Zur Spinpolarisation langsamer Elektronen nach der Streuung an Molekülen

Cross sections and spin polarization of low-energy electrons scattered by I₂ and C₂H₅I molecules were measured in the energy range from 200 to 600 eV and angular range from 30 to 150°. At the same time, several authors made calculations of cross sections and polarizations based on the following assumptions: The molecule consists of free atoms which are independent of each other (the influence of binding is negligible) and scattering of an electron does not occur more than once within the molecule. The agreement between theory and experiment in a wide angular range justifies these assumptions for the present problems. Polarization values lower than the theoretical ones were measured only at scattering angles where the theory predicts very narrow and high values of the spin polarization. Qualitative arguments show that intramolecular scattering very likely is responsible for the deviations found between theoretical and experimental polarization peaks. By means of the polarization of the scattered intensity one can easily decide how much of the scattered intensity comes from one part of the molecule and how much comes from the other part.     

Characteristics of potential-resonance elastic scattering of slow electrons by calcium atoms

The characteristics of elastic scattering of electrons by atomic systems are described by the potential resonance method in terms of the energy dependence of integral-type cross section S taken using a hypocycloidal electron spectrometer. The effect of ² D shape resonance on the run of the curve S(E) is demonstrated with scattering of slow (of energy no higher than 2 eV) electrons by calcium atoms. The energy and width of the resonance are derived from the extrema (minimum and maximum) of the experimental curve S(E). This dependence also serves to find the electron scattering differential cross sections. Two slightly differing scattering angles are taken into account. The differential cross sections derived from the experimental data qualitatively agree with theoretical results, albeit being somewhat lower.     

Assessment of the equivalent photon approximation for the process ee → ee π+π−

The contribution of the virtual process γγ → π⁺π^? is evaluated, first treating the quantum electrodynamics exactly and then using the equivalent photon approximation. The dependence on electron scattering angles, electron energies, ππ invariant mass and γπ momentum transfer is investigated. The approximation is very good if both electron scattering angles are less than 0.1 rad, but is 20%–40% too big (depending on the precise version used) if either angle is integrated over. It is explained that the approximation is not Lorentz invariant; numerical results are given only for beams with anti-parallel momenta.     

Untersuchung der Polarisationsebene von Photonen nach Compton-Streuung an polarisierten Elektronen

Two polarization phenomena in Compton scattering by polarized electrons were investigated. In the first experiment, the rotation of the polarization plane of photons passing through magnetized iron and gadolinium was measured. This effect arises from a spin dependence of the Compton forward scattering amplitude. For 228 and 333 keV photons and iron absorbers, the observed rotation angles areφ ₀=(3.90±0.57) ×10^?3 rad · cm^?2 and (4.75±0.58)×10^?3 rad · cm^?2, respectively. Secondly, the orientation of the photon polarization plane after scattering of unpolarized photons by polarized electrons was measured. This experiment tests time reversal invariance in quantum electrodynamics. No dependence of the polarization plane on the direction of the electron spin was found within 2×10^?3.     

Dynamic spin susceptibility of hole-doped high-temperature superconductors in a singlet-correlated conduction band model

We have derived an expression for the dynamical spin susceptibility of a hole-doped high-temperature superconductor taking into account a strong correlation between the magnetization of spins of the localized and itinerant electrons. This formula has been used to calculate the imaginary part of the susceptibility as a function of the frequency and wave vector. The results are compared to experimental data on the inelastic neutron scattering in compounds of the YBa₂Cu₃O_6+y type. A peak in the scattering intensity observed at an energy of about 40 meV in the region of wave vectors Q = (π, π) and an arc-shaped dispersion relief are interpreted as manifestations of the collective spin excitations in the system, the energy of which falls within a superconducting gap (spin exciton). The U-shaped divergent relief observed in the neutron scattering intensity is assigned to collective short-rage-order spin oscillations.     

Streuung von 25 keV-Elektronen an Gasen

The angular distribution of 25 kev electrons scattered elastically and inelastically by molecular hydrogen has been measured in the angular range 7·10^?4≦?≦4,3·10^?2. By the separation of the inelastically scattered electrons observation of deviations from the Debye Ehrenfest theory of the electron diffraction by molecules at small angles is possible. These deviations are due to the alteration of the electron density distribution of the hydrogen atoms induced by the bonding. The energy loss spectra at different scattering angles (energy resolution ≈1 ev) shows a strong peak atΔE=12,6 ev. At larger angles forΔE>15 ev a continuum appears. That part of the inelastic processes which leads to ionization of the molecule is raising with increasing scattering angle. Normalization of the experimental values to the theoretical elastic differential cross section enables comparison of the angular distribution of the 12,6 ev energy loss with the distribution calculated byRoscoe. The shape of the experimental curve is in fairly good agreement with the calculated one but the experimental values at small angles are 20–30% higher. For zero angle the energy loss spectrum is taken with better resolution (≈0,04 ev). It shows vibrational states of the Lyman and Werner band and higher terms. The probability of the excitation of some vibrational states of the Werner band (square of the overlapp integral) calculated here is inspite of the required approximations in excellent agreement with the measurement, while Hutchisson's result fails for the Lyman band.     

