Macroscopic and mesoscopic matter waves

It has been shown earlier [3,6] that matter waves which are known to lie typically in the range of a few angstrom, can also manifest in the macrodomain with a wave length of a few centimeters, for electrons propagating along a magnetic field. This followed from the predictions of a probability amplitude theory by the author [1,2] in the classical macrodomain of the dynamics of charged particles in a magnetic field. It is shown in this paper that this case constitutes only a special case of a generic situation whereby composite systems such as atoms and molecules in their highly excited internal states, can exhibit matter wave manifestation in macro and mesodomains, in one-dimensional scattering. The wave length of these waves is determined, not by the mass of the particle as in the case of the de Broglie wave, but by the frequency ω, of the classical orbital motion of the internal state in the correspondence limit, and is given by a nonquantal expression, λ = 2πv/ω, v being the velocity of the particle. For the electrons in a magnetic field the frequency corresponds to the gyrofrequency, Ω and the nonquantal wave length is given by λ = 2πv _|| /Ω; v _|| being the velocity of electrons along the magnetic field. Received 29 September 2001 / Received in final form 23 May 2002 Published online 19 July 2002     

On the role of secondary interactions in the production of bremsstrahlung spectra from a thick target

Bremsstrahlung emission, or radiation loss, is the dominant mechanism of energy dissipation of electrons at relativistic energies greater than a few MeV when it is subjected to acceleration in the field of the nucleus or of the electrons. In this study, the Monte Carlo calculations for bremsstrahlung spectra have been described for the case of a thick tungsten target with incident electron beams from 10 to 50 MeV, where secondary interactions induced by the electrons and photons in the target, such as energy loss, absorption, scattering, and (e ⁺, e ⁻)-pair production effects, were taken into account. The text was submitted by the authors in English.     

Influence of a magnetic field on the mutual rectification of alternating currents induced by electromagnetic waves in graphene

The direct component of the electric current induced in graphene placed in a constant magnetic field has been found in the case where two electromagnetic waves with two mutually perpendicular planes of polarization are normally incident on the surface of the sample. It has been demonstrated that the direct component of the current along the direction of the electric field vector of the wave with the frequency ω₁ arises only when the ratio between the frequencies of the incident waves is ω₁/ω₂ = 2 or 1/2. In the latter case, the direct current component appears only in the presence of a magnetic field.     

Evaluation of certain statistical sums

Summary Certain statistical ensembles,e.g. open chemical systems with randomly varying number of particles, are characterized by partition functions of the type ,n being a natural number anda _j ’s generalized temperatures. The state of the system is well defined if one knows the dependence ofa _j ’s on ensemble averages 〈n ^j 〉. For making the equations 〈n ^j 〉=〈n ^j 〉 (a ₁, ...,a _s) at least more accessible for numerical calculations a transformation of the partition function to a series of Fourier integrals is proposed. In the special case of the integrals can be calculated analytically transforming the statistical sum into a series of error functions.     

Arrays of interacting ferromagnetic nanofilaments: Small-angle neutron diffraction study

Magnetic properties of spatially ordered arrays of interacting nanofilaments have been studied by means of small-angle diffraction of polarized neutrons. Several diffraction maxima or rings that correspond to the scattering of the highly ordered structure of pores/filaments with hexagonal packing have been observed in neutron scattering intensity maps. The interference (nuclear-magnetic) and pure magnetic contributions to the scattering have been analyzed during the magnetic reversal of the nanofilament array in a field applied perpendicular to the nanofilament axis. The average magnetization and the interference contribution proportional to it increase with the field and are saturated at H = H _S . The magnetic reversal process occurs almost without hysteresis. The intensity of the magnetic contribution has hysteresis behavior in the magnetic reversal process for both the positive and negative fields that form the field dependence of the intensity in a butterfly shape. It has been shown that this dependence is due to the magnetostatic interaction between the filaments in the field range of H ≤ H _S . A theory for describing the magnetic properties of the arrays of interacting ferromagnetic nanofilaments in the magnetic field has been proposed.     

Motion and acceleration of electrons in high-intensity laser standing waves

The motion and the energy of electrons driven by the ponderomotive force in linearly polarized high-intensity laser standing wave fields are considered. The results show that there exists a threshold laser intensity, above which the motion of electrons incident parallel to the electric field of the laser standing waves undergoes a transition from regulation to chaos. We propose that the huge energy exchange between the electrons and the strong laser standing waves is triggered by inelastic scattering, which is related to the chaos patterns. It is shown that an electron's energy gain of tens of MeV can be realized for a laser intensity of 10²⁰ W/cm².     

