Dynamische Theorie der elastischen Elektronenbeugung unter Verwendung komplexer Atomformfaktoren

The two-beam approximation of dynamic electron diffraction in crystals is deduced from successive scattering by two-dimensional gratings. The scattering-amplitude caused by the single grating (phase-grating) is determined by the atomic scattering factors of the single atoms. The use of real atomic scattering factors leads here to the same solutions as the twobeam theory, using the Schroedinger-equation. Anomalous absorptions effects are described in the usual theory by introducing a complex lattice potential into the Schroedinger-equation, taking into account inelastic scattering. A more exact calculation of only elastic scattering by a single atom results in complex atomic scattering factors. Using the complex atomic scattering factors one can describe the anomalous absorption, if recursion-formulae for successive scattering are applied. On the other hand, the transformation to differential equations leads to results, which are not in agreement with experiments. The influence of inelastic scattering for the anomalous absorption can be neglected compared with the complex atomic scattering factors.     

Peak structure of polarized bremsstrahlung upon scattering by coupled atomic electrons

Peculiarities of polarized bremsstrahlung (PB) of relativistic electrons produced upon scattering by coupled atomic electrons are discussed; in this case, PB is regarded as scattering of virtual photons of the electromagnetic field of a fast charge by atomic electrons with their coupling taken into account. In this case, the atomic electron during scattering can acquire recoil energy only through separate portions, as a result of which the spectrum of scattered photons degenerates into a series of narrow peaks.     

Superelastic electron scattering by metastable strontium atoms

Superelastic electron scattering by metastable strontium atoms is experimentally studied using intersecting electron and atomic beams and an electron spectrometer. The energy dependence of the effective cross section of superelastic electron scattering in the energy range 0.15–2.0 eV has been obtained for the first time.     

X-ray scattering factors for ionic crystals with complete electron shells

Expressions of the X-ray scattering factors were derived for ionic crystals with complete electron shells by using the wave functions of free ions. The non-orthogonality of the atomic wave functions in a crystalline state was taken into account by means of Löwdin’s orthogonalization method when presenting the electron density of crystals. In the case of a small overlap between the wave functions localized at the lattice sites, it was plausible to describe mathematically a crystal ion containing small overlap charge contribution in addition to the free-ion contribution. As an application, the scattering factors for the LiF crystal were computed. The theoretical results obtained agree well with recent experimental data.     

Calculation of surface states using a one-dimensional scattering model

The complex electronic band structure of a one-dimensional solid is described using a one-dimensional scattering approach. The method yields the value of the wave function and its derivative between the atomic layers. These values can be matched at the surface to the corresponding values of the wave function on the vacuum side. The method is compared to the two-band approximation of the nearly free electron model. Advantages of the proposed scheme are the easy adaption for layered systems and alloys.     

Relativistic corrections to electron scattering: (II). Inelastic scattering

Relativistic corrections to inelastic electron scattering have been investigated using the results of a previous calculation on elastic scattering. A detailed discussion is made of the kinematics of inelastic scattering. Excitation of discrete states is treated in detail by two different methods, with particular attention paid to kinematical factors. Deuteron breakup is discussed and treated in a very similar manner to the discrete excitations. Comparison is made with analyses using plane wave final states and with previous work.     

The single scattering properties of the aerosol particles as aggregated spheres

The light scattering and absorption properties of anthropogenic aerosol particles such as soot aggregates are complicated in the temporal and spatial distribution, which introduce uncertainty of radiative forcing on global climate change. In order to study the single scattering properties of anthorpogenic aerosol particles, the structures of these aerosols such as soot paticles and soot-containing mixtures with the sulfate or organic matter, are simulated using the parallel diffusion limited aggregation algorithm (DLA) based on the transmission electron microscope images (TEM). Then, the single scattering properties of randomly oriented aerosols, such as scattering matrix, single scattering albedo (SSA), and asymmetry parameter (AP), are computed using the superposition T-matrix method. The comparisons of the single scattering properties of these specific types of clusters with different morphological and chemical factors such as fractal parameters, aspect ratio, monomer radius, mixture mode and refractive index, indicate that these different impact factors can respectively generate the significant influences on the single scattering properties of these aerosols. The results show that aspect ratio of circumscribed shape has relatively small effect on single scattering properties, for both differences of SSA and AP are less than 0.1. However, mixture modes of soot clusters with larger sulfate particles have remarkably important effects on the scattering and absorption properties of aggregated spheres, and SSA of those soot-containing mixtures are increased in proportion to the ratio of larger weakly absorbing attachments. Therefore, these complex aerosols come from man made pollution cannot be neglected in the aerosol retrievals. The study of the single scattering properties on these kinds of aggregated spheres is important and helpful in remote sensing observations and atmospheric radiation balance computations.     

