Atom scattering as a probe of the surface electron-phonon interaction at conducting surfaces

An atomic projectile colliding with a surface at kinetic energies in the thermal or hyperthermal range interacts with and is reflected by the electronic density well in front of the first layer of target atoms, and it is generally accepted that the repulsive interaction potential is proportional to the density of electrons extending outside the surface. This review develops a complete treatment of the elastic and inelastic scattering of atoms from a conducting surface in which the interaction with the electron density and its vibrations is treated using electron-phonon coupling theory. Starting from the basic principles of formal scattering theory, the elastic and inelastic scattering intensities are developed in a manner that identifies the small overlap region in the surface electron density where the projectile atom is repelled. The effective vibrational displacements of the electron gas, which lead to energy transfer through excitation of phonons, are directly related to the vibrational displacements of the atomic cores in the target crystal via electron-phonon coupling. The effective Debye-Waller factor for atom-surface scattering is developed and related to the mean square displacements of the atomic cores. The complex dependence of the Debye-Waller factor on momentum and energy of the projectile, including the effects of the attractive adsorption well in the interaction potential, are clearly defined. Applying the standard approximations of electron-phonon coupling theory for metals to the distorted wave Born approximation leads to expressions which relate the elastic and inelastic scattering intensities, as well as the Debye-Waller factor, to the well known electron-phonon coupling constant λ. This treatment reproduces the previously obtained result that the intensities for single phonon inelastic peaks in the scattered spectra are proportional to the mode specific mass correction components λ_Q,ν defined by the relationship λ = 〈λ_Q,ν〉. The intensities of elastic diffraction peaks are shown to be a weighted sum over the λ_Q,ν, and the Debye-Waller factor can also be expressed in terms of a similar weighted summation. In the simplest case the Debye-Waller exponent is shown to be proportional to λ and for simple metals, metal overlayers, and other kinds of conducting surfaces values of λ are extracted from available experimental data. This dependence of the elastic and inelastic scattering, and that of the Debye-Waller factor, on the electron-phonon coupling constant λ shows that measurements of elastic and inelastic spectra of atomic scattering are capable of revealing detailed information about the electron-phonon coupling mechanism in the surface electron density.     

Determination of nuclear parameters by inelastic electron scattering at low-momentum transfer

The second-order Born-approximation treatment of Cutler and Schucan was applied to inelastic electron scattering data on ⁶Li, ⁶⁰Ni, and ¹¹⁴Cd acquired at low momentum transfers. The form factors as a function of momentum transfer q in the range of 0.25–0.57 fm^?1 were obtained by angular distribution measurements performed at incident energies of 30 to 60 MeV. The correlation between two parameters deduced from the measurements, the reduced transition probability B(E2↑) and the transition radius R⁽²⁾_tr, is discussed. It is suggested that inelastic electron scattering data at low-q is best used either in conjunction with an accurate value of B(EL↑) (available from the model-independent analysis of “photon” experiments at zero momentum transfer) to allow accurate determination of R⁽²⁾_tr, or in conjunction with high-q inelastic electron scattering data to allow accurate determination of B(EL↑) as well as R⁽²⁾_tr.     

Response function of superfluid nuclei and low-lying quadrupole vibrations

The response of superfluid spherical nuclei to an external quadrupole field is considered. The mixed (r,λ) representation technique is developed, being the generalization of the coordinate (r) representation for magic nuclei. The transition densities p^tr(r) are shown to possess sharp surface bumps of hydrodynamical nature and pronounced volume quantum components. The shapes of transition densities of 2⁺₂ states in some typical nonmagic nuclei are predicted.     

Influence of multiple elastic scattering on the shape of the elastically scattered electron peak

The influence of multiple elastic scattering on the shape of the energy distribution of elastically scattered electrons is investigated. The energy of the maximum intensity of the detected electrons differs from the probe electron beam energy due to the elastic energy loss. The experimentally observed spectrum is adequately described by a Gaussian distribution with a maximum at the elastic energy loss value. In this paper the peak-broadening mechanisms due to energy-analyzer spread function, probe beam energy distribution and atomic vibration-induced broadening are considered to be independent and of random nature. Analysis of multiple elastic scattering shows some mechanisms leading to the broadening and a shift of the elastic scattering electron energy spectrum from the value defined by single elastic scattering at the certain angle. It is revealed that the magnitude of this shift and the width of energy distribution is determined by ratio (_lin/_ltr)$(l_{\text{in}}/l_{\text{tr}})$, where _lin$l_{\text{in}}$ is inelastic mean free pass, _ltr$l_{\text{tr}}$ is the transport length.     

