Showing papers on "Free electron model published in 1986"

An itinerant electron model with crystalline or magnetic long range order

Abstract: A quantum mechanical lattice model of fermionic electrons interacting with infinitely massive nuclei is considered. (It can be viewed as a modified Hubbard model in which the spin-up electrons are not allowed to hop.) The electron-nucleus potential is “on-site” only. Neither this potential alone nor the kinetic energy alone can produce long range order. Thus, if long range order exists in this model it must come from an exchange mechanism. N , the electron plus nucleus number, is taken to be less than or equal to the number of lattice sites. We prove the following: (i) For all dimensions, d, the ground state has long range order; in fact it is a perfect crystal with spacing √2 times the lattice spacing. A gap in the ground state energy always exists at the half-filled band point ( N = number of lattice sites). (ii) For small, positive temperature, T, the ordering persists when d ⩾ 2. If T is large there is no long range order and there is exponential clustering of all correlation functions.

The exact one-electron model of molecular structure

Abstract: The Schrodinger equation satisfied by the electron density is derived without approximation from the theory of marginal and conditional amplitudes. The equation arises from a factorization of the total N-electron wavefunction defined by the normalization appropriate to a conditional amplitude. This Schrodinger equation is an exact dynamical model for computing effective one-electron potentials from known N-electron wavefunctions. Results are presented for several small molecules. They display the shell structure of atoms, and the valence structure of both ionic and covalent molecules.

Nonlinear analysis of efficiency enhancement in free-electron-laser amplifiers

Abstract: A technique for efficiency enhancement in free-electron-laser and ``ubitron'' amplifiers (where the ubitron is essentially a free-electron laser operated at electron beam energies less than 500 keV) is analyzed which makes use of both tapered wiggler and axial guide magnetic fields A set of model equations is derived which describes the coupling between an ensemble of electrons and the radiation field The analysis is fully three dimensional, and treats the propagation of an electron beam of fi- nite cross-sectional area through a loss-free cylindrical waveguide in the presence of a helically symmetric wiggler field and an axial guide magnetic field The model equations are solved numerically, and substantial enhancements in the interaction efficiency are found for a variety of choices of the model parameters The efficiency enhancement is observed to be a sensitive function of both the degree of taper in the wiggler and axial magnetic fields as well as the point at which the taper is begun In order to illustrate the physical mechanism underlying the efficiency enhancement, a modified pendulum equation which describes the interaction is derived from the orbit equations under a set of idealized assumptions, and used to construct a small-signal theory of the efficiency enhancement

Ion-acoustic double layers in a magnetized plasma

Abstract: Solutions for double layers (DL), propagating obliquely to the magnetic field with a speed near the slow ion‐acoustic velocity are presented. Using fluid equations for the ions and an arbitrary equation of state for the electrons, it is shown that in such a system, DL solutions exist for the two‐electron Boltzmann model. No DL exists when the electrons are isothermal, and when the free and reflected electrons are described by Maxwell distributions.

Theory of a uranium impurity in metals fluctuating between two magnetic configurations

Abstract: The theory of a uranium impurity in a metal fluctuating between two magnetic valence states is presented. The authors examine the ground and a few excited states of the uranium ion with orbital degeneracy embedded in a free electron matrix fluctuating between f2 and f3 states. For the minimum allowed orbital degeneracy they construct variational states of different spin multiplicity, namely singlet, doublet, triplet and quarter, and calculate their binding energies relative to the Fermi sea. They show how the same results may be obtained in the large N(=2j+1) limit of the same model written in the j-j coupling scheme (for zero j.j coupling). They find that in the intermediate valence regime and in both Kondo regimes, the ground state is a singlet, in agreement with recent experiments on dilute alloys UxY1-xSb.

Free‐electron density and transit time in a finite superlattice

Abstract: In this paper we have calculated the free‐electron density in a finite superlattice. Resonant tunneling causes a buildup of particle density in the well regions, giving rise to an accumulation of electrons in those regions. Using our results, we have estimated the change in barrier heights and well depths caused by the electrostatic force. A negligible change is found for a double‐well structure having well widths of 40 A and barrier widths of 20 A. Our approach could be extended to calculate the tunneling current self‐consistently. Additionally we have used a time‐dependent solution of Schrodinger’s equation to estimate the trapping time of the electrons due to the resonant effect. The results show that the probability density oscillates several times between the two wells, leaking out gradually at each step. After about 2.4×10−13 s, most of the waves centered about the resonant energies have been transmitted.

