Electron-ion coupling factor for temperature relaxation in dense plasmas

We compare two formulas obtained from first principles to calculate the electron-ion coupling factor for temperature relaxation in dense plasmas. The quantum average-atom model is used to calculate this electron-ion coupling factor. It is shown that if the two formulas agree at sufficiently high temperature so that the potential energy is of limited importance, i.e., when the plasma is said to be kinetic, and are consistent with the Landau-Spitzer formula, then they strongly differ in the warm-dense-matter regime. Only one of the two is shown to be consistent with quantum molecular dynamics approach. We use this point to determine which formula is valid to describe temperature relaxation between electrons and ions in warm and hot dense plasmas.