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

TL;DR

This paper derives a general formula for the static dielectric permittivity of Coulomb systems at small wave vectors, applicable in both metallic and dielectric states, and introduces concepts of apparent dielectric and screening radius.

Contribution

It provides an exact relation-based formula for the dielectric function of Coulomb systems in the long-wavelength limit, encompassing different physical states and including RPA results for electron gases.

Findings

Derived a unified dielectric permittivity formula valid in both metallic and dielectric states.

Introduced the concepts of apparent dielectric constant and screening radius.

Obtained exact relations for the dielectric function of electron gas within RPA for arbitrary degeneracy.

Abstract

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.