Excess-electron surface states of helium clusters

Bound states of an excess electron attached to the surface of helium clusters ${}_{}{}^4{}_{}{}^{}\mathrm{He}_n^{}{}_{}{}^{}$ and liquid helium are calculated. The binding energy increases smoothly from 0.04 ${\mathrm{cm}}^{-1\mathrm{}}$ for $n=5\mathrm{}\times {10}^5 \mathrm{to} 5.57$ ${\mathrm{cm}}^{-1\mathrm{}}$ for bulk liquid helium. The splittings of the first two excited states of the excess electron on a liquid-helium surface are reproduced to within 1% of the experimental values. We expect similar accuracies for the cluster states.