Showing papers on "Free electron model published in 1971"

Optical Absorption and Dispersion in Solids

Abstract: 1. Macroscopic Theory.- 1.1 Electromagnetic field in a solid.- 1.2 Dielectric constant and optical conductivity.- 1.3 Crystal symmetry.- 1.4 Propagation of waves.- 1.5 Kramers-Kronig relations.- 1.6 The sum rule.- 1.7 Dispersion theory of classical oscillators.- 2. Crystal Lattice Absorption.- 2.1 Vibrational modes of a crystal lattice.- 2.2 Photon-phonon interaction.- 2.3 Microscopic theory of infra-red dispersion.- 2.4 Two-phonon absorption.- 3. Interband Transitions.- 3.1 Electron energy bands.- 3.2 Direct transitions.- 3.3 Critical points.- 3.4 Absorption band edges.- 3.5 Indirect transitions.- 3.6 Infra-red absorption in superconductors.- 4. Free Carrier Absorption.- 4.1 Classical theory.- 4.2 Intraband transitions.- 4.3 Electron transport.- 4.4 Surface admittance.- 4.5 Infra-red absorption in metals.- 4.6 Free carrier absorption in semiconductors.- 5. Plasma Effects.- 5.1 Free electron model.- 5.2 Volume plasmons.- 5.3 Surface plasmons.- 6. Exciton Effects.- 6.1 Electron-hole interaction.- 6.2 Optical absorption.- 6.3 Inert-atom solids and alkali halides.- 6.4 Semiconductors.- 6.5 Spatial dispersion.- 7. Non-Linear Optics.- 7.1 Classification of non-linear effects.- 7.2 Non-linear susceptibilities.- 7.3 Second harmonic generation.- 7.4 Parametric amplification and oscillation.- 7.5 Third order effects.- References.

Surface Plasmon in a Semi-Infinite Free-Electron Gas

Abstract: When electron-lifetime effects, electron-hole pair excitations, or both are included in the description of an electron gas, the frequency associated with the surface plasmon is a complex quantity, the imaginary part providing a measure of the damping of the plasmon. The surface-plasmon dispersion relation then involves the specification of this complex frequency as a function of the wave vector parallel to the surface. A general theory is developed for such a surface-plasmon dispersion relation in a semi-infinite free-electron gas bounded by a surface that scatters the electrons specularly. The properties of the electron gas enter through the nonlocal transverse and longitudinal dielectric functions ${\ensuremath{\epsilon}}_{t}(q,\ensuremath{\omega})$ and ${\ensuremath{\epsilon}}_{l}(q,\ensuremath{\omega})$, both of which include a finite electron lifetime here. The results obtained using local and hydrodynamic approximations for the dielectric functions are presented briefly, and the self-consistent-field approximation is discussed in detail. The calculations are done both with and without retardation.

X-Ray Parametric Conversion

Abstract: The observation of x-ray parametric conversion is reported. Results are in accord with the calculated nonlinear x-ray susceptibility. The appropriate nonlinear mechanisms are described in terms of classical free electrons.

Location of the Zn 3d states in ZnO

Abstract: UV photoemission measurements on hexagonal ZnO cleaved in vacuum, determining Zn 3d states location

High field magnetoresistance at low temperatures

Abstract: To explain recent experiments on n-InSb we calculate the transverse and longitudinal electrical conductivity in strong magnetic fields. We consider a free electron-point impurity system in the generalized Born approximation, and in the self-consistentt-matrix approximation. The position, shape and amplitude of the Shubnikovde Haas oscillations and the quantum limit behaviour are in good agreement with experiment.

Regularity of the density of states in Anderson's localized electron model

Abstract: It is proved that the density of states is analytic in the region in which Anderson (see abstr. A37378 of 1970) has shown that the transition from localized to nonlocalized electron states should occur. There is some discussion of the implications and generalization of this result.

Electronic structure of noble or transition metal based alloys

Abstract: We study the electronic structure of dilute alloys of noble or transition metals, in a modified Slater-Koster model. The pure metal band structure is described by an interpolation scheme of hybridized tight binding and nearly free electron orbitals. The matrix elements of impurity potential between `s' basis functions are treated by a perturbation method. Within these approximations, we obtain exact formulae for the Green functions of the alloy, and for the displaced charge. We discuss specially the displaced charge, the transition matrix t, and the residual resistivity in the case of a potential localized on its own cell. We present the results of a numerical study of CuNi alloy.

