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.     

原子吸收限附近Bragg情况的衍射波和透射波的观测

在Ｇａ的Ｋ吸收限附近的强反常散射条件下，测定了ＧａＡｓ（６００）对称Ｂｒａｇｇ情况的衍射波和透射波的摇摆曲线，并将其和Ｘ射线衍射动力学理论的相应计算结果作了比较，指出了原子吸收限附近Ｂｒａｇｇ情况的透射波在研究反常散射中的应用价值 关键词：     

Estimation of ion scattering by atomic chains on single crystal surfaces

Estimation of ion movement close to atomic chains taking into account the elastic and inelastic energy losses and vacancy type imperfections was performed on the basis of a model of binary interactions of ions with the atoms of a crystal.

An analysis of results shows that at scattering by atomic chains a phenomenon which makes a substantial contribution to scattering by the single crystal surface the inelastic energy losses exceed the single scattering ones by a factor of 5–6.     

Measurement of optical Feshbach resonances in an ideal gas

Using a narrow intercombination line in alkaline earth atoms to mitigate large inelastic losses, we explore the optical Feshbach resonance effect in an ultracold gas of bosonic (88)Sr. A systematic measurement of three resonances allows precise determinations of the optical Feshbach resonance strength and scaling law, in agreement with coupled-channel theory. Resonant enhancement of the complex scattering length leads to thermalization mediated by elastic and inelastic collisions in an otherwise ideal gas. Optical Feshbach resonance could be used to control atomic interactions with high spatial and temporal resolution.     

Multienergy anomalous diffuse scattering

A new approach to local structure determination is presented. A three-dimensional region of the reciprocal space of a SrTiO(3) single crystal was mapped by measuring x-ray diffuse scattering patterns at different sample orientations in order to reconstruct the local atomic structure. The phase problem was solved by means of anomalous scattering from strontium atoms at photon energies near their K absorption edge. Real-space reconstruction provides the average short-range order atomic arrangement in the vicinity of anomalous scatterers up to a distance of several unit cells.     

Inelastic collisions of medium energy atomic elements in solids

The stopping of medium atomic elements in solids has been calculated in the framework of classical approximation, taking into account elastic and inelastic collisions. The calculations are based on the 1) revised equations for the law of energy and impulse conservation, which were earlier used to describe inelastic collisions of atomic particles, 2) theory of quasi-small angle scattering, 3) power potential of LNS, and 4) limitation of the maximum distance of atoms approach determined by the interatomic distance in solids. Analytical equations have been obtained to calculate 1) a differential cross-section of elastic scattering in the presence of inelastic collisions, 2) energy transferred, 3) cross-sections of elastic and inelastic stopping, and penetration depth. Implantation into solids was found to be of threshold character.     

Untersuchungen zur normalen und anomalen Absorption von Elektronen in Silizium- und Germanium-Einkristallen bei verschiedenen Temperaturen

Absolute filtered intensities of the electrons scattered elastically in thin platelike Si and Ge crystals have been measured. From the intensities of the primary and the Bragg reflected beams measured as a function of incident direction the coefficients for normal and anomalous absorption can be obtained with good accuracy, using the two beam approximation of the dynamical theory. Moreover, for Si the foil thickness and structure potentials can be deduced which are in agreement with the thickness determined optically and with calculated structure potentials resp. The results partly are influenced by multiple beam effects, which, however, are shown to be describable by Bethe's second approximation. All absorption coefficients, measured for different reflections and different crystal temperatures, show an increase with temperature, which is rather weak for Si and stronger for Ge. This shows that there is an influence of temperature diffuse scattering on normal and especially on anomalous absorption, which increases with atomic number. The results can be interpreted quantitatively, using simple models for the various contributions to the absorption coefficients (excitation of single electrons, plasmons and phonons).     

