Study on the Effects Generated by Screening of large-Scale Inhomogeneity’s by an Electron Liquid in Metals

The simplest model of a metal is considered: a homogeneous, positively charged background and an electron liquid filling the same volume with the same average charge density. This article examines the response of an e-liquid to large-scale inhomogeneity’s created by external causes. Using two inhomogeneity’s as an example: the outer boundary of a positive background and a uniform magnetic field throughout the volume, it is shown that the electron liquid screens the inhomogeneity, transforming it into an exponential potential at the boundary. The exponential parameter is determined by the average charge density and is significantly less than the sample size. Some properties of the energy spectrum of the exponential well are proved. This made it possible to explain the laws of the photoelectric effect, to determine the energy dependence of the density of states of elementary excitations of an electron liquid in a magnetic field. The electric field created by the inhomogeneous density distribution of the electron liquid should affect the phenomena in the ionic lattice.