Quantum oscillations of the resistivity and hall coefficient and the quantum limit in Bi<Subscript>0.93</Subscript>Sb<Subscript>0.07</Subscript> alloys in a magnetic field along the trigonal axis

The dependences of the electrical resistivity ρ and the Hall coefficient R on the magnetic field have been measured for single-crystal samples of the n-Bi_0.93Sb_0.07 semiconductor alloys with electron concentrations in the range 1 × 10¹⁶ cm⁻³ < n < 2 × 10¹⁸ cm⁻³. It has been found that the measured dependences exhibit Shubnikov-de Haas quantum oscillations. The magnetic fields corresponding to the maxima of the quantum oscillations of the electrical resistivity are in good agreement with the calculated values of the magnetic fields in which the Landau quantum level with the number N intersects the Fermi level. The quantum oscillations of the Hall coefficient with small numbers are characterized by a significant spin splitting. In a magnetic field directed along the trigonal axis, the quantum oscillations of the resistivity ρ and the Hall coefficient R are associated with electrons of the three-valley semiconductor and are in phase with the magnetic field. In the case of a magnetic field directed parallel to the binary axis, the quantum oscillations associated both with electrons of the secondary ellipsoids in weaker magnetic fields and with electrons of the main ellipsoid in strong magnetic fields (after the overflow of electrons from the secondary ellipsoids to the main ellipsoid) are also in phase. In magnetic fields of the quantum limit ħω _c /2 ≥ E _F, the electrical conductivity increases with an increase in the magnetic field: σ₂₂(H) ∼ H ^k . A theoretical evaluation of the exponent in this expression for a nonparabolic semiconductor leads to values of k close to the experimental values in the range 4 ≤ k ≤ 4.6, which were obtained for samples of the semiconductor alloys with different electron concentrations. A further increase in the magnetic field results in a decrease of the exponent k and in the transition to the inequality σ₂₂(H) ≤ σ₂₁(H).     

Photodetachment of H- near an elastic surface in a magnetic field

This paper investigates the photodetachment of the negative hydrogen ion H near an elastic wall in a magnetic field.The magnetic field confines the perpendicular motion of the electron,which results in a real three-dimensional well for the detached electron.The analytical formulas for the cross section of the photodetachment in the threedimensional quantum well are derived based on both the quantum approach and closed-orbit theory.The magnetic field and the elastic surface lead to two completely different modulations to the cross section of the photodetachment.The oscillation amplitude depends on the strength of the magnetic field,the ion-wall distance and the photon polarization as well.Specially,for the circularly polarized photon-induced photodetachment,the cross sections display a suppressed(E E th) 1/2 threshold law with energy E in the vicinity above Landau energy E th,contrasting with the(E E th) 1/2 threshold law in the presence of only the magnetic field.The semiclassical calculation fits the quantum result quite well,although there are still small deviations.The difference is attributed to the failure of semiclassical mechanics.     

Electron scattering with open-shell molecules: R-matrix method

Many molecules with an even number of electrons belong to open-shell systems due to π ² ground state electronic configuration. This configuration gives rise to three low-lying states X ³ Σ ⁻, a Δ ¹ and b ¹ Σ ⁺. The inclusion of these target states in a trial wave function of the entire scattering system have important implications in the resonances that may be detected in these open-shell molecules. Various molecules like O₂, PX (X = H and halogens), SO, Si₂, BF have π ² ground state configuration. The R-matrix method is a well established ab initio formalism to calculate differential, integral and momentum-transfer cross sections for the elastic scattering of electrons by molecules. We have calculated these cross sections for PH and SO molecules in the incident electron energy range 0–10 eV. The results are obtained by using the R-matrix method in which the closecoupling expansion of the wave function of the scattering system includes only the ground state. This target state is described by configuration interaction wave function that includes correlation effects. The cross section for electron impact on PH and SO are presented.     

