Image potential states (IPS's) on periodically stepped metal surfaces have
been calculated within an impenetrable surface model. Band splittings and b
and anticrossings are predicted for IPS's caused by the lateral back scatte
rings of the stepped surfaces. A reduction in the binding energy of the low
est IPS's was found due to the lateral confinement, which agrees fairly wel
l with the experimental results. The calculated photoionization transition-
matrix elements show that the photoionization of the lowest-energy IPS's on
the stepped metal surface is nearly the same as that on planar metal surfa
ces, while fur the high-energy IPS's the umklapp, process becomes important
in the photoionization, giving rise to electron scattering in different di
rections.