Temperature relaxation in two-temperature states of dense electron-ion systems

It is shown that the Landau-Spitzer theory for temperature relaxation between electrons and ions, which was originally derived for ideal plasmas, is in fact more general. A relaxation formula is derived, for arbitrary ion-ion coupling that follows from elementary considerations combined with the fluctuation-dissipation theorem and the f-sum rule. The conditions for the validity of this theory are weak electron-ion coupling and that the spectrum of fluctuations of the ions lies at energies far below the resonances of the electrons spectrum. It is found that the rate of energy relaxation is not sensitive to the details of the ion-excitation spectrum. For classical electrons the formula reduces to the Landau-Spitzer form with minor modifications.