Saturation of Strong Electron-Electron Umklapp Scattering at High Temperature

We consider clean metals, at finite temperature, in which the inelastic rate, ħ∕τee, can become of the order of, or larger, than the band splitting energy. We show that in such systems, contrary to the common knowledge, the umklapp scattering rate becomes independent of both τee and the temperature T, in three dimensional systems. We discuss the relation of this phenomenon to the saturation of resistivity at high temperature.