Quasi-free scattering of pions on 3, 4He

Differential cross sections for ^{3, 4}He(π, π') are presented for angles of 60° and 120° at 200 MeV and 120° at 295 MeV. The momentum spectra for the scattered pions are dominated by a peak attributed to quasi-free scattering from individual nucleons. There are significant differences between the scattering on ³He and ⁴He as well as between the scattering of π⁺ and π^? on ³He. The data are compared to a simple model incorporating the free π+N scattering amplitudes. Modifications for the structure and dynamics of the target nucleus are discussed.     

Scattering from nonoverlapping potentials. III. Pion elastic scattering on 4He in the 3,3 region

The $\text{π}{}^{\mathrm{?}}{}^4\text{He}$ elastic scattering in the 3,3 resonance region is discussed in the framework of the nonoverlapping potentials model. Single and double scattering terms are considered together with their modification by reflection terms, which allow the projectile to oscillate back and forth an arbitrary number of times within a pair of nucleons. Reflections and spin and isospin flips are found to constitute a determining factor in a qualitative reproduction of the correct shape of observed angular distributions, in particular for backward scattering angles. Reflections are probably unimportant in πd scattering.     

Experimental and simulation investigations of the peculiarities of relativistic electron beam scattering at a small angle of incidence on a thin flat target

The refraction angles θ _d of electron beams passing through aluminum and thin flat copper foils and reflection angles θ _r are measured. A microtron with 7.4 MeV particles is used as a source of electrons. The angle between the particle trajectory and the target surface α is varied in the range 5°–30°. The dependences of the refraction and reflection angles on the α angle and foil thickness δ are measured. A dosimetric film is used to make pictures of cross sections of the electron beam scattered by a thin 50 μm copper foil. Image processing allows the spatial distributions of refracted and reflected particles to be obtained. The processes of relativistic electron scattering at a small angle of incidence on a flat target are simulated by the Monte Carlo method. The results of simulation are compared with experimental data. Particle scattering at a bimetallic target consisting of 200-μm aluminum and 70-μm lead layers are simulated. A dependence of the spatial-energy distributions on the order of metal layers placed along electron trajectories is found.     

Elektronenpolarisation im Energiebereich unterhalb 50 eV durch Streuung an freien Hg-Atomen

The angular dependence of spin polarizationP(Θ) of electrons elastically scattered by a beam of mercury atoms is measured in a double scattering experiment for electron energies of 45±1 eV; 23±1 eV; 7±1 eV; and 3,5±1 eV. Maximum degree of polarization obtained isP(100°)=0,39±0,07; electron energy 7±1 eV; electron current 10^?12–10^?11 A.     

Relaxation processes and mobility of electrons in a semiconductor quantum well with the modified Pöschl-teller confining potential

Relaxation processes and mobility of electrons in a semiconductor quantum well are studied. The modified Pöschl-Teller potential is used as a confining potential. Scattering rates due to impurity ions, acoustic and piezoacoustic phonons are calculated taking into account the screening of scattering potentials by charge carriers. It is shown that when degenerate electrons are scattered by acoustic phonons, the dependence of scattering rate on electron wave number ν_ac(k) is almost linear. At small k, the acoustic phonon piezoelectric scattering rate of degenerate electrons increases with k, and then it decreases slightly when k > 8 × 10⁷ m⁻¹. The ionized impurity scattering rate of degenerate electrons does not depend on temperature, is directly proportional to the electron density, and decreases with increasing k. Dependences of electron mobility on surface ion density and temperature are studied. It is shown that in the case of non-degenerate or slightly degenerate electron gas, a maximum appears in the temperature dependence of the mobility, and the screening effect is negligible. The screening significantly increases the mobility of electrons in the case of high degeneration. Obtained results are applied to GaAs-based quantum wells.     

