Showing papers on "Free electron model published in 1968"

Stability Criterion for the Localization of an Excess Electron in a Nonpolar Fluid

Abstract: In this paper we consider the properties of an excess electron in the nonpolar dense fluids 3He, 4He, Ne, Ar, and H2. The energy of the quasifree electron state was estimated through the use of an approximate polarization potential and of pseudopotential theory, together with average Wigner–Seitz boundary conditions. The Wigner–Seitz approximation was also applied to the study of the localized state. A stability criterion was derived for the localization of an excess electron in a dense fluid of nonpolar molecules. The stability criterion is expressed in terms of a relation between the energy of the quasifree electron state and the bubble surface energy. Three cases of physical interest which can be distinguished are those of the existence of a quasifree state, the existence of a metastable bubble, and the formation of an energetically stable bubble. The stability criterion predicts that excess electron states in liquid He and in liquid He, should be localized, the excess electron state in liquid Ar should be quasifree, while liquid neon provides a borderline case between the stable and the metastable bubble. The available experimental data concerning the energy barrier for adiabatic electron injection and electron mobilities in liquid He, liquid H2, and liquid Ar are consistent with the results of the present treatment.

Berechnung der Energieverluste schneller Elektronen in dünnen Schichten mit Retardierung

Abstract: Regarding the retardation of the electromagnetic field, a semiclassical formula for the energy-loss-probability of fast electrons penetrating a thin foil with a dielectric constantɛ=ɛ(Ω) is derived. This formula is discussed for the special cases of the free electron gas and the occurence of Cerenkov-radiation in substances with high dielectric constants. Numerical evaluations have been made for these cases. Significant deviations from the formula without retardation are found, which are confirmed by the experiments.

Plasma Oscillations Excited by a Fast Electron in a Metallic Particle

Abstract: The interactions between a fast incident electron and a metallic spherical particle full of a free electron gas as the conduction electrons are studied using the hydrodynamic equations of Bloch. The obtained energy spectrum of a transmitted electron is composed of the well known peak due to the bulk plasma oscillations with small corrections and the peak due to the surface plasma oscillations which are given by sum of various modes of oscillations with different energies. The energy value of the surface oscillations at maximum intensity increases with increasing particle size and tends to that in the foil case. Numerical examples are given for aluminum particle coated with aluminum oxide and for colloidal alkali metal in alkali halide. The latter example is compared with experimental observations. The possibility of the plasma radiation is also discussed. The radiated photon energy is the same as that in the Mie scattering from small particle. Energy spectrum, angular distribution and photon yield are num...

Superconductivity in metals with incomplete inner shells.

Abstract: Through screening by outer (s) electrons the plasma oscillations of inner (d) bands are transformed into an acoustic phonon branch if certain conditions are fulfilled. Similar to the lattice-phonon branch this provides an interaction with free electrons which leads to superconductivity. Dependence of the transition temperature Tc on the number of d electrons follows Matthias' rule. Suggestions for increasing Tc are discussed.

Recombination, radiative energy loss, and level populations in nonequilibrium cesium discharges.

Abstract: The transition rate equations for the populations of cesium states in a homogenous, optically thin plasma have been solved for the excited-state populations, the effective ground-state ionization and recombination coefficients, and the effective electron kinetic-energy and radiative loss coefficients. A table of values is presented for the nonequilibrium steady-state plasma which is analogous to the Saha equation for the equilibrium plasma. Free electron densities from 1012 to 1015 cm-3 are considered, and a Maxwellian electron velocity distribution at temperatures from 1500 to 3000°K is assumed. These conditions are typical of those in thermionic and magnetohydrodynamic energy converters and other cesium discharges. The rate coefficients used for collision-induced and radiative atomic transitions are described. Molecular processes, diffusion, wall losses, etc., are discussed but not included explicitly in the model. The absorption of resonance radiation is simulated by reduction of the spontaneous emission coefficients. Other radiative absorption processes are neglected. The populations are seen to depart significantly from the Boltzmann distribution in steady state, and it is seen that many excited states participate in the ionization and recombination processes. The implications of these results for spectroscopic diagnostics, volume ion production, and energy loss in a cesium-discharge plasma are discussed.