Experimental confirmation of the EPES sampling depth paradox for overlayer/substrate systems

Elastic-peak electron spectroscopy (EPES) has been one of the main tools for obtaining the inelastic mean free path of electrons in solids. Recently it has become clear that, if this type of experiment is done using an energetic electron beam (20-40 keV) and large scattering angles, then the recoil energies of the elastic scattering event for different elements can be resolved. This recoil energy is mass dependent and this fact makes it possible to separate the elastic-peak contributions due to electrons scattered from light and heavy elements. Here we use this energy separation to determine experimentally the sampling depth for an overlayer/substrate system. The sampling depth for a (high-Z) Au overlayer on a (low-Z) C substrate is found to be about two orders of magnitude smaller than for a C overlayer on a Au substrate, whereas the inelastic mean free path of electrons in both materials differ much less. This effect is shown to be a consequence the strong Z dependence of the elastic scattering cross section. The dependence of the spectra on the electron kinetic energy and sample rotation is also dramatically different for both sample geometries.     

Violation of P- and T-symmetries in double polarized elastic electron-proton scattering

Analytical expressions are obtained for the differential cross section and right-left asymmetry A _RL ^γ,γZ of the process of elastic scattering of longitudinally polarized electrons from a polarized proton target with account of anapole and electric dipole moments, and the neutral weak electric, magnetic and axial form factors of a proton violating the C, P- and T/CP invariance. Contributions from the P and T odd spin correlations to asymmetry A _RL ^γ,γZ are studied as a function of the electron energy, scattering angles, and the proton form factors.     

Efimov physics beyond universality

We report the characteristics of cavity polaritons in a CuBr microcavity consisting of a λ/2-thick CuBr active layer and HfO₂/SiO₂ distributed Bragg reflectors: λ corresponds to an effective resonant wavelength of the lowest-lying exciton. The excitonic system of a CuBr crystal has three kinds of excitons labeled Z_f, Z_1,2, and Z₃ in which the Z_f exciton originates from a triplet state. We have investigated the dispersion relations of the cavity polaritons in the CuBr microcavity with the use of angle-resolved reflectance spectroscopy. The experimental results demonstrate the formation of four cavity-polariton branches due to the strong coupling between the Z_f, Z_1,2, and Z₃ excitons and cavity photon. The cavity-polariton dispersions were well analyzed with a phenomenological Hamiltonian for the strong coupling. The evaluated Rabi-splitting energies are 28, 95, and 74 meV for the Z_f, Z_1,2, and Z₃ excitons, respectively. These Rabi-splitting energies reflect the magnitudes of the oscillator strengths of the relevant excitons. Furthermore, it was confirmed that the cavity polaritons are fully stable at room temperature. We discuss the temperature dependence of the cavity-polariton energies and detuning, comparing with that of the bare exciton.     

Cross sections for scattering of deuterium mesic atoms on deuterium nuclei

Cross sections have been calculated for elastic scattering of deuterium mesic atoms in ortho and para states on deuterium nuclei in the 0–50 eV energy range; cross sections for spin-flip have also been calculated. The calculations have been performed in the adiabatic representation where the initial problem of slow collisions in a three-body system is reduced to the multichannel scattering problem. The temperature dependence of the ortho-para transition rate λ_hf(T) for dμ atoms is obtained for a deuterium target. The calculated rate 37.2×10⁶ s^-1 (at 30 K) is in good agreement with the recent experimental value, λ_exp(30 K) = (37.0±0.74)×10⁶ s^-1 (Vienna-SIN group, 1983).     