Scattering of spin-polarized electron in an Aharonov-Bohm potential

The scattering of spin-polarized electrons in an Aharonov-Bohm vector potential is considered. We solve the Pauli equation in 3 + 1 dimensions taking into account explicitly the interaction between the three-dimensional spin magnetic moment of electron and magnetic field. Expressions for the scattering amplitude and the cross section are obtained for spin-polarized electron scattered off a flux tube of small radius. It is also shown that bound electron states cannot occur in this quantum system. The scattering problem for the model of a flux tube of zero radius in the Born approximation is briefly discussed.     

Stringent upper bounds on π−p charge-exchange differential cross sections

Unitary bounds on (dσ/dt) for π^?p charge-exchange reactions in terms of the π^?p elastic amplitudes are obtained. No assumptions have been made regarding the spin and helicity structure of the problem. Computation of the bounds at various energies reveal the severe restrictions unitarity places on a rapid rise of the spin-flip amplitude at near-forward angles. The near saturation of the bounds at some angles suggests that such bounds are of potential use in restricting the choice of elastic amplitudes fitting a given set of elastic observables.     

Messung der Spinpolarisation von 900 eV-Elektronen nach elastischer Streuung an Schwermetallfolien in Abhängigkeit von der Targettemperatur

900 eV electrons are elastically scattered by solid targets of tungsten, platinum and gold. The angular dependence of the scattered intensity and of spin polarizationP(Θ) is investigated as a function of the target temperature. The influence of hydrogen on the scattering process by a gold target is investigated too.     

Diffusion of electrons scattered by short-range impurities in a quantizing magnetic field

Formulas for transverse diffusion and conductivity in a semiconductor are obtained for electrons scattered by neutral impurities in a quantizing magnetic field. The formulas are valid for an impurity potential of arbitrary depth. Based on Kubo’s theory [1], calculations are performed using electron wavefunctions of the problem of single-impurity scattering in a magnetic field [2]. The poles of the scattering amplitude correctly determine electron eigenstates and magnetic impurity states. As a result, an exact expression is found for the dependence of transverse diffusion coefficient D _⊥ on longitudinal electron energy ? due to scattering by short-range (neutral) impurities. The behavior of D _⊥(?) is examined over an interval of magnetic field strength for several values of impurity potential depth. The experimental observability of diffusion and conductivity using IR lasers is discussed.     

Microwave scattering diagrams of three-layered SiC-metamaterial/gyrotropic ferrite-SiC cylinders

We present here for the first time the rigorous solution of the boundary diffraction problem of microwave scattering by a multilayered 2D cylinder. The cylinder layers may be made of isotropic, uniaxial anisotropic, electrically and (or) magnetically gyrotropic materials. The number and thickness of the layers may have arbitrary values in our solution. We calculated scattering diagrams (a radial component of real part of the Poynting vector) inside and outside of cylinder using the solution. Here we present scattering diagrams from a three-layered cylinder made of SiC and metamaterial or saturate magnetized ferrite. Diagrams were computed for wave incidence angles θ=π/2,π/3,π/6 inside of metamaterial/ferrite layer at a distance of 1 mm and outside of cylinder at a distance of 2.5 mm from the cylinder axis.     

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.     

2D scattering of unpolarized beams of electrons by charged nanomagnets

2D spin-dependent scattering of slow unpolarized beams of electrons by charged nanomagnets is analyzed in the Born approximation. The obtained scattering lengths are larger than those from the neutral nanomagnets approximately by one order. It is shown that for particular parameters of the system it is possible to polarize completely the scattered electrons in a narrow range of scattering angles. The most suitable system for realization of these effects is 2D Si electron gas with immersed nanomagnets.     

On resonance and nonresonance interactions between electrons and spatially periodic clusters

The effects of resonance and nonresonance interactions between electrons and spherical structures with spatial periodicity in the radial direction (clusters) were studied. It was shown analytically and by numerical calculations that the δ _l phase shift of the wave function, which arises in resonance electron scattering by such a periodic structure of a fairly large radius r₀, was not small even at a small ratio between the U₀ amplitude of the periodic potential and scattered electron energy E(ε₀=U₀/E?1) and equaled |δ _l |=π/4 (modulo π). This phase shift corresponded to the limiting case of a large Born parameter for the cluster, ξ₀=r₀U₀/?v?1, where v is the characteristic velocity of the electron. The effect of nonresonance electron scattering by a periodic potential whose spatial period was incommensurate with the Brillouin wavelength of the scattered electron was considered analytically. The effect of nonresonance scattering was shown to be of a higher order in the ε₀?1 parameter than resonance scattering. The cross section of electron scattering by a cluster was calculated, which allowed the conductivity of a medium containing clusters to be estimated.