Mean Free Path Effects in the Dielectric Function of a Liquid Metal

Abstract

Abstract Mean free path effects are introduced into the frequency and wavenumber dependent dielectric function e(q, ω) of a simple liquid metal such as Na. It is pointed out that, at least in principle, e(q, 0) can be brought into contact with experiment through (a) electrical resistivity and (b) effective ion-ion interactions. The frequency dependence of e(q, ω) is then considered, using the Lindhard expression as a starting point. This is shown to link the real parts of the dielectric function e(q, ω) and the conductivity [sgrave](q, ω) via a function dependent on Fermi surface blurring. The frequency dependence of this function is determined in the long wavelength limit, and contact with the Drude-Zener theory is established. Finally, the long wavelength form of e(q, ω) is related to plasmon properties of liquid metals and to the ion-ion dynamical structure factor.