Higher-order relativistic corrections to the polarization energies of helium Rydberg states

Accurate energies of helium Rydberg states have been obtained by Drachman using polarization potentials [Phys. Rev. A 26, 1228 (1982); 31, 1253 (1985); 38, 1659(E) (1988)]. The present work calculates the higher-order relativistic corrections up to order ${\mathrm{\alpha }}^2$〈(${\mathit{a}}_0$/${\mathit{r}}_2$ ${)}^6$〉${\mathit{e}}^2$/${\mathit{a}}_0$, where ${\mathbf{r}}_2$ is the position of the Rydberg electron. The results given simple formulas for these contributions, which can easily be evaluated for any Rydberg state. The results are compared (at lower L) to precise variational calculations, and are compared to recent precisely measured n=10 intervals.