Amorphous germanium III. Optical properties

The optical properties of thick sputtered films (～30μ) of amorphous Ge, grown with different substrate temperatures (0ˇ-T _sˇ-350°C), were obtained between 0·05 and 4·5 eV by a combination of reflectance, transmittance and ellipsometric measurements. The refractive index at 0·15 eV decreases monotonically with increasing T _s, or equivalently, with increasing density, and is 4·13±0·05 eV in the highest density films. The absorption edge is approximately exponential (10²?α?10⁴ cm^?1) but shifts monotonically to higher energy and increases in slope with increasing T _s. Similarly, the peak in ε₂ grows by about 10% and shifts by about 0·15 eV to higher energies, reaching a maximum of about 23 at 2·90±0·05 eV in the high density films. The peak in the transition strength ω²ε₂ occurs at 4·2±0·2 eV in all films, but increases in magnitude with increasing T _s. The sum rules for n _eff(ω) and ε_0,eff(ω) are evaluated for ▄ω?5 eV and vary monotonically with T _s. These trends are neither compatible with Galeener's void resonance theory nor with changes in the oxygen content of the films, determined by the examination of absorption peaks at 0·053 eV and 0·09 eV. An explanation, suggested here and expanded in I, is based on the observed changes in the structure of the network and voids.     

Thermally assisted hopping transport in disordered systems

The response to an external field of localized electrons coupled to phonons is investigated. The low frequency (ω<T) linear response function is shown to obey a kinetic equation. The transition probabilities (including multiphonon contributions) can be expressed in terms of the dynamical correlation functions(k, ?) of the phonons. The low temperature d.c. conductivity in three dimensions obeys a law σ(0)=σ₀ · exp(? (T ₀/T)^1/4). By a combined variational and “nearest neighbor” approximation upper limits for the exponential as well as the pre-exponential factor are obtained. In two dimensions the 1/4 in the exponent has to be replaced by 1/3. The one-dimensional case requires separate considerations which do not simply lead to an exponent 1/2. An expression for the thermopower in the hopping regime is derived and evaluated.     

Development of a Lyman-α laser system for spectroscopy and laser cooling of antihydrogen

Hydrogen Lyman-α radiation (121.56 nm) is important because it allows for the excitation and detection of ground-state hydrogen atoms by a one-photon process. The trapping of antihydrogen, recently reported by the ALPHA collaboration at CERN, has revived interest in Lyman-α lasers. In order to perform high precision tests of matter-antimatter symmetry violations or gravity-antimatter interactions with antihydrogen, laser cooling using the 1s ? 2p single photon transition is essential. Recent theoretical simulations predict that even with a pulsed Lyman-α source, laser cooling of antihydrogen would be possible. Here we describe the implementation of a high power vacuum-ultraviolet (VUV) laser at the Lyman-α transition of hydrogen. The VUV light was generated using a two-photon-resonant four-wave mixing process in a phase-matched mixture of krypton and argon. Two wavelengths (ω _R → 202.31 and ω _T → 602.56 nm) were mixed in a sum-difference scheme (ω _VUV = 2ω _R ? ω _T ) with a two-photon resonance at (4s ²4p ⁵5p[1/2]₀ ← 4s ²4p ⁶(1S ₀)) transition in Kr. With an Ar/Kr mixture of 3.9:1 we obtained 10 ns pulses of 0.1 μJ of energy at a repetition rate of 10 Hz.     

Transport cross sections for charged particle scattering in (dense-) cesium plasma; electrical conductivity

Transport cross sections for the electron-ion and electron-electron scattering in (dense) cesium plasmas is determined with the partial wave method. The scattering phase shifts δ_l(k) are calculated numerically by means of the usual Numerov method and the advantageous amplitude — phase method for energies E = 10^-4··· 5 ryd and for Debye screening lengths R_D = (10···10³)a₀. Besides the usual Debye potential, also a Thomas-Fermi potential is applied for the cesium electron-ion interaction. The resulting transport cross sections are compared with the Born and quasi-classical approximations. Furthermore, the electrical conductivity of fully ionized cesium plasmas is determined and compared with respective Spitzer results.     

