Rydberg states of helium: An optical-potential analysis

The Feshbach projection-operator technique has been applied to the problem of electrostatic level shifts in $1sNL$ Rydberg states of helium. It is assumed at first that, for sufficiently high $L$, only long-range terms in the optical potential affect the energy of the outer electron. These terms up to ${x}^{\ensuremath{-}8}$ are carefully derived, used in a first-order perturbation calculation, and compared with recent accurate experimental results. Second-order effects due to the leading ${x}^{\ensuremath{-}4}$ potential and some short-range terms are also calculated in a few cases; these effects are generally not negligible for $L\ensuremath{\le}4$.