Asymptotic Lamb shifts for helium Rydberg states

A global formula for the asymptotic Lamb shifts of the Rydberg states of helium is obtained by calculating the electric field perturbation due to the Rydberg electron on the ${\mathrm{He}}^{+}$ (1s) Lamb shift. The result substantially reduces theoretical uncertainties in calculated transition frequencies. A comparison with experiment for transitions among the n=10 states of helium reveals systematic discrepancies much larger than expected corrections due to higher-order relativistic and Casimir-Polder effects.