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Theory of the electron relaxation in metals excited by an ultrashort optical pump

The theory of the electron relaxation in metals excited by an ultrashort optical pump is developed on the basis of the solution of the linearized kinetic equation. The kinetic equation includes both the electron-electron and the electron-phonon collision integrals. The widely used two temperature model follows from the theory as the limiting case, when the thermalization due to the electronelectron collisions is fast with respect to the electron-phonon relaxation. It is demonstrated that the energy relaxation has two consecutive processes. The first and most important step describes the emission of phonons by the photo-excited electrons. It leads to the relaxation of 90% of the energy before the electrons become thermalized among themselves. The second step describes electronphonon thermalization and may be described by the two temperature model. The second stage is difficult to observe experimentally because it involves the transfer of only a small amount of energy from electrons. Thus the theory explains why the divergence of the relaxation time at low temperatures was never observed experimentally.