The mystery of the alkali metals; the induced anomalous Hall effect in thin Cs films

Sandwiches made from Fe and Cs films are investigated as a function of the magnetic field and the Cs thickness. Conduction electrons which cross from the Fe to the Cs are marked by a drift velocity component perpendicular to the electric field. The anomalous Hall effect in the Fe provides this “non-diagonal” kick to the electrons that cross from the Fe into the Cs. The ballistic propagation of the conduction electrons can be monitored as a function of the Cs film thickness. The free propagation into the Cs is measured in terms of the non-diagonal conductance L_xy which we denote as the “induced anomalous Hall conductance”L _xy ⁰. For a normal (non-magnetic) metal in contact with Fe, L_xy increases with the thickness of the normal metal until the film thickness exceeds (half) the mean free path of the conduction electrons. For Cs on top of Fe the induced anomalous Hall conductance increases up to a Cs coverage of about 100 A, then, in contrast to other non-magnetic metals, L _xy ⁰ decreases for larger Cs coverage and approaches zero. This behavior cannot be explained with the free electron model. The strange behavior of the induced AHC in Cs films adds an even more challenging mystery to the already poorly understood properties of thin Cs films. These results defy explanation in the free electron model. Received 29 April 1999 and Received in final form 10 July 1999     

Landau levels line widths in potential scattering in the presence of a strong magnetic field

Summary The FBA scattering cross-section in the presence of a strong magnetic field diverges at the Landau thresholds. Such divergences are eliminated by the introduction of a modified density of states, accounting for the finite Landau states lifetime of the electrons in a magnetized plasma.     

Charge-magnetic interference resonant scattering studies of ferromagnetic crystals and thin films

The element- and site-specificity of X-ray resonant magnetic scattering (XRMS) makes it an ideal tool for furthering our understanding of complex magnetic systems. In the hard X-rays, XRMS is readily applied to most antiferromagnets where the relatively weak resonant magnetic scattering (10⁻²–10⁻⁶ I _c ) is separated in reciprocal space from the stronger, Bragg charge scattered intensity, I _c . In ferro(ferri)magnetic materials, however, such separation does not occur and measurements of resonant magnetic scattering in the presence of strong charge scattering are quite challenging. We discuss the use of charge-magnetic interference resonant scattering for studies of ferromagnetic (FM) crystals and layered films. We review the challenges and opportunities afforded by this approach, particularly when using circularly polarized X-rays. We illustrate current capabilities at the Advanced Photon Source with studies aimed at probing site-specific magnetism in ferromagnetic crystals, and interfacial magnetism in films.     

Determination of the neutron electric form factor from the reaction 3 He(e,e'n) at medium momentum transfer

The electric form factor of the neutron G_En has been determined in double polarized exclusive ³ He(e,e'n) scattering in quasi–elastic kinematics by measuring asymmetries A _⊥, A _∥ of the cross section with respect to helicity reversal of the electron, with the nuclear spin being oriented perpendicular to the momentum transfer q in case of A_⊥ and parallel in case of A_∥. The experiment was performed at the 855 MeV c. w. microtron MAMI at Mainz. The degree of polarization of the electron beam and of the gaseous ³ He target were each about 50%. Scattered electrons and neutrons were detected in coincidence by detector arrays covering large solid angles. Quasi–elastic scattering events were reconstructed from the measured electron scattering angles ϑ_e, φ_e and the neutron momentum vector p _n ^′ in the plane wave impulse approximation. We obtain the result <G _En>_{(0.27 < Q2c2/GeV2 < 0.5)}= 0.0334 ± 0.0033_stat± 0.0028_syst which is averaged over the indicated range of Q ², the squared momentum transfer. This G _En value is significantly smaller than measured from the D(e,e'n) reaction under similar kinematical conditions. To what extent final state interactions in ³He quench the G _En result is subject of calculations currently in progress elsewhere. Received: 29 April 1999     

Quasiparticle lifetime of electron–electron interactions for two-dimensional electron gases with magnetic field

We theoretically study the electron–electron scattering rate τ_ee⁻¹for electrons in a two-dimensional electron gas with a perpendicular magnetic field, within theGWand plasmon-pole approximations, as functions of temperatureT, impurity scattering rate Γ and magnetic fieldB. The τ_ee⁻¹increases with increasingTand increasing Γ, and shows the structure of the Landau levels asBis changed.     

电子在激光驻波场中运动产生的太赫兹及X射线辐射研究

采用单电子模型和经典辐射理论分别对低能和高能电子在线偏振激光驻波场中的运动和辐射过程进行了研究. 结果表明: 垂直于激光电场方向入射的低速电子在激光驻波场中随着光强的增大, 逐渐从一维近周期运动演变为二维折叠运动, 并产生强的微米量级波长的太赫兹辐射; 高能电子垂直或者平行于激光电场方向入射到激光驻波场中, 都会产生波长在几个纳米的高频辐射; 低能电子与激光驻波场作用中, 激光强度影响着电子的运动形式、辐射频率以及辐射强度; 高能电子入射时, 激光强度影响了电子高频辐射的强度, 电子初始能量影响着辐射的频率; 电子能量越高, 产生的辐射频率越大. 研究表明可以由激光加速电子的方式得到不同能量的电子束, 并利用电子束在激光驻波场的辐射使之成为太赫兹和X射线波段的小型辐射源. 研究结果可以为实验研究和利用激光驻波场中的电子辐射提供依据.     