Influence of diffusion and nonequilibrium populations on noble-gas plasmas in electric arcs

Abstract: Measurements and calculations of temperatures, densities, and field-strength-current characteristics of cascade arcs burning in noble gases under atmospheric pressure are reported. The evaluation of measured arc data assuming Saha equilibrium [complete local thermal equilibrium (LTE)] is not in agreement with the detailed solution of the balance equations. The temperatures of electrons and heavy particles and the density of electrons and neutrals have to be determined from the set of rate equations, from the equation of state, connection with the electron energy balance and the equation of state, the energy balance of the electron gas, and of the total plasma. Solutions of these equations are compared with results following from measured line intensities only solving the rate equations in connection with the electron energy balance and the equation of state. For helium, both methods give results which agree within a few percent. The deviations from Saha equilibrium are caused by diffusion and the overpopulation of ground state atoms. The excited atoms, however, are nearly in equilibrium with free electrons in the range of electron densities reached in our experiment (partial LTE). Measurements of E-I characteristics agree with calculated data, if diffusion is taken into account. A simple criterion for the limit between diffusion-dominated plasma and a plasma in thermal equilibrium is derived.

Effect of Surface Electric Fields on Radiative Recombination in CdS

Abstract: Photoluminescence (edge emission) in a variety of CdS single crystals has been studied under the influence of the surface field generated near the Au–CdS interface of an Au–CdS Schottky‐barrier diode. Experimentally, above bandgap radiation is incident upon a semitransparent Au film evaporated on an air‐cleaved CdS surface. Free electrons and holes are generated within the region of the high barrier field which extends on the order of 0.5 μ into the crystal bulk. Variations of diode bias as small as 2.5 V were found to be sufficient to alter the luminescence efficiency by nearly two orders of magnitude. A model is presented (emphasizing the rapid removal of photoinjected free carriers from the barrier) which qualitatively accounts for the major features of the observed effects.

Calculation of the transport properties of liquid noble metals

Abstract: Numerical calculations based on the Ziman nearly free electron theory of the resistivity and thermopower of the noble metals are presented. The phase shifts of muffin-tin potentials are used to construct the t-matrix of a single scattering centre. Good agreement with experiment is achieved.

The pseudopotential theory and the impurity problem in transition and noble metals

Abstract: The electronic structure of the transitional alloys in the hybridized tight binding nearly free electron representation is studied. It is shown that the corresponding wave functions, scattering rates and densities of states can be obtained exactly from the extension of the pseudopotential theory for transition metals.

Effect of p 32 Intraband Polarization on the Mobility of Zero-Gap Semiconductors

Abstract: It is shown that in doped zero-gap semiconductors like α-Sn, the intraband part of the static screening function is considerably decreased from that of free electrons at large momentum transfer by the p-like character of the conduction-band wave function. However, it is also shown that this large screening loss produces a relatively small change in the ionized-impurity-limited mobility.

The decay of optically thick helium plasmas, taking into account ionizing collisions between metastable atoms or molecules

Abstract: The effective recombination rate of a helium afterglow plasma, which is optically thick towards the resonance lines, is calculated from the coupled rate equations for the number densities of free electrons and of metastable atoms or molecules. The model employed is a neutral plasma consisting of one kind of ion and one kind of metastable. The ions are lost by electron-ion recombination only, with subsequent formation of metastables, which are then deactivated in collisions with free electrons or with other metastables: in the latter case one electron is regained to the free state. When the rate constants for these various processes are time independent, it is found that after a certain transition time a transient equilibrium between the number densities of electrons and metastables is attained. In a dense afterglow plasma, where the recombination coefficient may be large, the transient equilibrium density of metastables may become significantly higher than the quasi-equilibrium value obtained by equating the time derivative of the metastable density to zero, and the effective recombination coefficient may be reduced by much more than a factor of two.