Band structure of Ag2F

Abstract: A self-consistent band-structure calculation using LAPW is performed for Ag2F which has a layered hexagonal structure. It is found that the material has two Fermi surfaces: a large and cylindrical one and a small and ellipsoidal one. The dispersion curve around the Fermi energy is like that of a nearly free electron. These results are consistent with the recent transport measurement.

II-VI Compounds with Fe - New Family of Semimagnetic Semiconductors

Abstract: Several experimental methods: absorption, photoemission and transport measurements were used to determine the energy position of substitutional Fe2+ (3d6) donor state in the band structure of the semimagnetic semiconductor Hg1-v-xCdvFexSe for 0≤v≤0.7 and v+x=l, and x≤0.15. For v≤0.40, Fe2+(3d6) level is a resonant donor located in the conduction band. For v=O (HgSe) we obtain 230 meV for the position of Fe2+(3d6) level with respect to the bottom of the conduction band which coincides with the position of the Fermi level for electron concentration N ≅5x1018 cm-3. Surprisingly, the mobility of free electrons (T∼4.2K) is abnormally high and the Dingle temperature measured in quantum magnetoresistivity oscillations (SdH effect) and magnetooptical measurements is abnormally low. Because of the Coulomb interaction between the ionized donors, at low T, there will appear some correlation of their positions. This may lead to a kind of “liquefying” of the system of ions and to its “crystallisation” (i.e. formation of a superlattice or hyperlattice of ionized donors) at even lower T. The space-ordering of ionized donors influences dramatically the free-carrier scattering and correspondingly explains the high mobility and low Dingle temperature. Finally, we shall also present some magnetic properties of these new semimagnetic materials.

Mode competition in Raman free electron lasers

Abstract: A relativistic electromagnetic particle code with conducting boundary conditions in the transverse direction has been developed to investigate mode competition in Raman free electron lasers. The model allows three-dimensional spatial motion for electrons, as well as transverse inhomogeneity of the wiggler magnetic fields and is capable of including a finite number of various relevant TEmn modes. The code also contains sufficient longitudinal modes to revolve the finite bandwidth of free electron laser radiation. The parameters used in the simulations are relevant to the most recent experiment carried out at NRL. The simulation results show that the generated radiation is dominated by the TE11 mode in the case of an axis-centered beam, and the TE01 mode is excited through a nonlinear effect at a later time. However, if the beam center is off axis, both TE11 and TE01 modes are excited with comparable growth rate and reach comparable amplitudes, which is in agreement with the experimental observation. Longitudinal mode competition is also observed in the computer simulation and the resulting bandwidth is about 10% that of the peak frequency.

Three Dimensional Modeling Of Free-Electron Lasers Using Rigorous Wave Propagation

Abstract: The essential features of generalized numerical models developed at Rocketdyne to compute rigorously the 3 D transverse mode structure of free-electron laser oscillators are presented. The oscillator may consist of a conventional standing or a traveling wave cavity, or may be more complex, and contain intracavity grazing optical elements. Numerical resolution needed to (1) compute the gain due to a spatially distributed electron beam and (2) propagate the electromagnetic field when coupled to this gain are discussed with illustrative examples.

Elastic Scattering of Electrons by a Cut‐Off Coulomb Potential at Low Energies

Abstract: Elastic scattering of electrons by cut-off Coulomb potential Uc(r) is investigated, where Uc(r) = 0, for r > rc and Uc(r) = −1/r + 1/rc for r ≦ rc. This is first considered in terms of classical, and later quantum mechanical (partial wave) methods in the low energy range 0 ≦ ϵ ≲ 1/rc, where ϵ is the energy of the free electron. Scattering in this energy region displays a number of particular characteristics, such as back scattering, at certain energies. It can be concluded that some agreement does exist between the classical and quantum mechanical results.

Method of producing electroluminescence and electroluminescing lamp

Abstract: A method of producing electroluminescence without a chemical reaction by providing a metal oxide containing electron traps, (i.e., holes or distortion of the lattice of the oxide by impurities or surface states), providing free electrons at an energy level in the conduction band and trapping the electrons to release photons. Alternatively, electroluminescence may be produced without a chemical reaction by the decay of the energy level of electrons from an excited state which results from collision of accelerated free electrons with ions in the oxide, the free electrons being provided externally of the oxide (e.g., by an electron gun or the application of a high field to an insulator contiguous to the oxide) or by space charges within the oxide or adjacent to the boundary thereof. Electroluminescing lamps are also disclosed.