Simulating the oxygen K-edge spectrum from grain boundaries in ceramic oxides using the multiple scattering methodology

In this paper we demonstrate the use of the multiple scattering methodology to interpret oxygen K-edge spectra from both the bulk and grain boundaries in a variety of ceramic oxides. The experimental electron energy loss spectra (EELS) used in this study, were obtained from a dedicated scanning transmission electron microscope (STEM). Using the STEM to obtain the spectra has the advantage that each spectrum can be acquired with atomic spatial resolution. While the energy resolution is limited to approximately 0.8 eV, and the angular integration in the microscope apertures precludes momentum resolved spectroscopy, this unprecedented spatial resolution allows the electronic structure at individual defect sites to be determined. Additionally, as the microscope can also provide an atomic resolution image of the defect, the relationship between the atomic structure of the defect and its local electronic structure can be determined. In practice, this is achieved by using the structure observed in the image to build the real space atomic cluster for multiple scattering simulations. Detailed interpretation of the simulations of oxygen K-edge spectra from bulk MgO, CaO, SrTiO3, TiO2, MnO2, Mn3O4, Mn2O3 and MnO are presented. In addition, the simulations from grain boundaries in TiO2 (undoped) and SrTiO3 (undoped and Mn doped) are discussed in relation to quantifying the changes in the local electronic structure that are a direct consequence of the defect structure. The simulations are used to make interpretations of the structure-property relationships at these grain boundaries.     

Distorted wave eikonal approximation for elastic electron-atom scattering

By treating the static field of the atom exactly and using the eikonal wavefunction to bring in the couplings to all remaining atomic states, a simple formula for elastic scattering amplitude is derived. Its usefulness is demonstrated by applying it to electron—hydrogen scattering.     

Anomalous X-ray scattering studies on semiconducting and metallic glasses

In order to explore local- and intermediate-range atomic structures of several semiconducting and metallic glasses, anomalous X-ray scattering (AXS) experiments were performed using an improved detecting system suitable for third-generation synchrotron radiation facilities, and the obtained data were analyzed using reverse Monte Carlo (RMC) modelling to obtain partial structure factors and to construct three-dimensional atomic configurations of these glasses. Examples of GeSe₂ semiconducting and Pd₄₀Ni₄₀P₂₀ metallic glasses are demonstrated to exhibit the feasibility of the combination of AXS and RMC techniques. Importance of an additional combination with neutron scattering is also described for alloys containing light elements.     

Low energy positron scattering from atoms in and on solids observed with low energy positron diffraction and reemission microscopy

The present status of low energy positron diffraction (LEPD) and positron reemission microscopy (PRM) is reviewed in the context of unanswered questions regarding the elastic scattering of positrons in the 1–300 eV energy range from atoms in solids and at solid surfaces. Recent LEPD studies yield an agreement between theoretical and experimental diffraction intensities for semiconductors that has never been equalled in electron diffraction studies. This situation is discussed in terms of the repulsive interaction between the positron and the embedded atomic potential and the lack of exchange with the nonspherically distributed valence electrons. The scattering of re-emitted positrons in PRM from atoms chemisorbed or physisorbed on the re-emitting surface has not yet received the same theoretical attention as scattering from embedded atoms in LEPD. Possible ways in which positron scattering from overlying atomic structures manifests itself in PRM as well as positron re-emission holography are discussed, both from the practical viewpoint of observing these structures and in the context of fundamental questions regarding the positron re-emission process itself.     

Coupled-channel optical calculation for positron—lithium scattering

Positron scattering with atomic lithium is investigated by using a coupled-channel optical method.The ionization continuum and positronium formation channels are taken into account via a complex equivalent-local optical potential.The positronium formation cross sections and the ionization cross sections,as well as the total scattering cross sections,are reported at energies above 3 eV and compared with available experimental and theoretical data.     

Determination of atomic scattering factors of vanadium and chromium by means of vanishing Kikuchi line method

The X-ray atomic scattering factors <f;^X for the 110 reflection of V and Cr have been determined by high voltage electron diffraction, and the results are compared with theoretical values.     

