The photoionization cross section for spherical alkali metal clusters
is predicted to oscillate as a function of the photon wavenumber with
a frequency determined by the diameter of the cluster. The oscillation
s and other principal features of the photo cross section can be worke
d out analytically using semiclassical techniques. An accurate numeric
al calculation with different cluster potentials confirms these result
s qualitatively. Quantitative details depend sensitively on the actual
potential. Hence, properties of the true cluster potential can be inf
erred from the experimental cross section. This might turn out to be u
seful for improving theoretical cluster potentials.