Nodal expansions for strongly coupled classical plasmas

The canonical equilibrium properties of classical Coulomb systems are investigated in 2 + ? dimensions for any value of the plasma parameter $\text{Λ}{}_{\mathrm{?}}\text{=}\text{e}{}^2\text{k}{}_{\mathrm{B}}\text{Tλ}{}^{\mathrm{?}}{}_{\mathrm{D}}$, through the nodal expansion of the two-particle correlation function g₂(r), wh ere e is the electronic charge, k_B the Boltzmann constant, T the absolute temperature and λ_D the Debye length. We first consider the one-component plasma (OCP) model. An attention is especially paid on the higher order bridge (non-convolution type) graphs. The long-ranged resummations of the convolution-like geometric series which build up the hypernetted chain (HNC) approximation are considered at length. The short-range resummations are also performed in view of their specific interest for evaluating the enhancement rates of nuclear reactions in Astrophysics and Fusion Physics. Next, we shall extend the classical nodal expansions to high-temperature OCP models in which the short distance interactions have to be corrected for the ? ≠ 0 diffract ion effects. A second generalization concerns the high-temperature two-component plasma(TCP) model of point charges of opposite signs at high temperatures. In both cases, the bare Coulomb interaction is modified by a temperature-dependent effective interaction which allows for an entirely classical treatment of the small quantum corrections. Finally, the equilibrium properties of the TCP are used to work out the density corrections to the hydrodynamic (Bohm) diffusion transverse to an arbitrarily strong and static magnetic field.     

A slice theorem for the space of solutions of Einstein's equations

A slice for the action of a group G on a manifold X at a point x ? X is, roughly speaking, a submanifold S_x which is transverse to the orbits of G near x. Ebin and Palais proved the existence of a slice for the diffeomorphism group of a compact manifold acting on the space of all Riemannian metrics. We prove a slice theorem for the group $\text{D}$ of diffeomorphisms of spacetime acting on the space $\text{E}$ of spatially compact, globally hyperbolic solutions of Einstein's equations. New difficulties beyond those encountered by Ebin and Palais arise because of the Lorentz signature of the spacetime metrics in $\text{E}$ and because $\text{E}$ is not a smooth manifold- it is known to have conical singularities at each spacetime metric with symmetries. These difficulties are overcome through the use of the dynamic formulation of general relativity as an infinite dimensional Hamiltonian system (ADM formalism) and through the use of constant mean curvature foliations of the spacetimes in $\text{E}$. (We devote considerable space to a review and extension of some special properties of constant mean curvature surfaces and foliations that we need.) The conical singularity structure of $\text{E}$, the sympletic aspects of the ADM formalism, and the uniqueness of constant mean curvature foliations play key roles in the proof of the slice theorem for the action of $\text{D}$ on $\text{E}$. As a consequence of this slice theorem, we find that the space $\text{D}$ = $\text{E}$/$\text{D}$ of gravitational degrees of freedom is a stratified manifold with each stratum being a sympletic manifold. The spaces for homogeneous cosmologies of particular Bianchi types give rise to special finite dimensional symplectic strata in this space $\text{G}$. Our results should extend to such coupled field theories as the Einstein-Yang-Mills equations, since the Yang-Mills system in a given background spacetime admits a slice theorem for the action of the gauge transformation group on the space of Yang-Mills solutions, since there is a satisfactory Hamiltonian treatment of the Einstein-Yang-Mills system, and since the singularity structure of the solution set is known.     

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.     

Submillimetre cyclotron resonance of electrons in GaP

The first observation of cyclotron resonance in n-type GaP is reported. The electrons were thermally excited at a temperature of 100 K and the resonance was observed at submillimetre wavelengths (337 μm) using a pulsed magnetic field of 0–300 kG. From experiments with B∥〈100〉, 〈110〉 and 〈111〉 it was found that the transverse effective mass for electrons is $\text{m}{}^1{}_{\mathrm{\perp }}\text{= 0.25 ± 0.01 m}{}_0$ and that the anisotropy factor for the conduction band ellipsoids is K = 20⁺¹⁰_-6.     