On the dynamic conductivity for an electron-impurity system

The correlation function formula for the dynamic conductivity of a system of non-interacting electrons in the field of impurities is analyzed in terms of proper connected diagrams. By selecting those diagrams appropriate in the region of weak coupling and low impurity concentration, a set of coupled equations for the energy broadening γ (ω, ε, n_s) and the energy shift Δ(ω, ε, n_s) is derived, where both γ and Δ depend on the frequency ω of a probing field, the energy ε of the electron, and the concentration, n_g, of impurities. With the assumption of a finite range potential, these equations are solved. It is found that γ (ω, n_s) is smaller than that extrapolated value which the conventional expression γ₀ for the low-concentration collision frequency would predict, in the entire region studied, that the difference γ₀-γ becomes appreciable when the ratio of the average time between scatterings, τ_c, to the average duration of a scattering, τ_d, is 100 or less, that γ (ω, n_s) decreases monotonically from its static value γ (0, n_s), and becomes vanishingly small in the region ω≈1/τ_d, and that in the static limit (ω=0), γ=γ₀[1?(2/π) (γ₀τ_d)+…], that the energy shift Δ is positive, and increases from 0 and reach a peak of magnitude γ₀ as ω is raised from 0. By using the γ and Δ obtained, the dynamic conductivity σ(ω, n_s) for degenerated electrons is calculated. The deviation, σ-σ₀, from the conventional expression σ₀=(?i) (n_ee²/M) [ω-iΓ₀]^?1, (n_e]=number density of electrons), for 0°K, is appreciable when the ratio τ_c/τ_d is 100 or less. The field-term correction, which arises from the modification of the scattering due to the probing field, is found to be negligible in the entire region studied.     

Perturbation of the Laplacian supported by null sets,with applications to polymer measures and quantum fields

We discuss hamiltonians in L²(R^d, dx) of the form H = ?Δ + V, with V a potential supported by a zero measure set C. In particular if C is a path of a brownian motion b such that V(x) = ∫₀¹λ(x, ω)δ(x-b(s, ω)) ds, we show that H exists as a nontrivial, self-adjoint, lower bounded perturbation of ?Δ when d ?5. We must choose λ to be an infinitesimal, negative function for d = 4,5, but for d ? 3 any bounded real-valued function λ will do. The connection with Edward's model of polymers as well as with quantum fields of the ?_d⁴-type is also discussed. The proofs use methods of nonstandard analysis.     

Dynamic stabilization of the helicalm=1 instability in a linear screw pinch

Dynamic stabilization of the helicalm=1 instability was studied in the linear high-β screw pinch ISAR III (T _i ≈50 to 500eV;n _e ≈5·10¹⁶ cm^?3; β≧0.5). The experimentally determined growth rates ω _i (0.5 to 3·10⁶ s^?1) and wavelengths (100 to 200 cm) of these modes are about the same as in a toroidal screw pinch and both agree well with theory. Two methods of dynamic stabilization were investigated. In both cases the stabilizing effects were better than expected from existing theory. In the first method an axially uniform oscillating field \(\tilde B_{zo} \) ·sin (ω _s t) was superposed on the quasi-steadyB _zo field (ω _s >ω _i ). Them=1 mode is stabilized and a stabilization condition \(\tilde B_{zo} /B_{zo} \gtrsim 2\omega _i /\omega _s \) holds. This stabilizing effect is very likely caused by inertial forces produced by enforcedm=0,k=0 oscillations of the plasma column. When working in resonance with the natural plasma oscillations, it is easier to satisfy the above condition. In the second method oscillating currents \(\tilde I_{zo} \) · sin (ω _s t) were added to the axial plasma currentI _zo to study the stabilization by dynamic shear (ω _s >ω _i ). Magnetic probe measurements showed that the \(\tilde I_z \) flows in the dilute plasma outside the dense plasma column. The measured skin depths and resistivities are larger than those expected from classical theory. Nevertheless, a reduction of the growth of them=1 mode occurred which was larger the more closely \(\tilde I_z \) flowed alongside the plasma column, giving a stabilization condition \(\tilde I_{zo} /I_{zo} > \omega _s /(5\omega _i )\) .     

