True Dielectric and Ideal Conductor in Theory of the Dielectric Function for Coulomb System

TL;DR

This paper derives an exact formula for the static dielectric permittivity of Coulomb systems, unifying metallic and dielectric states, and identifies parameters distinguishing these states.

Contribution

It introduces a general formula for the dielectric function of Coulomb systems applicable to both metallic and dielectric states, based on exact relations.

Findings

Derived the static dielectric permittivity formula for Coulomb systems.

Identified parameters distinguishing dielectric and metallic states.

Obtained an exact relation for the pair correlation function g_ei(r).

Abstract

On the basis of the exact relations the general formula for the static dielectric permittivity e(q,0) for Coulomb system is found in the region of small wave vectors q. The obtained formuladescribes the dielectric function e(q,0) of the Coulomb system in both states in the "metallic" state and in the "dielectric" one. The parameter which determines possible states of the Coulomb system - from the "true" dielectric till the "ideal" conductor is found. The exact relation for the pair correlation function for two-component system of electrons and nuclei g_ei(r) is found for the arbitrary thermodynamic parameters.