Magnetic properties of amorphous sputtered CoxSi1−x films

Magnetic properties have been measured by transverse magneto-optic Kerr effect (MOKE) in amorphous sputtered Co_xSi_1?x films which are ferromagnetic and amorphous at room temperature with 0.55<x<0.80. These as-sputtered films show an in-plane easy axis with the ratio of coercitive force in the hard axis H_c (HA) to easy axis H_c (EA) and the value of the blocking field H_B almost constant with 0.60<x<0.80. Transverse magnetic susceptibilities with bias magnetic field parallel (χ_t0) and perpendicular $\text{(χ}{}_{\mathrm{<mtext>t\pi </mtext><mtext>2</mtext>}}\text{)}$ to the easy axis has been measured. These measurements show a deviation of Hoffmann's micromagnetic law for the susceptibilities.     

非线性电子磁漂移波

本文采用重整化方法处理了无剪切磁场漂移近似下的非线性电子磁漂移波,并分析了它与托卡马克电子反常输运之间的关系。所得到的扩散系数D_⊥～(ω_pe(T_e/cB₀L_nk_⊥²)与现有托卡马克实验结果大致符合。 关键词：     

Applications of photoconductivity measurements in n-InSb under crossed fields

The photocurrent in n-InSb at 85K was measured as function of the applied longitudinal voltage and an additionally applied transverse magnetic field. In the driftconfiguration the photoionized electron-hole plasma was driven into the sample volume, and negative photocurrents resulted from the negative feedback of this motion. With the magnetic field being reversed, in the Suhl configuration, only positive photocurrents were measured. All results are in agreement with the theory in [1]. They were used to determine recombination coefficients in n-InSb, and, principally, the transverse diffusion coefficientD _⊥. As first observed in [13],D _⊥ proved to be anomalously enhanced above classical values if plasma instabilities were generated in the samples.     

Large p⊥ lepton production and the ψ(3100)

We determine the invariant cross section $\text{E}\text{d}\text{σ}\text{d}{}^3\text{p(s,x}{}_6\text{,pp}{}_{\mathrm{\perp }}\text{)}$ for pp→ψ(3100)+X near x₆=0 at NAL and ISR energies using the assumption that all large p_⊥ single leptons originate from the ψ. We adequately reproduce the single lepton data, and by suitable extrapolarion in x₆ ensure agreement with the NAL ψ production data (x₆?0.3). The magnitude of the resulting ψ production cross section is, however, roughly a factor of 3 larger than that observed by the recent CCRS-ISR experiment.     

Diffusion in thermotropic liquid crystals

Diffusion coefficients in mesophases of thermotropic liquid crystals have been measured to a considerable extent only during the last twelve years. Some theories on diffusion in mesophases have been developed too. Measurements in nematic, smectic A, smectic B, and smectic C mesophases have been carried out by mass transport techniques, detected by radio-tracers or optically, by NMR spin-echo techniques, and by quasi-elastic neutron scattering. The diffusion is anisotropic in most of the cases. In nematics self-diffusion parallel to the molecular director (D₆) is somewhat faster than perpendicular (D_⊥). Both diffusion coefficients show about the same activation energy. Impurity diffusion (small molecules dissolved in mesophases) demonstrates the same behaviour with less anisotropy. In smectics A and C the diffusion coefficients D₆ and D_⊥ can be nearly equal. The anisotropy is now shown in their respective activation energies with E₆>E_⊥. This effect is more pronounced in impurity than in self-diffusion. In addition impurity diffusion shows a strong anisotropy of the diffusion coefficients (D_⊥?D₆). In smectics B the activation energies E₆ and E_⊥ of self-diffusion seem again to be equal and the diffusion coefficients show a small anisotropy (D_⊥≥D₆).     