Monte Carle simulation of quantum transport through nanostructures

We describe a numerical scheme of combining Monte Carlo procedure and quantum scattering theory to simulate electron transport processes through nanostructures. The transport of electrons through a nanostructure is a highly nontrivial nonequilibrium process in which we should consider the interplay of (i) complicated many-body quantum states in nanostructure, (ii) thermal relaxation processes keeping the leads (electron reservoirs) in local equilibrium, (iii) the coupling between the leads and the nanostructure, and (iv) the bias causing nonequilibrium, current, and evolution of quantum states in the nanostructure. Considering the quantum coherence within the nanostructure, we include the degrees of freedom of the nanostructure and a single tunneling electron and solve the Schrödinger equation for the many-body states to obtain the scattering matrix in the Fock space from which both the transmission of the electron and the variation of the states in nanostructure can be full quantum-mechanically calculated. The transport is investigated by the Monte Carlo simulation of successive scattering events of single electrons which are sampled with the Metropolis scheme governed by the scattering probabilities, the thermal statistics in the leads, and the applied bias. By this way from a given initial nanostructure state we can calculate the time evolutions of the current and the internal state. As examples we investigate the transmission of electrons through a two-level system. It is shown that the proposed method can properly deal with the inelastic effects in transport processes.     

Crystalline fields in systems with exchange and magnetoelastic interaction

The influence of the Kondo effect on the state of the crystalline field in the localized-moment regime is studied. It is shown that the exchange interaction leads to an anomalous temperature dependence of the intensity of the inelastic magnetic scattering of neutrons. An unconventional theory is constructed for the magnetoelastic interaction induced by Kondo scattering. The proposed model is in quantitative agreement with the results of neutron and thermodynamic investigations of the compound CeAl₃. Pis’ma Zh. éksp. Teor. Fiz. 66, No. 7, 460–465 (10 October 1997)     

Resonance inelastic scattering of an x-ray photon by the xenon atom

The effect of many-particle and relativistic effects on the absolute values and the shape of the doubly differential cross section of resonance inelastic scattering of a linearly polarized x-ray photon by the free xenon atom in the energy region of the K ionization threshold is studied theoretically. The evolution of the spatially extended structure of the scattering cross section in the Kα,β structure of the x-ray emission spectrum of the xenon atom is demonstrated. The calculations were performed in the dipole approximation for the anomalous dispersion part of the total amplitude of probability of inelastic scattering and in the impulse approximation for the contact part of this amplitude. The radial relaxation of electronic shells, the spin-orbit splitting, the double excitation/ionization of the ground atomic state, as well as the Auger and radiative decays of the atomic core vacancies being formed were taken into account. In constructing the probability amplitude of the process, the relativistic effects were taken into account as a passage from the nonrelativistic Hartree-Fock wave functions to the relativistic Dirac-Hartree-Fock wave functions of the one-particle scattering states and as the passage (for the radiative transition amplitudes) to the relativistic form of the operator of the photon-atom interaction. The calculation results are predictive in character and, at the incident photon energy 34.42 keV, agree well with the results of the synchrotron experiment.     

Compton scattering of an X-ray photon by an open-shell atom

A nonrelativistic quantum theory for the nonresonant Compton scattering of an X-ray photon by a free many-electron atom with an open shell in the ground state has been constructed in the single-configuration Hartree-Fock approximation outside the impulse approximation widely used in the literature. The transition to an atom with closed shells reproduces the results obtained previously in [6, 7]. The results of a test calculation for atoms with open (Ti, Fe) and closed (Zn) 3d core shells are presented. The effects of the radial relaxation of one-electron states in the field of core vacancies have been taken into account. The results of the calculation agree well with the experimental results [15, 16]. It has been established that the results of the impulse approximation in the investigated X-ray photon energy ranges disagree with those of our theory not only quantitatively but also qualitatively. In particular, the impulse approximation near the elastic (Thomson and Rayleigh) scattering line leads to a gross overestimation of the contributions from the deep atomic shells involved in the inelastic photon scattering only virtually to the scattering probability. The presented theory is general in character and its applicability to a particular element of the Mendeleev table with an open core shell or to a many-electron atomic ion is limited only by the requirement that the nonrelativistic Hartree-Fock approximation be properly used in describing the scattering-state wave functions.     

Most probable and average energy losses of the beam of monoenergetic charge particles with average and low energies at multiple scattering

The results of statistical modeling of the discrete process of multiple inelastic scattering are presented. This process is modeled to find the most probable and average energy losses of a beam of charged particles (electrons and protons) passing through a material layer with a given thickness. The proposed approach is based on determining the most probable energy loss at single small-angle scattering, on including the effect of the statistical probability on this quantity at multiple scattering, and on determining the average number of inelastic interactions for particles in a film with a known thickness. The dependence of the particle energy lost during interaction with atomic electrons on their relative motion is taken into account for low-energy particles. A new interpretation is offered for the parameter J in the logarithmic term in the formulas for the average and most probable energy losses of charged particles. A computational scheme for this parameter as an average potential energy of atomic electrons is given.     

