  We study the electron and phonon thermalization in simple metals excited by a
laser pulse. The thermalization is investigated numerically by solving the
Boltzmann transport equation taking into account all the relevant scattering
mechanism: the electron-electron, electron-phonon (e-ph), phonon-electron
(ph-e), and phonon-phonon (ph-ph) scatterings. In the initial stage of the
relaxation, most of the excitation energy is transferred from the electrons to
phonons through the e-ph scattering. This creates hot high-frequency phonons
due to the ph-e scatterings, followed by an energy redistribution between
phonon subsystems through the ph-ph scatterings. This yields an overshoot of
the total longitudinal-acoustic phonon energy at a time, across which a
crossover occurs from a nonequilibrium state, where the e-ph and ph-e
scatterings frequently occur, to a state, where the ph-ph scattering occurs to
reach a thermal equilibrium. This picture is quite different from the scenario
of the well-known two-temperature model (2TM). The behavior of the relaxation
dynamics is compared with those calculated by several models, including the
2TM, the four-temperature model, and nonequilibrium electron or phonon models.
The relationship between the relaxation time and the initial distribution
function is also discussed.
