Perturbation in an electron gas

A first order perturbation method is used for treating localized defects in metals in a self-consistent way. The calculations are performed under the Hartree approximation using both the ordinary Coulomb interactions between electrons appropriate for the one electron approximation and the effective short-range potential resulting from the Bohm-Pines plasma theory of metals. The results of the above approximations are tested for self-consistency by the application of the Friedel sum rule. The results are then compared with the statistical approximation of the Thomas-Fermi method. It is found that they are very similar.