Dispersion in the loss spectra from Na overlayers on Al(111)

The dispersion of the energy-loss peaks for the ordered system, (✓3 × ✓3)R 30° Na adsorbed on Al(lll) surface, has been measured using angle-resolved electron energy-loss spectroscopy (EELS). We have created a simple but realistic model to evaluate the dispersion of EELS in terms of an interband transition in the Na layer. The previously published inverse photoemission data are used to determine the dispersion of the unoccupied Na bands. Our analysis indicates that the dispersion seen in the EELS measurements is inconsistent with a single-particle picture of interband transitions. We find that it is impossible to create any simple parabolic initial-state band capable of yielding the loss dispersion. One possible explanation is that as q1 increases the interband transition couples to the collective excitation of the Na electrons, leading to a stonger dispersion of the measured energy loss than predicted by a single-particle picture.