  We quantify the effect of the spin-orbit interaction on the Rydberg-like
series of image state electrons at the (111) and (001) surface of Ir, Pt and
Au. Using relativistic multiple-scattering methods we find Rashba-like
dispersions with Delta E(K)=gamma K with values of gamma for n=1 states in the
range 38-88 meV Angstrom. Extending the phase-accumulation model to include
spin-orbit scattering we find that the splittings vary like 1/(n+a)^3 where a
is the quantum defect and that they are related to the probability of spin-flip
scattering at the surface. The splittings should be observable experimentally
being larger in magnitude than some exchange-splittings that have been resolved
by inverse photoemission, and are comparable to linewidths from inelastic
lifetimes.
