Magnetic and electric fine structure in helium Rydberg states

An improved method for calculating magnetic fine structures in helium Rydberg states is developed and the results are compared with previous calculations and with existing precise experimental determinations. Agreement with experiment is markedly improved in $D$ manifolds, but systematic anomalies in $F$ and $G$ manifolds remain unexplained. Relativistic and mass-polarization contributions to electric fine structure are evaluated and found to be significant at the same order as recently calculated radiative corrections. Agreement with experimental determinations is no better than about 1%.