We present a simplified model for the electron-ion energy relaxation in dense two-temperature systems that includes the effects of coupled collective modes. It also extends the standard Spitzer result to both degenerate and strongly coupled systems. Starting from the general coupled-mode description, we are able to solve analytically for the temperature relaxation time in warm dense matter and strongly coupled plasmas. This was achieved by decoupling the electron-ion dynamics and by representing the ion response in terms of the mode frequencies. The presented reduced model allows for a fast description of temperature equilibration within hydrodynamic simulations and an easy comparison for experimental investigations. For warm dense matter, both fluid and solid, the model gives a slower electron-ion equilibration than predicted by the classical Spitzer result
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