On the Static Dielectric Permittivity for Coulomb System in the Long Wavelength Limit

On the basis of the exact relations the general formula for the static dielectric permittivity for Coulomb system is found in the region of small wave vectors. The obtained formula describes the dielectric function of the Coulomb system in both limits: in the "metallic" state and in the "dielectric" one. On this basis the determinations of the "apparent" dielectric and the "apparent" radius of screening are introduced. In the random phase approximation (RPA) the exact relations for the function dielectric function of the electron gas in the long-wavelength region of the wave vectors are found for an arbitrary degeneration of the particles.