Long-wavelength limit of the dynamical local-field factor and dynamical conductivity of a two-component plasma

A systematic approach to the optical conductivity is given within a dielectric function formalism. The response function as well as the dynamical local-field factor $G(\stackrel{\ensuremath{\rightarrow}}{k},\ensuremath{\omega})$ of an electron-ion plasma can be expressed in terms of determinants of equilibrium correlation functions which allow for a perturbative treatment. The dynamical collision frequency $\ensuremath{\nu}(\ensuremath{\omega})=\ensuremath{-}i{\ensuremath{\omega}}_{\mathrm{pl}}^{2}G(0,\ensuremath{\omega})/\ensuremath{\omega}$ for fully ionized weakly coupled plasmas is evaluated in the low-density limit. A renormalization function is given to describe the effects of higher moments of the distribution function, thus the Spitzer formula is reproduced in the static limit. The existence of the third moment sum rule can be shown analytically. Numerical calculations are presented for the dynamical conductivity of hydrogen plasmas at solar core conditions.