Excitons and Plasmons in Insulators

Abstract: The relation between excitons and “plasmons” in insulators is studied, and it is shown that both excitons and “plasmons” may be obtained in the singlet longitudinal states. When the energy of interband transition is nearly equal to the free electron plasmon energy \(\hbar\omega_{p}\), the energy and the angular dispersion of “plasmon” loss peaks are closely related to the structure of the pair band. In this case the “plasmon” solution of the dispersion relation is expected on the higher energy side of M 3 -(or M 2 -) van Hove singularity provided the mean value of imaginary part of the dielectric constant exceeds some critical value below this energy and is small above this energy. Recent experimental data of energy loss spectra on alkali-halides are analyzed making use of the optical data and the results of band structure calculations.

The temperature dependence of the spin wave energy in the itinerant electron model of ferromagnetism

Abstract: The long wavelength non-interacting spin wave energy for metals at low temperatures is expressed as ћω q = Dq 2 = ( D + D 1 T 2) q 2. The dependence of the coefficient D 1 on the density of states function, the number of electrons per atom, n, and the effective short range interaction energy, I , is discussed. The variation of D with T 2 comes from the change with temperature of the relative occupation ζ and the chemical potentials of the ± spin sub-bands as well as from the direct asymptotic expansion of the Fermi distribution functions occurring in the expression for D .

Electron and Phonon Tunneling Spectroscopy in Metal-Germanium Contacts

Abstract: Electron and phonon tunneling spectroscopy in metal Ge contacts, noting improved agreement with one electron model

Collisions in the Ionosphere

Abstract: Publisher Summary The ionosphere of the Earth is produced mainly by the ionization of the neutral particle constituents of the atmosphere by solar ultraviolet radiation, leading to the production of free electrons and positive ions The electrons possess initially a broad range of kinetic energies The thermal electron gas is removed by recombination processes, and the recombination of electrons and positive ions is an important source of heating of the neutral particle atmosphere Electrons can also be removed by attachment processes leading to the formation of negative ions at low altitudes Fast electrons lose energy by exciting and ionizing the neutral particle constituents in optically allowed transitions Because of scattering, electrons do not travel along a straight path in the atmosphere, and the calculation of the spatial distribution of the dissipation in energy of an incident electron stream is complicated There are no measurements of the energy distribution of the secondary electrons ejected in an ionization collision, although calculations have been performed within the first Born approximation for hydrogen and helium

Optical Study of Electronic Structure of Graphite

Abstract: Reflectance spectra of pyrolytic graphite are measured in the range 0.13 to 0.006 eV. The results are analyzed by a Kramers-Kronig relation to determine the complex dielectric constant e(ω)=e 1 + i e 2 and energy loss function. Structures in e 2 are all identified with interband transitions between the doubly degenerate levels at the points K and H of the Brillouin zone split by the effect of spin-orbit interaction. From the above fact, the strength of the coupling λ and the band parameter Δ are estimated as 0.004 eV (at the point K ) or 0.0023 eV (at the point H ) and -0.016 eV, respectively. Two peaks observed in -Im e -1 are interpreted as plasma frequencies of free electrons at the Fermi surface perpendicular and parallel to the crystallographic c axis.

The Problem of Scattering by Magnetic Impurities in Metals

Abstract: The ``s‐d'' model of interaction of a free electron gas with a magnetic impurity is treated by the methods of scattering theory. Older transport‐theory results are reviewed, and two additional measurements are proposed: frequency dependence of the resistivity (at low frequencies), and the Hall coefficient. The latter should show a broad maximum. It is suggested that because the ``s‐d'' model leads to strong coupling effects, it is necessary to return to fundamentals. A preliminary indication of how this might be done is given at the end of the paper.

Temperature Dependence of the Spin‐Wave Energy in the Itinerant Electron Model of Ferromagnetism

Abstract: The long‐wavelength noninteracting spin‐wave energy for metals at low temperatures is expressed as ħωq = Dq2 = (D0+D1T2)q2. The dependence of the coefficient D1 on the density‐of‐states function, the number of electrons per atom n and the effective short‐range interaction energy I is discussed. The variation of D with T2 comes from the change with temperature of the relative occupation ζ and the chemical potentials of the ± spin subbands as well as from the direct asymptotic expansion of the Fermi distribution functions occurring in the expression for D. Although the calculation is based essentially on the random phase approximation this is here used in an improved version due to Izuyama and Kubo where these distribution functions replace the thermal averages 〈akσ*akσ〉 which would occur in a strict r.p.a. formulation. The general relation for D1 which is obtained reduces to a very simple form giving D = D0ζ/ζ0 in the limit zgr;0→0, where ζ0 is the value of ζ at 0°K.The general relation for D1 is evaluated...

