Electron-solid scattering models

In this contribution we will deal with electron-electron correlation in solids and how to learn about these by means of inelastic X-ray scattering both in the regime of small and large momentum transfer. We will compare the predictions of simple models (free electron gas, jellium model) and more sophisticated ones (calculations using the self-energy influenced spectral weight function) to experimental results. In a last step, lattice effects will be included in the theoretical treatment. 

The scattering models employed in data processing invariably involve the assumption of particle sphericity. Size data obtained from the analysis of suspensions of asymmetrical particles using laser diffraction tend to be somewhat more ambiguous than those obtained by electronic particle counting, where the solid volumes of the particles are detected. 

Fig. 19.9 Plot of scaled total decay rates n3r of Ba 6pmn( J = l + 1 autoionizing states in atomic units vs (. For ( = 0-4 the measured rates (O) shown are the average rates from many n values. The data for the rates for > 4 are for n = 12. The solid line is a simple theoretical calculation based on the dipole scattering of a hydrogenic Rydberg electron from the 6p core electron. Note that the core penetration of the lower states reduces the actual rate from the one calculated using the dipole scattering model. The constant total decay rate for > 8 is the spontaneous decay rate of the Ba+ 6p state (from ref. 39).

The focus then shifts to the delocalized side of Fig. 1.1, first discussing Hartree-Fock band-structure studies, that is, calculations in which the full translational symmetry of a solid is exploited rather than the point-group symmetry of a molecule. A good general reference for such studies is Ashcroft and Mermin (1976). Density-functional theory is then discussed, based on a review by von Barth (1986), and including both the multiple-scattering self-consistent-field method (MS-SCF-ATa) and more accurate basis-function-density-functional approaches. We then describe the success of these methods in calculations on molecules and molecular clusters. Advances in density-functional band theory are then considered, with a presentation based on Srivastava and Weaire (1987). A discussion of the purely theoretical modified electron-gas ionic models is... 

It is well known that the energy profiles of Compton scattered X-rays in solids provide a lot of important information about the electronic structures [1], The application of the Compton scattering method to high pressure has attracted a lot of attention since the extremely intense X-rays was obtained from a synchrotron radiation (SR) source. Lithium with three electrons per atom (one conduction electron and two core electrons) is the most elementary metal available for both theoretical and experimental studies. Until now there have been a lot of works not only at ambient pressure but also at high pressure because its electronic state is approximated by free electron model (FEM) [2, 3]. In the present work we report the result of the measurement of the Compton profile of Li at high pressure and pressure dependence of the Fermi momentum by using SR. 

Figure 14.3 Experimental Cu KL23L23 Auger spectrum (dots) photoexcited from a approximately 100-nm thick polycrystalline layer using Mo bremsstrahlung [11]. The solid and dashed lines indicate the contributions from electrons scattered inelastically within the solid sample, estimated by different models [11],...

Figure 14.9 Resonant Cu KL23L23 Auger spectra excited from Cu metal foil using near-threshold- and sub-threshold-energy X-ray photons [25]. The energies of the photons related to the K-absorption threshold are indicated. Dots experimental data corrected for inelastic electron scattering solid line calculated spectra using the resonant X-ray scattering theory and the DV-Xa cluster MO model.

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