Rydberg helium and the helium dimer: Relativistic and retardation effects

The energy level structure of a Rydberg helium atom with one electron in a highly-excited $nl$ state can be modeled with high accuracy using an effective potential based on a long-range expansion in powers of the distance $r$ between the Rydberg electron and the nucleus. In addition to the dominant Coulomb interactions, small relativistic $O( \alpha^2)$ terms and smaller quantum electrodynamical $O(\alpha^3)$ effects, as well as retardation effects, can be included. For the helium dimer He${}_2$ a similar effective potential in powers of the internuclear distance $R$ can be developed [Przybytek et al. PRL 108, 183201 (2012)]. The interpretations of the effective potentials for Rydberg He and for the He dimer are discussed.