Semiconductor particle spectrometers

Abstract: Publisher Summary An important difference between the solid and the gas is that many more electron-hole pairs are produced in the solid than electron. A collection of the liberated charge in a solid is more complicated than in a gas. The depletion layer is the sensitive region of the detector. The number of hole-electron pairs produced in the depletion layer is proportional to the energy expended by the incident particle. The main features of the process of charge collection in solid-state detectors can be illustrated by considering the case of a silicon junction diode. A free electron, which has been captured by an imperfection, may be released by thermal excitation. The collection of the liberated charge is a necessary but not sufficient condition for obtaining the optimum energy resolution. Lattice defects in the single crystals depend critically on the mass, charge, and energy of the incident particles

Self-trapping of Radiation Produced Electrons

Abstract: THE problem treated here is the trapping of free electrons produced by ionizing radiation in dielectric systems. Detailed theoretical descriptions of the equilibrium properties of the solvated electron are available1–3, but its formation is still under discussion. Electrons are formed and thermalized in the coulomb field of the positive ions, but not fully recaptured by the ions. Magee4 considered the auto-ionization of the H3O radicals as a possible secondary source of electrons; Freeman5–7 assumed the electrons to be trapped in the defect sites of the medium at the instant of thermalization, while we thought8,9 that in polar dielectrics the escape of the electrons from the ions can be a free-energy decreasing, and therefore spontaneous, process. In our approach, the electrons which escape are treated as quasi-free, and the question of the kinetics and mechanism of electron trapping arises. Diffusion kinetic calculations on the radiolysis of water10,11 suggest very high initial hydrated electron densities, which require fast trapping processes.

Quantum Theory of Electrical Transport in a Magnetic Field. I

Abstract: The relationship between the quantum theory of electrical transport in the presence of a magnetic field and the corresponding Boltzmann transport equation is established for a simple system. The model consists of noninteracting free electrons being elastically scattered by an arbitrary potential in the presence of uniform electric and magnetic fields. Without the aid of a representation, the exact gauge-dependent Liouville equation for the density operator of this system is transformed into a completely gauge-independent equation satisfied by a new density operator. The new density operator is shown to give the correct current density, using the ordinary gauge-independent free-particle velocity operator. No approximations are made in performing the transformations, and the physical content of the new gauge-independent transport formalism is identical in all respects with that contained in the initial gauge-dependent equations. A new density matrix is defined which is essentially the Fourier sum of the matrix of the gauge-independent density operator. By considering the scattering potential resulting from a set of fixed impurity centers, it is shown that the diagonal elements of this new density matrix satisfy the ordinary time-dependent Boltzmann transport equation in which the spatial gradient term appears explicitly. The possible existence of a spatial variation in the average density of scatterers is also taken into account. The final equation for the quantum-mechanical distribution function represents the result obtained by treating the electric field and the effective scattering potential to the lowest possible order in which they contribute.

Approach to Radiative Equilibrium of Free Electrons through Čerenkov Emission and Absorption

Abstract: The approach to radiative equilibrium of a system of free electrons in a background medium whose index of refraction is larger than unity is studied in the light of the basic principles of elementary nonrelativistic quantum theory. It is shown that the radiative equilibrium arises as a consequence of a balance between Cerenkov emission (spontaneous plus the induced emission) and absorption of photons by the uniformly moving electrons. A coupled pair of equations, one describing the time evolution of the photon distribution function and the other describing the time evolution of the electron distribution function, is thus derived. The equation for the time rate of change of the electron distribution function reduces, in the classical limit, to a Fokker-Planck equation.

Calculation of the dependence of emitted light on charge density for two-electron collisional-radiative recombination in the hydrogenic approximation.

Abstract: Emitted light and excited state populations resulting from two electron collisional radiative recombination related to free electron density

Thermodynamic Functions of Free Protons and Electrons in a Hydrogen Plasma

Abstract: Electrostatic contribution to free protons and free electrons internal energy in hydrogen plasma, using modified Poisson-Boltzmann equation