Momenta electrons

In an electron scattering or recombination process, the free center of the incoming electron has the functions Wi = ui U u, and the initial state of the free elechon is some function v/ the width of which is chosen on the basis of the electron momentum and the time it takes the electron to aiTive at the target. Such choice is important in order to avoid nonphysical behavior due to the natural spreading of the wavepacket. 

Crystal can compute a number of properties, such as Mulliken population analysis, electron density, multipoles. X-ray structure factors, electrostatic potential, band structures, Fermi contact densities, hyperfine tensors, DOS, electron momentum distribution, and Compton profiles. 

Semiconductors can be divided into two groups direct and indirect band gap materials. In direct semiconductors the minimum energy in the conduction band and the maximum in the valence band occur for the same value of the electron momentum. This is not the case in indirect materials. The difference has profound consequences for the transitions of electrons across the band gap in which light is emitted, the radiative transitions, of interest here. 

Since IR detector materials are direct bandgap materials (with no change in electron momentum required), they are very efficient absorbers (and emitters) of light - all IR photons are absorbed within the first few /rm of material. The reason that infrared detectors are 10 to 15 ptm thick is for structural and fabrication reasons, not for light absorption reasons. 

In the ideal case being performed at X-ray energy transfers much higher than the characteristic energies of the scattering system, the impulse approximation [14] is applicable. In this case, the dynamical structure factor is directly connected with the electron momentum density p(p) ... 

Schulke, W., Stuz, G., Wohlert, F. and Kaprolat, A. (1996) Electron momentum-space densities ofLi metal a high-resolution Compton-scattering study, Phys. Rev., B54, 14381-14395. 

Cooper, M.J. (1985) Compton scattering and electron momentum determination, Rep. Prog. Phys., 48, 415—481. 

The measurement of spectral momentum densities of solids by electron momentum spectroscopy... 

Figure 1. The electron momentum density for atomic hydrogen measured by EMS for the indicated energies compared with the square of Schrodinger wave function (solid curve) [4].

Three-dimensional reconstruction of electron momentum densities and occupation number densities of Cu and CuAl alloys... 

The reconstruction of the electron momentum densities and the occupation number functions of Cu and Cuq.953A10 047 could not produce results on an equal profound base as those based on the results of Li and LiMg reconstructions. This would need approximately 100 times the number of counts per spectrum which was not achieved. 

Mijnarends, P.E., (1979) Electron momentum densities in metals and alloys. In Positrons in Solids, (Ed.) Hautojarvi, P., Springer. 

Hansen, H., (1980) Reconstruction of the electron momentum distribution from a set of experimental Compton profiles, Hahn Meitner Institute (Berlin), Report HMI B 342. 

The spherical coordinates of the ejected electron momentum k are k, 0, and < ), where 0 = cos-1 (k v). Because the impact velocity lies along the Z axis, then v v Z. The three Sommerfeld parameters are defined by... 

Normally these conditions are satisfied in fast highly charged ion-atom collisions. From Eq. (66) we can derive the equations for the singly differential cross sections with respect to the components of the longitudinal momentum distributions for the electron, recoil-ion, and projectile. The longitudinal electron momentum distribution da/dpe for a particular value of p, may be derived by integrating over the doubly differential cross section with respect to the electron energy Ek ... 

Figure 8. Longitudinal momentum distribution for single ionization of helium by 945-keV antiproton (data points) in comparison with proton collision (full curve), (a) Electron momentum data [26] (b) recoil-ion data [26], The theoretical calculations represent antiproton collisions dotted curve, CDW results [26] broken curve, CTMC result [26], Here pze and pzr are equivalent to the notation of pey and pRy of Figs. 1 and 2, respectively.

Figure 20. Electron emissions at 0 = 0° for 40-keV H+ ion impact in H2. The double differential cross section (DDCS = ifia/dfldE ) is plotted against k/v, where v is the impact velocity, k is the ejected-electron momentum, and dU — 2k sin 0 dd. The filled circles represent the experimental data [38], and the CDW-EIS results are given by the solid line [38].

Several experimental techniques such as Compton scattering, positron annihilation, angular correlation, etc., are used for measuring momentum densities. One of the most popular techniques involved in measuring momentum densities is termed as electron momentum spectroscopy (EMS) [29]. This involves directing an electron beam at the surface of the metal under study. Hence EMS techniques fall under what is classified as coincidence spectroscopy. 

Electronic structure is often visualized with the help of the electron density p(r), which tells us where the electrons are likely to be found. A different perspective of electronic structure is provided by the electron momentum density IT(p) because II( ) Ap is proportional to the probability of finding an electron with... 

Several review articles on the theoretical aspects of electron momentum densities of atoms and molecules were written in the 1970s by Benesch and Smith [9], Epstein [10,11], Mendelsohn and Smith [12], Epstein and Tanner [13], Lindner [14], and Kaijser and Smith [15]. Since that time (e,2e) spectroscopy and the momentum densities of Dyson orbitals have been reviewed very often [16-28]. However, to my knowledge, a review article on molecular electron momentum densities has not been written recently apart from one [29] devoted solely to the zero-momentum critical point. The purpose of this chapter is to survey what is known about the electron momentum density of atoms and molecules, and to provide an extensive, but not exhaustive, bibliography that should be sufficient to give a head start to a nonspecialist who wishes to enter the field. 

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