Transient thermal and nonthermal electron and phonon relaxation after

Several dynamic thermal and nonthermal scattering processes affect ultrafast heat transfer 7 in metals after short-pulsed laser heating. Even with decades of measurements of electron8 phonon relaxation, the role of thermal vs. nonthermal electron and phonon scattering on 9 overall electron energy transfer to the phonons remains unclear. In this work, we derive 10 an analytical expression for the electron-phonon coupling factor in a metal that includes 11 contributions from equilibrium and non-equilibrium distributions of electrons. While the 12 contribution from the nonthermal electrons to electron-phonon coupling is non-negligible, 13 the increase in the electron relaxation rates with increasing laser fluence measured by ther14 moreflectance techniques can not be accounted for by strictly only considering electron15 phonon relaxations. We conclude that electron-electron scattering along with electron16 phonon scattering have to be considered simultaneously to correctly predict the transient 17 nature of electron relaxation during and after short-pulsed heating of metals at elevated 18 electron temperatures. Furthermore, for high electron temperature perturbations achieved 19 at high absorbed laser fluences, we show good agreement between our model, which ac20 counts for d-band excitations, and previous experimental data. Our model can be extended 21 to other free electron metals with the knowledge of the density of states of electrons in the 22 metals and considering electronic excitations from non-Fermi surface states. 23