Stress induced preferred orientation and phase transition for ternary WCxNy thin films

We deposit ternary WC_xN_y thin films on Si (1 0 0) substrates at 500 °C using direct current (DC) reactive magnetron sputtering in a mixture of CH₄/N₂/Ar discharge, and explore the effects of substrate bias (V_b) on the intrinsic stress, preferred orientation and phase transition for the obtained films by virtue of X-ray photoelectron spectroscopy (XPS), X-ray diffraction (XRD), and selective area electron diffraction (SAED). We find that with increasing the absolute value of V_b up to 200 V the carbon (x) and nitrogen (y) atom concentrations of WC_xN_y films keep almost constant with the values of 0.75 and 0.25, respectively. The XPS and SAED results, combined with the density-functional theory (DFT) calculations on the electronic structure of WC_0.75N_0.25, show our obtained WC_xN_y films are single-phase of carbonitrides. Furthermore, we find that the compressive stress sharply increases with increasing the absolute value of V_b, which leads to a pronounced change in the preferred orientation and phase structure for the film, in which a phase transition from cubic β-WC_xN_y to hexagonal α-WC_xN_y occurs as V_b is in the range of −40 to −120 V. In order to reveal the relationship between the stress and phase transition as well as preferred orientation, the DFT calculations are used to obtain the elastic constants for β-WC_xN_y and α-WC_xN_y. The calculated results show that the preferred orientation is dependent on the competition between strain energy and surface energy, and the phase transition can be attributed to a decrease in the strain energy.     

Scattering effects of primary electrons in Co/Cu(1 1 1) measured by Auger; elastic and loss electrons

Electron energy losses were measured as a function of the incidence angle of the primary electron beam for the Co/Cu(1 1 1) adsorption system. The measurements performed for the clean and covered substrate reveal characteristic intensity maxima associated with the close packed rows of atoms, as it was observed in the so called directional Auger and directional elastic peak electron spectroscopy profiles. The incidence angle dependent signal of electron energy losses measured for the clean (Cu 3p_3/2) and covered (Co 3p_3/2) substrate gives the so called directional electron energy loss spectroscopy (DEELS) profiles which contain structural as well as chemical information. The scattering of primaries and different emission processes associated with electron energy losses, Auger, and elastically backscattered electrons are discussed. A change in the h_Cu (Cu M_2,3VV transition) Auger signal recorded during the continuous cobalt deposition shows that the growth mode is not a pure layer by layer type. The complete covering of the substrate by Co at higher coverages is confirmed by the comparison between experimental and theoretical ratios of the Auger peak heights.     

Cross sections of electron capture by Boron ions in gaseous media

We study the cross sections σ_{i, i?1}, σ_{i, i?2}, and σ _{i, i?3} of capture of one, two, and three electrons by boron ions with charges i=1?5 and velocities V=(1.83?5.50)V₀ in gaseous media with atomic numbers Z_t varying from 1 to 54. The oscillatory form of the Z_t dependence of electron capture cross section by boron ions, which has been established for lighter ions, is confirmed.     

Growth and vibrational properties of MnOx thin films on Rh(111)

The growth, structures, and vibrational properties of ultrathin manganese oxide films on Rh(111) had been investigated using high-resolution electron energy loss spectroscopy (HREELS), X-ray photoelectron spectroscopy (XPS), low energy electron diffraction (LEED), low energy ion scattering spectroscopy (LEIS) and Auger electron spectroscopy (AES). MnO_x grew in a layer-by-layer fashion on the Rh(111) surface. HREELS phonon features and XPS binding energies showed that an OMnO like tri-layer formed initially. Which was stable on the Rh(111) surface with MnO_x coverage less than one monolayer. At above one monolayer, Mn₃O₄ was preferred as indicated from a four-phonon feature peaked at 13.3, 39, 68 and 83 meV in HREELS. Higher temperature oxidation and annealing were found to improve the long-range order of the MnO_x films.     

Inelastic electron scattering in nickel

Using a 200 keV electron spectrometer, with an energy resolution of ～0.25 eV and a momentum resolution of ～0.2 A^-1, we have measured the energy loss spectra for transmission of electrons through thin (～600 Å) Ni films. These results address the general question of the validity of momentum transfer estimates in electron loss scattering.Using low-energy electron backscattering, we have observed the dipole forbidden M₁ transition at 112 eV. For high-energy scattering, we have observed this transition only at high momentum transfer (q? 2 A^-1). These results indicates sizable contributions from high momentum transfer collisions in the low-energy experiments.     

Resonances at slow electron collisions with zinc atoms and ions

The optical excitation functions of four spectral lines corresponding to the transitions from the 4¹ D ₂, 5³ S ₁, 4³ D _j, and 6¹ S ₀ levels of atomic Zn were investigated with an electron spectrometer of a new construction. For the first time, elastic scattering of slow electrons from the Zn ions at an angle close to 180° was studied. In the energy range under investigation (0–7 eV), both the optical excitation functions of atomic spectral lines and the differential cross section of elastic scattering manifested the resonant structure caused by the contribution of autoionization states of the atom.     

