Electrons momentum distribution

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. 

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

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 ... 

I. R. Epstein, Electron momentum distributions in atoms, molecules and solids, in MTP International Review of Science, Series 2, Theoretical Chemistry, A. D. Buckingham, ed. (Butterworths, Lx)ndon, 1975), Vol. 1, pp. 107-161. 

L. Mendelsohn and V. H. Smith, Jr., Atoms, in Compton Scattering The Investigation of Electron Momentum Distributions, B. G. Williams, ed. (McGraw-Hill, New York, 1977), pp. 103-138. 

A. J. Thakkar, Electron momentum distributions at the zero momentum critical point, in Reviews of Modem Quantum Chemistry—a Celebration of the Contributions of Robert G. Parr, K. D. Sen, ed. (World Scientific, Singapore, 2002), pp. 85-107. 

Figure 8.1 Shape of the statistical factor for 3 decay, which represents the expected shape of the electron momentum distribution before distortion by the Coulomb potential.

Ignoring quantum-mechanical features such as spreading and interference, the essential classical physics then are described by the electron-momentum distribution function [17]... 

Fig. 4.10. Electron momentum distributions for neon ( 75oi = 0.79 a.u. and /. 02 = 1.51 a.u.) subject to a linearly polarized monochromatic field with frequency ui = 0.057 a.u. and intensity I = 3.0 x 1014W/cm2, as functions of the electron momentum components parallel to the laser-field polarization. The left and the right panels correspond to the classical and to the quantum-mechanical model, respectively. The upper and lower panels have been computed for a contact and Coulomb-type interaction Vi2, respectively. In panels (a) and (d), and (h) and (e), the second electron is taken to be initially in a Is, and in a 2p state, respectively, whereas in panels (c) and (/) the spatial extension of the bound-state wave function has been neglected. The transverse momenta have been integrated over...

This simple statistical model is compatible, for the case of neon, with the data available thus far. Moreover, it allows one to infer a value of the thermalization time. This value comes out to be in the attosecond regime. In principle, such bounds can be made even tighter by reducing the widths of the electron-momentum distributions. This can be done by limiting the temporal range of return times for the first electron using, for instance, an additional perpendicularly polarized driving wave at twice the frequency. 

The annihilation characteristics of a positron in a medium is dependent on the overlap of the positron wavefunction with the electron wavefunction [9]. From a measurement of the two photon momentum distribution, information on the electron momentum distribution can be obtained and this forms the basis of extensive studies on electron momentum distribution and Fermi surface of solids [9]. In the presence of defects, in particular, vacancy type defects, positrons are trapped at defects and the resultant annihilation characteristics can be used to characterize the defects [9, 10], Given these inherent strengths of the technique, in the years following the discovery HTSC, a large number of positron annihilation experiments have been carried out [11, 12]. These studies can be broadly classified into three categories (1) Studies on the temperature dependence of annihilation characteristics across Tc, (2) Studies on structure and defect properties and (3) Investigation of the Fermi surface. In this chapter we present an account of these investigations, with focus mainly on the Y 1 2 3 system (for an exhaustive review, see Ref. 11). 

Additional information on orbital type and composition is available from (e,2e) or electron momentum spectroscopy (Moore et al., 1982 see Appendix B) performed on Sip4 by Fantoni et al. (1986). Electron momentum distributions measured at various binding energies have been compared with those from ah initio Hartree-Fock-Roothaan SCF calculations using a double- wave function with a single Si 3of polarization... 

The Compton effect is the inelastic scattering of a photon by an electron. When radiation is Compton scattered, the emerging beam is Doppler broadened because of the motion of the target electrons. Analysis of this broadened line shape, the Compton profile, provides detailed information about the electron momentum distribution in the scatterer... 

Causa, M., R. Dovesi, C. Pisani, and C. Roetti (1986b). Electron charge density and electron momentum distribution in magnesium oxide. Acta Cryst. B42, 247-53. 

Fantoni, R., A. Giardini-Guidoni, R. Tiribelli, R. Cambi, and M. Rosi (1986). Ionization potentials and electron momentum distributions for Sip4 valence-shell orbitals an (e,2e) spectroscopic investigation and Green s function study. Chem. Phys. Lett. 128, 67-75. 

Abstract The momentum representation of the electron wave functions is obtained for the nonrelativistic hydrogenic, the Hartree-Fock-Roothaan, the relativistic hy-drogenic, and the relativistic Hartree-Fock-Roothaan models by means of Fourier transformation. All the momentum wave functions are expressed in terms of Gauss-type hypergeometric functions. The electron momentum distributions are calculated by the use of these expressions, and the relativistic effect is demonstrated. The results are applied for calculations of inner-shell ionization cross sections by charged-particle impact in the binary-encounter approximation. The reiativistic effect and the wave-function effect on the ionization cross sections are discussed. 

In quantum chemistry, the state of a physical system is usually described by a wave function in the position space. However, it is also well known that a wave function in the momentum space can provide complementary information for electronic structure of atoms or molecules [1]. The momentum-space wave function is especially useful to analyse the experimental results of scattering problems, such as Compton profiles [2] and e,2e) measurements [3]. Recently it is also applied to study quantum similarity in atoms and molecules [4]. In the present work, we focus our attention on the inner-shell ionization processes of atoms by charged-particle impact and study how the electron momentum distribution affects on the inner-shell ionization cross sections. 

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