Unoccupied surface states on Cu(001): A comparison of experiment and theory

We compare new high-resolution inverse-photoemission spectra of the unoccupied surface states on Cu(001) with a first-principles calculation of the same surface. This theoretical calculation includes the asymtotic long-range image potential. The commonly observed image state is found to correspond to the n=1 member of the Rydberg series of states derived from the image potential, i.e., the wave function has a single extremum beyond the crystal edge characteristic of the hydrogenic n=1 state. Agreement between theory and experiment for all states is excellent. The experimentally determined binding energies and effective masses are 0.62 eV and 0.98$m_e$ for the n=1 image state and 0.8 eV (with respect to $E_F$) and 0.4$m_e$ for the n=0 surface resonance. The results indicate that surface corrugation effects are negligible.