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 dielect ric function formalism. The response function as well as the dynamical loca l-field factor G((k) over right arrow,w) of an electron-ion plasma can be e xpressed in terms of determinants of equilibrium correlation functions whic h allow for a perturbative treatment. The dynamical collision frequency v(w ) = - iw(pl)(2)G(0,w)/w for fully ionized weakly coupled plasmas is evaluat ed in the low-density limit. A renormalization function is given to describ e the effects of higher moments of the distribution function, thus the Spit zer formula is reproduced in the static limit. The existence of the third m oment sum rule can be shown analytically. Numerical calculations are presen ted for the dynamical conductivity of hydrogen plasmas at solar core condit ions.