物质动态结构的非弹性散射研究

在静态结构的基础上，考虑原子的振动，分子键的振动、转动和振－振运动的结构称为动态结构，它是用非弹性散射方法来测定的。本文评述研究动态结构的实验方法：中子非弹性散射，非弹性X射线散射、核非弹性散射和Raman散射以及红外吸收谱。简单介绍了声子散射理论基础，继后，分三节描述了用这些方法来研究动态结构的若干结果。1）结晶物质，包括晶内，表面和界面，高纯近完整晶体中杂质引起的，多晶中、薄膜和纳米晶体中的点阵动力学研究；2）非晶物质，包括非晶固体，高聚合物，生物大分子，准晶和液体的动态结构研究；3）高温超导体的点阵动力学研究，文末给出了小结和最后评论。     

Focusing of electrons reflected from layered crystal

The mechanism of the formation of the diffraction patterns upon inelastic reflection of mean-energy electrons from the VSe₂(0001) layered crystal has been investigated. It is found that the strong scattering of electrons by short atomic chains of the Se-V-Se layer triads leads to the weakening of electron focusing and the enhancement of diffraction scattering in deeper layers, which gives rise to the Kikuchi lines. It is demonstrated that, at an energy of 2 keV, the diffraction pattern is adequately described by the cluster model of single scattering. The atomic structure of thin near-the-surface layer of VSe₂ has been investigated by the computer simulation of experimental data.     

Absorption and scattering of microwaves by falling snow

Fluffy snow flakes are modeled by a polydispersion of hexagonal plates for which analytical expressions for absorption and scattering coefficients are derived using the anomalous diffraction approximation. Comparison with results obtained using the dipole superposition method demonstrates that the accuracy of the anomalous diffraction approximation is within 15%. We also show that replacement of hexagonal plates by equal volume or equal surface area spheres leads to large errors in both scattering and extinction cross sections.     

Wirkungsquerschnitt und Winkelverteilung der elastischen und unelastischen Elektronenstreuung in Aluminiumschichten

Absolute intensity measurements of the electrons scattered by a polycrystalline Aluminium foil were carried out in the energy range between 25 and 50 keV. The electrons scattered elastically were separated from those scattered inelastically by means of a retarding field. The intensities of the electrons having passed the foil unscattered and of those which were scattered elastically into the Debye-Scherrerrings and into the continuous background can be interpreted by the assumption of reasonable thicknesses of the crystalline Aluminium and the amorphous Aluminium-Oxide. These values agree approximately with the thickness measured by light absorption. Additionally the probability of the inelastic scattering process can be deduced from these measurements. Investigations of the angular distribution were carried out in order to study the influence of the inelastic scattering on the shape of the primary beam, the rings and the continuous background. The results are discussed in detail. Some results are given in particular, concerning the increase of the half width of the rings due to inelastic scattering processes.     

Synchrotron and neutron-scattering methods for studies of properties of condensed matter: Competition or complementarity?

Comparative analysis of modern possibilities of synchrotron-radiation and neutron-scattering methods for studies of collective excitations, atomic and magnetic structure of condensed matter is presented in this review. The opportunities for research using techniques based on inelastic scattering, diffraction, and small-angle scattering of synchrotron radiation and neutrons, as well as synchrotron-radiation resonance elastic and inelastic scattering and absorption, have been considered. The application limits and complementarity of the considered synchrotron-radiation and neutron-scattering methods have been discussed.     

Inelastic light scattering in the Eu chalcogenides and in YbTe

First-order inelastic light scattering exhibiting broad linewidths and multiphonon lines has been measured in the magnetically ordering EuO, EuSe, and EuTe as well as in the diamagnetic YbTe. Whereas the light scattering of EuSe is similar to that of the earlier investigated EuS, we find that EuO, EuTe, and YbTe exhibit in part an anomalous behaviour. We conclude, that the inelastic broad-line light scattering found in these compounds cannot be explained by Raman theory. Instead, we suggest that this light scattering is better characterized by a recombination process.