Effect of relaxation of secondary electrons and holes on time-resolved two-photon photoemission from Cu(111)

We investigate the time-resolved two-photon photoemission (time-resolved 2P PE, TR2PPE) spectrum of the image state on Cu(111) by nonequilibrium pertur bation theory. We show that, in the 2PPE process, the scattering of photoex cited quasiparticles (electrons and holes) due to Coulomb interactions betw een electrons causes excitation of secondary quasiparticles in the vicinity of the Fermi level as well as electron transitions to the image state. We demonstrate quantitatively on the basis of numerical results how the effect of relaxation of secondary quasiparticles is manifested in the TR2PPE spec trum.