Return current instability and its effects on beam-plasma system

The return current induced in a plasma by a relativisitc electron beam generates a new electron-ion two-stream instability (return current instability). Although the effect of these currents on the beam-plasma e-e instability is negligible, there exists a range of wave numbers which is unstable only to return current (RC) instability and not to e-e instability. The electromagnetic waves propagating along the direction of the external magnetic field, in which the plasma is immersed, are stabilized by these currents but the e.m. waves with frequencies,ω ²≪Ω _e ² ≪ω _pe ² (Ω _e andω _pe being cyclotron and plasma frequency for the electrons of the plasma respectively) propagating transverse to the magnetic field get destabilized. Heuristic estimates of plasma heating, due to RC instability and due to decay of ion-acoustic turbulence generated by the return current, are made. The fastest time scale on which the return current delivers energy to the plasma due to the scattering of ion-sound waves by the electrons can be ∼ω _pi ⁻¹ (ω _pi being the plasma frequency for the ions).     

Magnetic and EPR studies of the EuFe<Subscript>3</Subscript>(BO<Subscript>3</Subscript>)<Subscript>4</Subscript> single crystal

Magnetic and electron paramagnetic resonance (EPR) properties of EuFe₃(BO₃)₄ single crystals have been studied over the temperature range of 300–4.2 K and in a magnetic field up to 5 T. The temperature, field and orientation dependences of susceptibility, magnetization and EPR spectra are presented. An antiferromagnetic ordering of the Fe subsystem occurs at about 37 K. The easy direction of magnetization perpendicular to the c axis is determined by magnetic measurements. Below 10 K, we observe an increase of susceptibility connected with the polarization of the Eu sublattice by an effective exchange field of the ordered Fe magnetic subsystem. In a magnetic field perpendicular to the c axis, we have observed an increase of magnetization at T < 10 K in the applied magnetic field, which can be attributed to the appearance of the magnetic moment induced by the magnetic field applied in the basal plane. According to EPR measurements, the distance between the maximum and minimum of derivative of absorption line of the Lorentz type is equal to 319 Gs. The anisotropy of g-factor and linewidth is due to the influence of crystalline field of trigonal symmetry. The peculiarities of temperature dependence of both intensity and linewidth are caused by the influence of excited states of europium ion (Eu³⁺). It is supposed that the difference between the g-factors from EPR and the magnetic measurements is caused by exchange interaction between rare earth and Fe subsystems via anomalous Zeeman effect.     

Nonlinear Thomson scattering of an ultrashort laser pulse

The nonlinear scattering of an ultrashort laser pulse by free electrons is considered. The pulse is described in the “Mexican hat” wavelet basis. The equation of motion for a charged particle in the field of a plane electromagnetic wave has an exact solution allowing, together with the instant spectrum approximation, the calculation of the intensity of nonlinear Thomson scattering for a high-intensity laser pulse. The spectral distribution of scattered radiation for the entire pulse duration is found by integrating with respect to time. The maximum of the emission spectrum of a free electron calculated in 10¹⁹–10²¹ W/cm² fields lies in the UV spectral region between 3 and 12 eV. A part of the continuous spectrum achieves high photon energies. One percent of the scattered energy for the field intensity 10²⁰ W/cm² is concentrated in the range ħω > 2.7 × 10² eV, for a field intensity of 10²¹ W/cm² in the range ħΩ > 7.9 × 10² eV, and for an intensity of 10²² W/cm² in the range ħΩ > 2.45 × 10⁵ eV. These results allow us to estimate nonlinear scattering as a source of hard X-rays.     

<Emphasis Type="Italic">K</Emphasis><Subscript>α</Subscript> radiation of foil under interaction with laser pulse of relativistic intensity

An analytical model of K _α radiation of thin laser targets has been developed. It has been shown that, for such targets, the motion of fast electrons is significant not only in the target itself but also in vacuum. The considered dependences for the free path length of a fast electron and for the absorption coefficient of laser radiation on the laser intensity with allowance for the electron motion in vacuum make it possible to match the results of the proposed model with the experimental data on generation of K _α radiation in wide ranges of laser intensities (10¹⁸–10²¹ W/cm²) and thicknesses (1–100 μm) of targets.