Band structure of transverse-energy eigenvalues and strong electron scattering by atomic planes in single crystals

The interaction between electrons and atomic planes in a single crystal is discussed via a bound-state model; the transverse-energy spectrum allows one to classify many electron states as bound to individual planes, semibound to a system of planes, or free de Broglie waves. Expressions are derived for the channeling probability and the probability of strong Rutherford scattering. There is a detailed discussion of the states for the (100) and (110) planes of silicon, which play a part in strong electron scattering.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 1, pp. 112–117, January, 1978     

Hyperfine fields and neutron scattering in ferromagnetic metals

The origin of ferromagnetism in the transition metal ferromagnets, iron, cobalt, and nickel is discussed, from an ab initio band structure point of view, with proper attention to the explicit roles of exchange, correlation and hybridization effects. The influence of these effects and all the mechanisms such as direct, exchange core polarization and many-body effects that have been found important for the hyperfine properties of atomic systems are included in attempting to understand the experimentally observed hyperfine fields at the nuclei in these metals. Spin-density distributions using calculated spin polarized band wave-functions are used to make comparisons with experimental neutron scattering data. The impact of the results of analyses of hyperfine fields at the nuclei and spin density distributions on the origin of hyperfine fields at muon sites is discussed. This talk, and the corresponding article for the proceedings of this conference, will deal with the theoretical understanding of the hyperfine fields at the nuclei and neutron scattering form factors in the three ferromagnetic metals, iron, cobalt and nickel and the impact of this understanding on that of the origin of the hyperfine fields at positive muon sites in these metals. With these aims in mind, the plan of my talk will be the following.

1. Discussion of a first-principle principle procedure to obtain the energy bands and electronic wave-functions in these metals and the understanding of the origin of their ferromagnetism from a band point of view.
2. Mechanisms contributing to hyperfine fields in atomic systems and their relevance for ferromagnetic metals.
3. The mechanisms for the origin of hyperfine fields in these metals, corresponding theoretical results and comparison with experiment.
4. Comparison between calculated spin-density distributions and experimental results from neutron scattering data.
5. Remarks on the origin of hyperfine fields at muon sites in these metals.

     

Resonances in positron-atom scattering

Theoretical studies of atomic resonances involving positrons will be discussed in this talk. Investigations on resonances in positron-hydrogen scattering below various hydrogen and positronium thresholds are reviewed, as well as resonances in positronalkali and e⁺-He⁺ scattering. Resonance phenomena in other atomic systems involving positrons will also be discussed. These systems include positronium ions Ps⁻, positronium molecules Ps₂, and positronium hydride PsH.     

低速分子离子在固体电子气中的散射与能量损失

利用量子力学中的电子分子散射理论，研究了低速双原子分子离子在固体电子气中的散射与能量损失，重点讨论了两离子之间的干扰效应对能量损失的影响。根据原子的ｉｎｄｅｐｅｎｄａｎｔ ｐａｒｔｉｃｌｅ－ｍｏｄｅｌ（ＩＰＭ）势和变相法，确定了单原子离子的散射相移和阻止本领，并与非线性密度泛函理论的结果进行了比较。 关键词：     

Relativistic effects in low energy electron scattering from atoms

Recent relativistic calculations on low energy elastic scattering of electrons from atoms are reviewed. Two aspects are emphasized : mathematical transformations and numerical methods used in the solution of the Dirac equation and the summation of the partial wave series ; and the results of relativistic calculations, in particular the behaviour of the cross sections and spin polarizations for different atoms, different energies of the incident electron, and in different approximations. The effects of the screening of the nucleus by the atomic electrons, electron exchange (including the use of approximate exchange potentials) and the distortion of the atom by the incident electron are discussed. Detailed results for cross sections and spin polarizations are given for mercury and the inert gases. The differences arising from use of the Dirac equation instead of the Schrödinger equation are considered.     

Magnetic neutrino scattering on atomic electrons revisited

We reexamine the role of electron binding effects in the inelastic neutrino–atom scattering induced by the neutrino magnetic moment. The differential cross section of the process is presented as a sum of the longitudinal and transverse components, according to whether the force that the neutrino magnetic moment exerts on electrons is parallel or perpendicular to momentum transfer. The atomic electrons are treated nonrelativistically. On this basis, the recent theoretical predictions concerning the magnetic neutrino-impact ionization of atoms are critically discussed. Numerical calculations are performed for ionization of a hydrogenlike Ge⁺³¹ ion by neutrino impact.     

Panoramic measurements of electron beam densities by Thomson scattering of laser radiation

The possibility of using a panoramic detector with a television signal-recording system in an apparatus to observe Thomson scattering of laser radiation by a nonrelativistic electron beam is discussed. Panoramas of Thomson and Rayleigh scattering and of the electron beam luminescence are presented. Estimates are given of the sensitivity and spatial resolution of the apparatus. Results of panoramic and single-point methods of investigation are compared. Possibilities for extending the range of the Thomson scattering method to measure the density distribution in nonrelativstic electron beams are discussed. Zh. Tekh. Fiz. 69, 80–83 (June 1999)