Stress-induced optical dichroism of V−-centers in MgO

The stress-induced optical dichroism and optical absorption spectra of the V^?-centers in electron irradiated MgO are reported. The dichroism spectrum can be largely attributed to a paraelastic alignment of inherently-dichroic V^?-centers. A curve-fit analysis of the lower-energy portions of the dichroism and absorption spectra yields the ratio of the transition dipole strengths, $\text{D}{}_{\mathrm{\parallel }}\text{D}{}_{\mathrm{\perp }}\text{= 1.55 ± 0.2}$, and the energy splitting, E_∥ ? E_⊥ = 0.22 ± 0.07 eV, for light polarized parallel (∥) and perpendicular (⊥) to the defect symmetry axis. The spectra also have considerable intensity in their high-energy tails, and it is speculated that a portion of this intensity is due to the V-center. The implications of the results with regard to the electronic structure of the center are discussed.     

Diffusion and NMR spin lattice relaxation of 1H in α′ TaHx and NbHx

The concentration and temperature dependence of the self diffusion coefficient, D, of H in Group V transition metals Nb and Ta has been measured for the α^' phase. The nuclear magnetic resonance spin lattice relaxation time, T₁, was measured in Ta only. A pulsed field gradient, NMR spin echo technique was utilized to measure D. In both systems, the activation energy increases with hydrogen concentration while the pre-exponential factor is not strongly concentration dependent. The diffusion results are compared with published values of the macroscopic diffusion coefficient, $\text{D}{}^1$, obtained from Gorsky effect measurements. Values of the thermodynamic factor [$\text{(}\text{ρ}\text{kT}\text{)(}\text{?μ}\text{(?ρ)}$] are found for selected ρ and T, where μ is the chemical potential and ρ is the density of hydrogen atoms. These values agree with known determinations of the same factor obtained from the Gorsky effect relaxation strengths, but the agreement with results from solubility measurements is less satisfactory. NMR relaxation is partitioned into conduction electron (T^?1_1e) and dipolar (T^?1_1d) relaxation rates. The observed x dependence of ($\text{D}\text{T}{}_{\mathrm{1d}}$) is inconsistent with random occupancy of tetrahedral sites, and it is suggested that a repulsive interaction exists between H atoms on nearest neighbor sites.     

Ambipolar drift and breakdown of oscillistor effect in strong magnetic fields

The drift mechanism of helical instability suppression (oscillistor) in electron-hole plasma Ge was, for the first time, investigated. It was found that in strong magnetic fields ($\text{γ}{}_{\mathrm{i=e,h}}\text{= μ}{}_{\mathrm{i}}\text{H/c}\text{a}\text{?}\text{1}$) due to anisotropy of mobility (μ_i ≠ μ_i⊥) the ambipolar drift of helical disturbances of density along the electric field occurs even in quasineutral plasma (n = p), provided μ_e ≠ μ_h. To corroborate the drift mechanism of oscillistor effect breakdown in strong fields the experiments were carried out under the conditions of uniaxial crystal deformation oriented towards 〈111〉 (H, E  〈111〉) resulting in the intervalley redistribution of electrons and additional anisotropy of mobility. Variation in the ambipolar drift velocity connected with the deformation influences essentially the conditions of the helical instability breakdown in strong fields.     

Evidence for assignment of 14.0 MeV state in 11B from 10B(n,n)10B

The differential cross section and polarization for neutrons scattered from ¹⁰B have been measured at E_n = 2.63 MeV (E_x = 13.85 MeV). The results of this experiment and other available neutron scattering data in the range 1 < E_n < 4 MeV are interpreted through a single-level R-matrix calculation over the region 12 < E_x < 15 MeV. Based on this analysis the most probable J^π assignment for the 14.0 MeV level in ¹¹B is $\text{11}\text{2}{}^{\mathrm{+}}$. The anomaly near E_x = 13.1 MeV can only be explained in terms of two overlapping levels having assignments of ($\text{5}\text{2}$, $\text{7}\text{2}$)^? and ($\text{3}\text{2}$, $\text{5}\text{2}$, $\text{7}\text{2}$)⁺.     

