On the Static Permittivity of the Coulomb System in the Long-Wavelength Limit

The general expression for the static permittivity e(q, 0) of the Coulomb system in the region of small wave vectors was derived based on exact limit relations. The relation obtained describes the function e(q, 0) in both “metal” and “dielectric” states of the Coulomb system. On this basis, the concept of the “true” dielectric is introduced and the definition of the “true” screening length was discussed. Exact relations were derived for the function e(q, 0) in the region of small wave vectors q within the random phase approximation at an arbitrary degeneracy.