Collective Grain Interactions II. Non‐linear Collective Drag Force

It is found that the collective effects operating at large distances from the grain surface can produce substantial scattering of the ion flux and create an additional collective drag force dominant for large grain densities. The consideration is restricted to large grain charges β = Z_de ²a /T_iλ_Di ? 1 and T_i /T_e ? 1 (–eZ_d being the grain charge in units of electron charge, a being the grain size, λ_Di being the ion Debye radius and T_e,i being electron and ion temperatures, respectively). For present dusty plasma experiments β ≈ 10–50, the large charges of grains are screened non‐linearly and the ion scattering creates non‐linear drag force. The present investigation considers effects of scattering by collective grain fields at large distances from the grains. It is found that the physical reason of the importance of collective drag force, calculated in this paper, is related to presence of weakly screened collective field of grains outside the non‐linear screening distance depending on grain densities. The amplitude of this collective fields of the grains is determined by non‐linear screening at non‐linear screening radius. It is shown that for dust densities of present experiments the collective drag force related to this scattering can be of the order of the non‐linear drag force caused by scattering inside the non‐linear screening radius or even larger. (© 2005 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Focused scattering of low energy Li+ from Mo(001): Experimental and computer simulation results

The azimuthal dependence of the energy distribution of Li⁺, specularly scattered from Mo(001), has been obtained for several incident energies E_i. The energy distributions exhibit one or two peaks, which always lie below the kinematical single scattering energy and which have intensity and energy that depend upon the azimuth. Due to trajectory focusing, the intensity is strongly peaked along the [100] azimuth for E_i ? 500 eV, but at higher E_i the intensity enhancement is shifted toward the [310] azimuth. Results of computer simulation give reasonable agreement with experimental observations. Analysis of the simulated trajectories allows identification of the scattering mechanisms which contribute to each portion of the spectrum.     

Theory of “Resonant” lattices for synchrotrons with negative momentum compaction factor

In synchrotrons the transition energy W _tr=m ₀ c ²(γ_tr?1) is fundamentally important because it determines the maximum attainable accelerated currents. From this point of view it is desirable that the momentum compaction factor α = 1/γ _tr ² as small as possible or even negative, which makes γ_tr imaginary and accordingly rules out transition energy crossing by particles under acceleration. In this connection a theory of “resonant” lattices with negative momentum compaction factor based on the correlation principle of simultaneous superperiodic modulation of the orbit curvature and lens gradient functions is worked out.     

Relative intensities in X-ray photoelectron spectra: Part VII. The effect of elastic scattering in a solid on the angular distribution of photoelectrons escaping from samples covered with thin films of various thicknesses

The angular distributions of X-ray photoelectron peak intensity for (1) a semi-infinite sample, (2) a substrate sample covered with a film, and (3) an overlayer sample are calculated by the Monte-Carlo method. The elastic as well as the inelastic scattering of electrons in a solid is taken into account. In all cases the elastic scattering is shown to have a significant effect on both the absolute value of peak intensity and the angular distribution of photoelectrons. The electron mean free paths without inelastic collisions (λ_n) calculated using formulas derived without taking account of elastic scattering are shown to differ significantly from the real values. Moreover, the λ_n values calculated in this way are not physical constants at all, but depend for example on the film thickness and the intervals of photoelectron take-off angles under consideration. The elastic scattering effect is shown capable of explaining some difficulties which arise in the interpretation of experimental data reported in the literature on the basis of expressions derived taking into account only the inelastic interactions of photoelectrons with a solid.     

Dispersion of the acoustic phonon concerned with C66 of KD2PO4 observed by light scattering

we vector dependence of the light scattering spectra of DKDP is investigated for the scattering angles π/4, π/2 and 3π/4. Brillouin shift concerned with an elastic stiffness C₆₆ is obtained from the angular dependence of the quasi-longitudinal and quasi-transverse mode frequencies in the ab plane observed in the VV scattering. The results indicate that the phase velocity associated with C₆₆ decreases slightly near T_tr in the case of π/4 scattering, but does not in π/2 and 3π/4 scatterings.