Optical spectroscopy in semiconductors in high magnetic fields using polarization modulation

Differential magneto-reflection spectra in the 1.8 to 5 eV energy range are presented for GaP, Ge, GaAs, InSb, and Si. These spectra were obtained using polarization-modulated light from [111] faces of samples in the Faraday configuration. In medium strength magnetic fields, the results are similar to those obtained using other techniques, such as electric field modulation and wavelength derivative spectroscopy in the same energy range. In higher magnetic fields (B of 50 kG or larger) more detailed structure is resolved. Oscillations attributed to Landau level transitions have been seen at critical points in the visible in InSb and in GaSb in fields up to 100 kG. At the E₁ edge an unexpected anomaly has been observed in InSb. Within experimental error, the Landau levels are equally spaced for n < 5 and n > 5 but at n = 5 there is an abrupt change in the cyclotron energy. Here n is the usual magnetic quantum number. The transverse masses are measured as $\text{m}\text{μ}{}_1\text{= 18.9 ± 0.9 (n < 5)}$, and $\text{m}\text{μ}{}_2\text{= 16.0 ± 0.9 (n > 5)}$. Possible causes of this effect are discussed. In GaSb at the corresponding threshold. Landau level observations give a mass value of $\text{m}\text{μt}\text{= 21.4 ± 1.5}$.     

Theoretical study of the electric field effect on ion-molecule reactions in diluted gases and solutions

In diluted gases the rate coefficients of ion-molecule reactions in an electric field depend on the characteristic ratio $\text{E}{}_{\mathrm{<mtext>P</mtext>}}\text{k}{}_{\mathrm{<mtext>B</mtext>}}\text{Θ}$ where E_P represents the energetic threshold for the reaction and k_BΘ is the mean kinetic energy summarizing both electric field effects and collision processes within a two-temperature model. Using the Lorentz-gas concept the model can be precised from a microscopic point of view by solving a kinetic equation for the ionic component.In diluted solutions like in gases the field effect on ion-molecule reactions depends on the energy gain of the ions by the electric field. However, the field effect is considerably reduced here because of the small magnitude of the mean free path in liquids. In addition the rate constant modification by the field depends on the ratio of the ion diffusion coefficient to the sum of the diffusion coefficients of both the reactants.     

The effect of the parton transverse motion in large-p⊥ reaction

The parton transverse motion within the incident hadrons cannot be neglected when calculating large-p_⊥ reaction cross sections in the framework of hard scattering models. We give a general discussion of this effect for a large class of models. The results depend strongly on the parametrization of the hard scattering cross section at small momentum transfer in the parton-parton center of mass. With reasonable assumptions, we find that the parton transverse motion enhances the hard scattering model predictions for Edσ/dp by a factor of two and reduces

$\text{E}\text{d}\text{N}\text{d}\text{p}\text{=}\text{∫}\text{d}\text{p′}\text{E′}\text{EE′}\text{d}{}^{\mathrm{(2)}}\text{σ}\text{d}\text{p}\text{d}\text{p′}\text{E′}\text{E′}\text{d}\text{σ}\text{d}\text{p′}$

by a comparable factor, in the range p_⊥ ? 2?3 GeV/c. We study the correlations between the large-p_⊥ trigger and the background low-p_⊥ secondaries and give an estimate of the encountered azimuthal asymmetry around the beam momentum with a simple model.     

