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.
@article{arxiv.cond-mat/0407211,
title = {Spin-orbit splitting of image states},
author = {J R McLaughlan and E M Llewellyn-Samuel and S Crampin},
journal= {arXiv preprint arXiv:cond-mat/0407211},
year = {2007}
}