Mössbauer studies of europium and ytterbium hydrides

Mössbauer absorption spectra were obtained for the 21·6 ke V transition of ¹⁵¹Eu in EuH₂ at various temperatures and for the 84·3 keV transition of ¹⁷⁰Yb in YbH₂ at 4·1°K. The isomer shift of EuH₂ relative to Eu³⁺: Sm₂O₃ is ? 12·1 ± 0·3 mm. sec^?1, and the magnetic hyperfine field equals ? 305 ± 5 kOe at saturation. The Curie temperature is found to be 16·2 ± 0·05°K, and the critical parameters of the transition are D = 1·17 ± 0·02 and β = 0·35 ± 0·01. The magnetic field is perpendicular to the principal axis of the electric field gradient and the values of the quadrupole hyperfine interaction e²qQ₀(3 cos² θ ? 1)/8 is ? 28 ± 4 Mc . sec^?1. A large increase of the resonance area (21%) occurs at the transitio to the ferromagnetic state. The isomer shift of YbH₂ relative to Yb: TmAl₂ is ?0·11 ± 0·01 mm . sec^?1. The value of the quadrupole coupling constant e²qQ_c/4is ? 91·5 ± 2 Mc . sec^?1 and the asymmetry parameter of the electric field gradient equals 0·89 ± 0·05. The data for EuH₂ and YbH₂ is shown to be consistent with the hydridic model for the rare earth hydrides.     

Study of the OZI selection rule in hadronic processes

In the experiments with LEPTON-F and SPHINX spectrometers the pion-induced charged exchange reactions π- + p → ? + n and π- + p → ω + n at Pπ-=32.5 GeV, as well as proton-induced diffractive reactions p + N → [p?] + N and p + N → [pω] + N at E _p =70 GeV were studied. The comparison of the cross-sections for ? and ω-production in these reactions is used for testing the OZI selection rule in hadronic processes. It has been demonstrated that in pion reactions the ratio of the yields of ? and ω-mesons R(?/ω) = (3 ± 1) · 10^?3 is in a good agreement with naive quark model prediction based on the mixing in vector meson nonet and on the OZI rule (R(?/ω)ozi = tg ²Δθ _V ? 4 · 10^?3). At the same time in proton reactions the effective ratio of ? and ω yields is ～ (4 ÷ 7) · 10^-2, i.e. a strong violation of the OZI rule is observed in proton-nucleon interactions. This violation can be in favor of possible existence of some exotic ss? component in the quark structure of protons.     

Influence of the surface on the quantum P.E.M. effect in InP

The photoelectromagnetic effect of InP is studied in quantizing magnetic fields at 4·2 K in an energy range 1·4–1·5 eV for linearly polarized light. Depending on the sample surface condition two types of spectral oscillations may appear, those associated with interband transitions between Landau levels or the LO phonon type usually seen in photoconductivity. An analysis of the spectral oscillations gives: E₀ = 1·423±0·001 eV; Δ₀ = 0·102±0·006 eV; hω_L = 0·036 eV.     