Spin waves in an itinerant electron model of an antiferromagnet

Abstract: The spin wave velocity in a one band itinerant electron model of an antiferromagnet is calculated using the equations of motion for the generalized transverse susceptibility. The formula is written down approximately, in terms of the ground state antiferromagnetic energy bands and is then evaluated in limits corresponding to wide and narrow antiferromagnetic energy gaps. A special case of the former yields an expression corresponding to the energy of a spin wave in a Heisenberg antiferromagnet. In the latter case it is found that the spin wave velocity tends to zero as the energy gap tends to zero, which is a new result. The problem of whether the spin wave velocity is real when the Fermi level is not in the gap is discussed.

Measurements of electron temperature in the solar chromosphere and corona.

Abstract: The electron temperatures at which the lithium-like ions 0 VI, Ne viii, and Mg x are formed in the solar chromosphere and corona were determined in a rocket experiment by measuring the intensity ratio of pairs of emission lines from the same ion. The ratios compared the intensity of the resonance multiplet 2s-2p with the multiplets 2s-3p, 2p-3s and 2p-3d. The theoretical dependence of the three ratios on electron temperature was determined by assuming that the free electrons have a Maxwellian distribution of velocities and that the electron distribution over the excited levels is given by a coronal-type equation. Collisional excitation cross-sections given by Bely and Burke et al. were used in the calculation. The experimental temperatures are in fairly good agreement with the theoretical temperatures of the maximum abundance of the ions obtained by assuming ionization balance.

Bindungsverhältnisse und Elektronenverteilung im Br 4 2− -Ion

Abstract: The linear ions Br 4 2− which has been discovered for the first time by Siepmann and Schnering [13] in W6Br16 have been studied theoretically using the free electron model for the valence electrons. Electronic structure, binding energy and charge distribution show that Br 4 2− is a typical electron deficient compound stabilized by a 4c-6e bond.

On the electron band structure of liquid metals

Abstract: The electronic structure and the density of states of simple liquid metals is discussed on the basis of a nonlocal and energy-dependent pseudopotential of the Phillips-Kleinman type. As an example we treat lithium. To calculate this pseudopotential we need to know the states and the eigenvalues of the liquid metal ion cores. For these quantities we use: first, the core data of the free atom; second, of the free ion; third, the data we have determined from the measured phonon dispersion curves. The deviations between the band structures, the density of states as calculated with these pseudopotentials and those of free electrons are considerable.

Crystal nucleation given rise by fracturing or by mechanical shock

Abstract: Sudden crystallization takes place frequently in supercooled liquids or in supersaturated solutions (usually of ionic compounds) when solid substances immersed in the liquids are cut or fractured mechanically. Rupture of chemical bonds in the solid is essential for the nucleation and the effect disappears momentarily. Crystallization is also frequently given rise by mechanical shock in the above mentioned liquids, and may be explained as follows: electrons of the shocked molecules become labile and may behave like free electrons in metals momentarily as demonstrated experimentally. Generated free radicals and free electrons cluster into a metal-like structure and are compressed into the closest-packed structure with higher regularity by forces analogous to metallic bond. The cluster may act as the embryo and the nucleus of the crystal, if its structure resembles to that of the crystal or if it is easily convertable to the latter. Nucleation in supercooled liquids given rise by fracturing of solids is explained in an analogous way. Fractured surface of solids is momentarily covered with free radicals. The labile electrons and positively polarized part of liquid molecules in contact with the surface may form a two-dimensional metallic structure and the resulting compressed layer may act as the nucleus, if its structure is appropriate.

Theory of the Non-linear Longitudinal Kerr Magneto-optic Effect in Ferromagnetic Metals

Abstract: A theory of the non-linear longitudinal Kerr magneto-optic effect in ferromagnetic metals is developed. The material model is based on the classical equation of motion for a free electron with a finite relaxation frequency under the action of a Lorentz force. A second harmonic current density is found of the form: J2 = αE2 + β h (H 1)E1 + σ (E1∇ · E1), where α, βh (H 1) and σ are non-liner conductivity tensors, E1 and H1 are the fundamental electric and magnetic fields, and E2 is the induced second harmonic electric field. Results of this theory reduce, in the limit of a vanishing ferromagnetic state, to results obtained by Jha [1] from the Boltzmann transport equation for conduction electrons subject to a potential barrier at the metal surface. As required, the theory reduces to the linear longitudinal Kerr magneto-optic effect in the absence of second harmonic generation. The second harmonic reflection coefficients are derived. To the degree of approximations made, all four coefficients vanish at grazin...