Within a theoretical model based on the Boltzmann equation, we analyze in detail the structure of the unusual peak recently observed in the energy dependence of the relaxation time in Cu. In particular, we discuss the role of Auger electrons in the electron dynamics and its dependence on the d-hole lifetime, the optical transition matrix elements, and the laser-pulse duration. We find that the Auger contribution to the distribution is very sensitive to both the d-hole lifetime ${\tau }_h$ and the laser-pulse duration ${\tau }_l,$ and that it largely dominates the excited-electron distribution for realistic parameters. It is shown that it can be expressed as a monotonic function of ${\tau }_l/{\tau }_h$ and that for a given ${\tau }_h,$ it is significantly smaller for a short pulse duration than for a longer one. Our results indicate that the relaxation time at the peak depends linearly on the d-hole lifetime, but interestingly not on the amount of Auger electrons generated. We provide a simple expression for the relaxation time of excited electrons which shows that the shape of the peak can be understood by a phase-space argument and its amplitude is governed by the d-hole lifetime. We also find that the height of the peak depends on both the ratio of the optical transition matrix elements $R=|M_{\overrightarrow{d}\mathrm{sp}}{|}^2/|M_{s\overrightarrow{p}\mathrm{sp}}{|}^2$ and the laser-pulse duration. Assuming a reasonable value for the ratio, namely, $R=2,$ and a d-hole lifetime of ${\tau }_h=35\mathrm{}$ fs, we obtain for the calculated height of the peak $\Delta {\tau }_{\mathrm{th}}=14\mathrm{}$ fs, in fair agreement with $\Delta {\tau }_{\exp }\approx 17$ fs measured for polycrystalline Cu.

• Received 18 February 2000

DOI:https://doi.org/10.1103/PhysRevB.63.094306