Peak in the magnetic-field dependence of diffusion-induced thermopower for n-Bi-Sb semiconducting alloys

A peak is detected on the dependence of the diffusion-induced thermopower on transverse magnetic field in degenerate semiconducting alloys n-Bi_1?x Sb_x (0.07≤x≤0.15) doped with tellurium donor impurity. The temperature gradient is directed along the bisector axis C ₁ of the monocrystalline sample and the magnetic field is along the triad axis C ₃. The electron spectrum of the Bi-Sb alloys under investigation consists of three equivalent ellipsoids with distinctly different effective masses along the axes of the ellipsoid (m _∥/m _⊥). A simple kinetic theory shows that the presence of the peak on the diffusion thermopower is a manifestation of this strong anisotropy in the electron spectrum and of the additive contribution of all three ellipsoids to electron transport. The nonmonotonic dependence of thermopower on the transverse magnetic field makes it possible to determine the electron relaxation time, while the temperature dependence of this relaxation time can be used to separate the relaxation time for electrons scattered from ionized impurities and from acoustic phonons.     

A magneto-transport anomaly in semiconductors at low carrier-densities,a wigner condensation?

Transport properties of the narrow-gap semiconductors PbTe, PbSnTe, and HgCdTe were studied in the extreme magnetic quantum limit. With low carrier densities an anomalous behaviour was found for the longitudinal (?_□) and the transverse (?_⊥) magnetoresistance, for the Hall effect, and in the IU-characteristic. ?_□ increased near a critical magnetic field by almost two orders of magnitude. A pronounced kink in the ?_⊥ ∝ B^α dependence took place at the critical field. This critical magnetic field of the anomaly shows the features predicted for a Wigner condensation, i.e. the dependence on carrier density in all the three semiconductors. The new state at high magnetic fields is obviously a free carrier effect since it can be annihilated by heating the electrons in an electric field.     

Toroidal hydromagnetics

The complete set of hydromagnetic equations is transformed into Poisson equations and equations of motion for flux densities and their associated variables. The toroidal components of the vector potential A and of the momentum density $\text{a}\text{≠}\text{πv}$ are represented by the po loidal flux densities Ψ and Ψ, respectively, for which the equations of motion are derived. The poloidal components A_⊥ and a_⊥ are represen ed by the potentials atΦ, U and φ, u, for which we obtain Poisson equations in the poloidal plane. Thus one has to solve two Dirichlet and two von Neumann problems at every time step. The source terms of the four Poisson equations define the remaining four variables, namely, $\text{Λ = ▽ ·}\text{A}$,$\text{Ω=(▽×}\text{A}\text{)ζ/R}$, $\text{λ=?·}\text{a}$, and $\text{ω=(?×}\text{a}\text{)ζ/R}$, for which equations of motion are also derived. In the limit of small toroidicity ? we look fo r a selfconsistent scaling of the equations with v_⊥～ε. But the curl of v_⊥×B in Faraday's law creates a toroidal plasma component of B which is one order of magnitude larger than in the case of a low β equilibrium; therefore, the motion becomes fully three-dimensional. Finally, an artificial pressure law is needed to balance the lowest order of the Lorentz force. The conclusion is then that the scaling laws previously used are not applicable for toroidal geometry, and that the effort to obtain numerical solutions is not dramatically higher than without using any scaling law.     

2D laser collimation of a cold Cs beam induced by a transverse <Emphasis Type="Italic">B</Emphasis> field

We describe transverse collimation of a continuous cold cesium beam (longitudinal temperature 75 μK) induced by a two-dimensional, blue-detuned near-resonant optical lattice. The mechanism described for a lin-‖-lin configuration is made possible by the application of a transverse magnetic field B_⊥. The phenomenon described differs from gray molasses, for which any small magnetic field degrades cooling, as well as from magnetically induced laser cooling in red-detuned optical molasses, where there are no dark states. The lowest transverse temperature is experimentally found to vary as B _⊥ ² . The collimated flux density shows a dip as a function of B_⊥, the width of which is proportional to the cube root of the laser intensity, general features predicted by our semiclassical model. This technique provides a sensitive tool for canceling transverse magnetic fields in situ at the milligauss level.