Rydberg states of helium: Some further small corrections

The optical-potential method based on the Feshbach projection-operator formalism has been successfully applied to the computation of fine-structure splittings between highly excited levels of helium [R. J. Drachman, Phys. Rev. A 26, 1228 (1982)]. In this paper, I report additional terms in the nonrelativistic effective potential decreasing as ${\mathit{x}}^{\mathrm{-}9}$ and ${\mathit{x}}^{\mathrm{-}10}$, where x is the distance of the outer electron from the ${\mathrm{He}}^{+}$ core. They involve higher-multipole distortions of the wave function of the core electron, higher nonadiabatic corrections, and perturbation theory up to fourth order in the electrostatic potential. Energy shifts due to these terms are compared with the extremely accurate variational results of Drake [Phys. Rev. Lett. 65, 2769 (1990)].