Free electron model

About: Free electron model is a research topic. Over the lifetime, 4678 publications have been published within this topic receiving 103535 citations.

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 .

Modeling of nonlocal electron kinetics in a low-pressure inductively coupled plasma.

Abstract: Two different kinetic calculations have been employed to model electron behavior in a low-pressure inductively coupled plasma (ICP) in order to investigate the processes governing the formation of the electron distribution function (EDF). One approach involves a numerical ``propagator'' treatment of time-resolved electron motion in five-dimensional phase space (two spatial and three velocity coordinates) based on the ``convected scheme'' (CS). The other one, referred to as the ``nonlocal'' approach, uses the difference between momentum and energy relaxation rates of electrons to simplify the Boltzmann equation. For the majority of electrons, the nonlocal approach reduces the kinetic equation for the isotropic part of the EDF to a form that exhibits a resemblance to that for homogeneous plasmas. Both calculations incorporate the principal physical effects in a collisional ICP: electron heating by an inductive electric field and nonlocal electron kinetics in which the electrons rapidly lose momentum but travel long distances before suffering a substantial energy loss in collisions. The collision processes that are important in the discharge include quasielastic and inelastic collisions with heavy particles and electron-electron interactions. A comparison of the results of the two methods validates the assumptions employed in the nonlocal approach for the considered range of discharge conditions. To good accuracy the EDF of the majority of the electrons in the ICP is found to be solely a function of the total (kinetic plus potential) electron energy and to be largely independent of the spatial coordinates. The extent to which this is true, and the circumstances under which it is true, are a major focus of this paper. In a rare gas ICP, as a result of Coulomb collisions between electrons, a Maxwell-Boltzmann distribution is typically found in the elastic energy range. The CS calculations demonstrate that trapped electrons can carry a substantial circulating current within the plasma that exceeds the current of free electrons to the walls. \textcopyright{} 1996 The American Physical Society.

Electron angular distribution in near-threshold double photoionization: extended Wannier ridge model

Abstract: In order to account properly for the dynamics of the electron angular correlations near the double ionization threshold the extended Wannier model is formulated in which the electrons recede from the reaction zone being at equal distances from the nucleus but in arbitrary directions. 1Se and 1Po states of the two-electron continuum are considered. The boundary conditions on the border of the reaction zone are imposed corresponding to the double photoionization process. The wavepacket propagation to the free electron regime is calculated numerically. The asymmetry parameter beta is in good agreement with recent experiments.

Electronic Eigenvalues of Copper

Abstract: The cellular method as developed by Howarth & Jones (1952) is applied to the face-centred cubic crystal, and, in particular, the eigenvalues and wave functions of the 3 d and 4 s electrons in metallic copper are obtained for states whose wave vectors lie at the ends of the three- and four-fold axes in the Brillouin zone. The conduction electrons approximate closely to free electrons inside the first Brillouin zone, but the energy gaps at the zone faces are found to be sensitively dependent upon the potential used to represent the copper ion. The eigenvalues of the 3 d band agree closely with Fletcher’s results for nickel, and show a band width of 3·46 eV. An approximate solution of the Hartree equations for the metal shows the top of the d -band to lie 3·7 eV below the Fermi level in the conduction band.