Angle-resolved photoemission spectra obtained from the clean Cu (001) surface with photon energies in the range 40-120 eV and emission both normal and non-normal to the surface are well predicted by a simple constant-matrix-element model based upon direct ($\overrightarrow{\mathrm{k}}$ conserving) transitions between initial electronic states with full bulk translational symmetry and final states with a free-electron dispersion relation and a correction for refraction at the crystal surface. In addition, the quantitative agreement between theory and experiment improves significantly by including broadening in the final-state wave vector for spectra obtained in the highly-surface-sensitive region around 100 eV. A strong contribution of phonon-assisted indirect transitions to the spectra also appears to be present. The photoemission spectra have been obtained at two different polarization orientations with respect to the electron emission direction and this can be used for assigning contributions from various initial states.

• Received 15 January 1980

DOI:https://doi.org/10.1103/PhysRevB.23.724