Self-diffusion in a series of plastic organic solids studied by NMR

Proton nuclear magnetic resonance relaxation times and linewidth measurements have been made on five polycrystalline organic compounds, triethylenediamine, 3-azabicyclononane, norbornane, norbornylene and norbornadiene. Measurements for each sample were made throughout the plastic crystal phase. The results are analysed in terms of molecular motion. Correlation times τ and activation enthalpies for translational self-diffusion of molecules are evaluated: triethylenediamine τ=7·6×10^?19 exp (96·4/RT)s, 3-azabicyclononane τ=1·7×10^?16 exp (83·6/RT)s, norbornane for 131K<T<306 K, τ=4·6×10^?15 exp (54·5/RT)s for 306K<T<360K, τ=1·1×10^?16 exp (64·8/RT)s, norbornylene, τ=4·×10^?15 exp (48·6/RT)s and norbornadiene τ=6·8×10^?15 exp (39·9/RT)s, where R is the gas constant in units of kJ K^?1mol^?1. The results and mechanism of diffusion are discussed in relation to the thermodynamic properties of the materials.     

Diagnostics of the solar corona structure by the refraction effects on radio emission

The solar disc radio brightness distribution observed at RATAN-600 can be interpreted as the angular directivity of the disk center emission at viewing anglesΘ=arcsin(R/R₀) over an angular range of R<0.9R ₀ at several wavelengths in the 2.0–32 cm region. These spectra can be treated as an emission enhancement due to refraction effects in free-free corona emission. The model simulations show good agreement with the observations and lead to estimation of the electron density N_e=1·10 ⁹ cm^?3 and emission measureEM=6·10 ²⁶ cm^?5 for the quiet Sun.     

Effect of series resistance and interface states on the I-V, C-V and G/ω-V characteristics in Au/Bi-doped polyvinyl alcohol (PVA)/n-Si Schottky barrier diodes at room temperature

The forward and reverse bias current-voltage (I-V), capacitance-voltage (C-V) and conductance-voltage (G/ω-V) characteristics of the Au/PVA (Bi-doped)/n-Si Schottky barrier diodes (SBDs) have been investigated at room temperature by taking the interface states (N_ss) and series resistance (R_s) effects into account. The voltage dependent profiles of resistance (R_i) were obtained from both the I-V and C/G-V measurements by using Ohm’s Law and Nicollian methods. The obtained values of R_i with agreement each other especially at sufficiently high bias voltages which correspond the value of R_s of the diode. Therefore, the energy density distribution profile of N_ss was obtained from the forward bias I-V data taking the bias dependence of the effective barrier height (BH) Φ_e and R_s into account. The high value of ideality factor (n) was attributed to high density of N_ss and interfacial polymer layer at metal/semiconductor (M/S) interface. In order to examine the frequency dependence of some of the electrical parameters such as doping donor concentration (N_D), Φ_e, R_s and N_ss values, C-V and G/ω-V measurements of the diode were performed at room temperature in the frequency range of 50 kHz-5 MHz. Experimental results confirmed that the N_ss, R_s and interfacial layer are important parameters that influence electrical characteristics of SBD.     

Microwave heating of electrons of a dense plasma column at frequencies higher than electron cyclotron frequency

In the overdense collisionless plasma column inserted through the narrow sides of a rectangular waveguide, the excited electron cyclotron harmonic waves (CHWs) are studied by means of two movable probes and a phase interferometer in the range of parameters of 2 >ω/ω _ce >1; 0·5 < (ω _pe /ω)² < 15. Two kinds of CH waves have been found in the dipole mode:

1. Stable backward CH waves with the phase velocity in the direction from the axis to the periphery.
2. Unstable backward CH waves with the phase velocity in the opposite direction.

From the correlation measurements and amplitude distribution of the CH waves at the applied frequency and its second harmonic frequency it has been found that in the range of 2 >ω/ω _ce > >1·5 efficient nonlinear resonant interaction of CH waves takes place. The position of the loci of resonant interaction inside the plasma column has been found both experimentally and by a simple new graphical procedure for the resonant conditions of the formω ₂=2ω ₁; k₂=2¦k₁¦. In absence of this condition, no effective generation of the second harmonic frequency has been found. The resonant interaction of CHWs atω/ω _ce =1·85 is the cause of self-trapping of CH waves between the zones of resonant interaction in radial direction and of the anomalous heating rate of electrons.     

