Effective collision frequency method in the theory of the conductivity of Coulomb systems. I. Weakly nonideal plasma and the classical limit

The effective collision frequency method proposed earlier by the authors is developed to calculate the frequency-dependent conductivity of a Coulomb system. In part I, the equation of motion for the two-particle Green's function is used to obtain an exact diagram representation for the electron effective collision frequency $\nu_e(p,\omega)$. This representation makes it possible to separate the main contribution in the limit of a weak interaction. The function $\nu_e(p,\omega)$ is calculated for a weakly nonideal plasma for arbitrary degeneracy with allowance for the effects of screening and the the ion dynamics. A comparison with the corresponding results of the kinetic equation method is made. The problem of eliminating the Coulomb divergence for the conductivity of a weakly nonideal plasma on the transition to the classical limit is considered.