Periodicity and thickness effects in the cross section of quantum well states

The photoemission cross section of quantum well states in very thin Cu films has been analyzed as a function of photon energy within a wide energy range. We show that this cross section is periodical in k space, peaking around vertical transitions of the respective Cu bulk band. The cross section peak width is analyzed in terms of final- and initial-state wave vector broadening. The latter can only be detected at low kinetic energies due to reduction of final state broadening. The initial state $k_{\perp }$ broadening increases when the Cu film gets thinner, as simply expected from the uncertainty principle.