Momentum distribution of photoelectrons emitted from Cu and Ag single crystals, and its polarization dependence

The angular-resolved energy-distribution functions for photoelectrons emitted from (111) Cu and Ag are presented at photon energies below 6.2 eV. They show a characteristic dependence on the polarization of the radiation in spite of the fact that the experiments are done at normal incidence. No such polarization dependence is observed for (110) and (001) Cu surfaces. The polarization dependence is traced to the angular dependence of the dipole matrix element characteristic for direct transitions; it allows one to separate the elastically emitted electrons from those emitted after being scattered. An interpolation scheme is used to calculate $E\left(\overrightarrow{\mathrm{k}}\right)$ consistent with the experiments of this paper and with independent optical and de Haas—van Alphen measurements. The nearly-free-electron case is used as a guide in the interpretation, it reveals only qualitative similarities with the actual experiments.