Landau-level population inversion in crossed electric and quantizing magnetic fields.

Abstract: The problem of the electron distribution in crossed electric and quantizing magnetic fields is treated for free electrons in a parabolic band. The master equation for the diagonal elements of the density matrix is solved, neglecting the ${k}_{z}$ dependence of the electron distribution. It is shown that population inversion between Landau levels can be achieved if scattering by optical phonons and a quasielastic scattering process are taken into account.

Gain physics of rf‐linac‐driven XUV free‐electron lasers

Abstract: In an rf‐linac‐driven XUV free‐electron laser oscillator, the gain depends on the details of the shape of the electron beam’s phase‐space distribution, particularly the distribution of electrons in the transverse (to the direction of propagation) position and velocity coordinates. This strong dependence occurs because the gain in this device is inhomogeneously broadened. Our previous theoretical studies have assumed that the transverse phase space distribution is a product of uncorrelated Gaussian functions. In the present work, we present the results of a theoretical study of the gain for non‐Gaussian phase‐space distributions. Such distributions arise either from a better representation of the electron beam from an rf‐linac or from an emittance filter applied to the beam after the linac.

A two-dimensional numerical model of amorphous silicon thin-film transistors

Abstract: Electrical characteristics of amorphous silicon thin-film transitors (a-Si TFTs) are strongly affected by trapped electrons in localized states in the energy gap. In this paper, we present a two-dimensional numerical model of amorphous silicon thin-film transistors including a trapped electron model. Use of an accurate localized state density distribution ensures high simulation accuracy. A compact model is derived that can describe crowding characteristics was derived based on the observation of simulation results.

Time resolved fluorescence and quenching of excited sodium in a crossed-beam experiment

Abstract: The authors have observed the time resolved fluorescence of excited sodium atoms in a pulsed crossed-beam experiment. This new technique allows the multiple collisional energy transfer paths to be disentangled and it can be used for unreactive as well as reactive studies. The deexcitation of the 4D level of Na by N2 molecules is given as an example. The experimental values of the different electronic cross sections are compared with the predictions of the resonant quasi-free electron model of Bottcher and Sukumar (1977).

Double wave description of a single relativistic free electron

Abstract: Introduces two wavefunctions to describe a single relativistic free electron, from which the authors can obtain the value of an arbitrary physical quantity at any time t. They find that the motion of free electrons is the same as that given by special relativity.

Theory of continuum surface Raman scattering from electrons in metals

Abstract: A theory for continuum Raman scattering from a bounded free electron gas is developed. The theory is able to account for the observed magnitude of the effect. By suitably generalizing the theory we are also able to account for the observed spectral features. Our theory implies that it is possible to measure densities of states to photon spectroscopic accuracy.

Free electron diode oscillator

Abstract: A crossed-field microwave power tube. Electrons are emitted from a tubularlectrode at ground potential. The electrons are accelerated by an electric field toward a high voltage anode located within the tubular electrode. A magnetic field is oriented along the axis of the tube; the magnetic field is perpendicular to the electric field. The electrons follow curved paths in the space between the tubular electrode and the anode, while producing electromagnetic radiation in a TEM mode. The TEM radiation is easily coupled from the tube.

Study of particles trapped by a magnetic field

Abstract: A new type of radiation which occurs when particles are accelerated in the field of a longitudinal wave and in a transverse magnetic field is studied. The characteristics of such spontaneous radiation are obtained, and the influence of collective effects on the radiation is analyzed. The application of the findings to the theory of free electron lasers is discussed. 8 references.

On the invariance of the 2d Hall conductivity for integer fillings

Abstract: A system of independent electrons interacting with an arbitrary number of fixed point scatterers on the surface of an infinitely long cylinder is considered. It is shown that (at zero temperature) the equilibrium Byers-Yang Hall current takes the same value as for free electrons if the Fermi energy lies in an energy gap.

Second Harmonic Generation from Alkali Thin Films on AG(110)

Abstract: The sensitivity of second harmonic generation at interfaces has been utilized to probe the spatial and frequency dependence of the local field generated near the surface of a nearly free electron metal by an externally imposed electromagnetic field. The longitudinal screening field was found to oscillate with a wavelength on the order of 10A and to propagate into the bulk several layers deep.