The long-wavelength limit of the dielectric function for dense plasmas

The dielectric function of a system of charged particles is investigated for arbitrary degeneracy within a linear response theory. This approach allows for inclusion of collisions, thus going beyond the RPA and treating the electrical conductivity in consistency with the dielectric function. A general expression for the collision integral in the whole (k,w) plane is presented. Special attention is given to the long-wavelength limit deriving a frequency-dependent collision term. In the limit k = 0 and w = 0, the Ziman formula for the electrical conductivity in metallic systems is reproduced. By inspection of the high-frequency limit, it is shown that the third moment of the response function is in accordance with the well-known third moment sum rule.