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

Recent high precision helium n=10 fine-structure measurements are compared to the precise variational calculations of Drake and to predictions of long-range polarization calculations (which treat the system in terms of potentials between the He+ core and a distant Rydberg electron). New calculations are presented for the α2 < r2-6 > relativistic correction to the polarization energies. The results give simple formulas for these contributions which can be evaluated for any Rydberg state. With these new corrections, the variational and polarization energies show good agreement. Both, however, show significant disagreement with recent measurements, indicating the possible presence of physical effects not included in present calculations