A rotationally-resolved Rydberg transition of I2

Rotationally-resolved bands leading to a Rydberg state R 0 _u ⁺ of molecular I₂ are observed in a two-stage, three-photon transition from the ground state. The R 0 _u ⁺ state interacts homogeneously with high vibrational levels, ν_F ≈ 200–250, of an ionic state F 0 _u ⁺, the perturbation being directed by the vibrational overlap integrals towards even-numbered vibrational levels of R. Spectral constants of R 0 _u ⁺ are (in cm^-1): T _e = 61665·15, ω_e = 209.29, ω_e x _e = 0·859, B _e = 0·03842 and α_e = 1·6 × 10^-4. The electronic matrix element for the R, F interaction (excluding one deviant result) is |W _e| = 107 ± 1 cm^-1; thus W _e/ω_e ≈ 0·5, corresponding to ‘intermediate’ coupling. Energy considerations indicate that R should be assigned to the 0 _u ⁺ state of either the configuration (2430 Π_1/2g )6pσ _u , or of (2421 ⁴Σ _u ^-)6sσ _g . This state is the first extra-valence state of I₂ to be rotationally analysed.     

Super-exponential inflation from a dynamical foliation of a 5D vacuum state

We introduce super-exponential inflation (ω<−1) from a 5D Riemann-flat canonical metric on which we make a dynamical foliation. The resulting metric describes a super accelerated expansion for the early universe well known as super-exponential inflation that, for very large times, tends to an asymptotic de Sitter (vacuum dominated) expansion. The scalar field fluctuations are analyzed. The important result here obtained is that the spectral index for energy density fluctuations is not scale invariant, and for cosmological scales becomes ns(k<k_?)?1. However, for astrophysical scales this spectrum changes to negative values ns(k>k_?)<0.     

L ∞ estimates for the space-homogeneous Boltzmann equation

This paper studies the boundedness of solutionsf of the initial-value problem for the space-homogeneous Boltzmann equation for inverse kth power forces, whenk>5, and under angular cutoff. The main result is that if the initial value isf ₀ ? 0 with (1 + ¦υ¦²)φ₀ εL ¹ and (1 + ¦υ¦)^s f ₀ε L^∞ for somes > 2, then (1 + ¦υ¦^s'f _tεL ^∞ fort>0 and ess_υ,t sup(1 + ¦υ¦)^s'f(υ, t,) < ∞ for anys′ ? s whens ? 5, and anys′ ? s ifs > 5.     

On the configuration of systems of interacting particles with minimum potential energy per particle

Previous work on infinite one-dimensional systems of interacting particles is continued. In the case of two-body potentials φ(x) = φ(-x), whose Fourier transform ?f(k) eicsts, it is shown that a necessary condition that the equidistant configuration has for a certain range of densities minimum potential energy per particle among all configurations of the same density, is that ?f(k)?0 for all k. An analogous theorem is proved for systems of particles in two and three dimensions.Furthermore some properties are discussed of one-dimensional systems for which ?f(k)?0 for all k and moreover ?f(k) = 0 for |k|?k₀.     

Messung derL-Auger-, Fluoreszenz- und Coster-Kronig-Ausbeuten von Gold

An apparatus is described, with which, for the first time, the spectra of Augere-lectrons and of X-rays, produced by the impact of electrons, were measured simultaneously. The electron spectrometer was a magnetic 180°-spectrometer with a half-width of 0·5%. The X-ray spectrometer was a NaJ-crystal with a photomultiplier. The electron- and the X-rays were produced in metallic foils of a thickness of 50 Å by the impact of 55-keV-electrons. The knownK-fluorescence-yields of copper and selenium were used to determine the various yields for theL-shells of gold. TheL-fluorescence-yields areω _L1 =0·08±0·01;ω _L2 =0·26±0·03;ω _L3 =0·24±0·02.