Modelo para propriedades estáticas de um gás de elétrons interagentes

Abstract

In the present work were proposed models for the static dielectric function: the screening charge density, the structure factor, the pair distribution function and the interacting energy of the uniform electron gas. The parameters of the dielectric function are determined by imposing the charge conservation principle, the compressibility sum rule for large wavelength and the Kato s condition for the screening charge density at small distances. A similar model is adopted for the structure factor, which parameters are obtained from normalization of the pair distribution function and from the Kimball s cusp condition for the behavior of this function at small distances, as well as from the RPA limit of the structure factor at long wavelength. The imposition of these boundary condition leads to a set of non-linear equations which allows a complete analytical solution for the parameters of the theory. Besides of satisfying elfconsistence conditions, the obtained models are well behaved and leads to a positive-definite pair distribution function and a convergent screening charge density which exhibit Friedell s oscillations, as expected for an uniform electron gas.