Within the one-electron formalism, the elementary electronic excitations of a crystalĪre constituted by individual electron-hole pairs.
Independent particle approximation and investigate the many-body effects on the band The whole treatment was based on the one-electronĪpproximation in spite of its great merits, it is often necessary to proceed beyond the In the previous two chapters we have considered the band theory of crystals and provided some specific applications. Quantum Expression of the Transverse Dielectric Function in Materials Lindhard Dielectric Function for the Free-Electron Gas 325Īppendix D. Quantum Expression of the Longitudinal Dielectric Function in MaterialsĪppendix C. Friedel Sum Rule and Fumi Theorem 318Īppendix B. Static Dielectric Screening in Simple Metals with the Lindhard Model 304ĭynamic Dielectric Screening in Simple Metals and Plasmon Modes 307ħ.6 Quantum Expression of the Longitudinal Dielectric Function in Crystals 312ħ.7 Surface Plasmons and Surface Polaritons 314Īppendix A. The Longitudinal Dielectric Function within the Linear Response Theory 301ĭielectric Screening within the Lindhard Model 304 Current analysis can provide useful information on the effects of relativistic correction to the charge screening for a wide range of plasma density, such as the inertial-confined plasmas and compact stellar objects.Static Dielectric Screening in Metals within the Thomas-Fermi Model 298 This is equal to saying that in an ultrarelativistic degeneracy limit of electron-ion plasma, the screening length couples with the system dimensionality and the plasma becomes spherically self-similar. It is discovered that the total number of screening electrons, (N are the Thomas-Fermi and interparticle distance, respectively) has a distinct limit for extremely dense plasmas such as WD-cores and neutron star crusts, which is unique for all given values of the atomic-number. Calculation of the total number of screening electrons around a nucleus shows that there is a position of maximum number of screening localized electrons around the screened nucleus, which moves closer to the point-like nucleus by increase in the plasma number density but is unaffected due to increase in the atomic-number value. Moreover, the more » variation of relative Thomas-Fermi screening length shows that extremely dense quantum electron fluids are relatively poor charge shielders.
It is revealed that our nonlinear screening theory is compatible with the exponentially decaying Thomas-Fermi-type shielding predicted by the linear response theory. By numerically solving a second-order nonlinear differential equation, the Thomas-Fermi screening length is investigated, and the results are compared for three distinct regimes of the solid-density, warm-dense-matter, and white-dwarfs (WDs). A generalized energy-density relation is obtained using the force-balance equation and taking into account the Chandrasekhar's relativistic electron degeneracy pressure. In this paper, we study the charge shielding within the relativistic Thomas-Fermi model for a wide range of electron number-densities and the atomic-number of screened ions.