are presented. The influence of core polarizability, oscillator strength coupling between core and valence electrons, and exchange corrections is included. The contributions to the mean-free path and stopping power from ionization of inner shells have been evaluated from sum-rule-constrained classical binary-collision model.

Sum-rule-constrained classical binary-collision model for inner-shell ionizations

A model calculation of cross sections for inner-shell ionization by electrons is described. This model is based on the classical binary-collision model and modified with the application of several sum rules. It is found that the model predicts quite accurately generalized oscillator strengths and cross sections for inner-shell ionization of atoms. A comparison is made with experiment and other theoretical results.