High Precision theory for the Rydberg P-states of helium and comparison with experiment up to principal quantum number n = 35

Recent high-precision measurements of transition frequencies in helium [1] for principal quantum number n as high as 100 have confirmed a 9σ disagreement between theory and experiment for the ionization energy of the 1s2s ³S₁ state. However, traditional theoretical methods of calculation fail in this range of high n for comparison. We have now developed variational methods in correlated Hylleraas coordinates that yield nonrelativistic energies accurate to a few parts in 10²² for the singlet and triplet P-states of helium up to n = 35 [2]. Relativistic and quantum electrodynamic effects effects are included to yield a final uncertainty of ±1 kHz for n ≧24. This allows a direct comparison between theory and experiment for 11 singlet and triplet transitions of the form 1s2s ³S₁ - 1snp ^1,3P_J for 24 ≦ n ≦ 35. By combining theory with the experimental transition frequencies, this provides 11 independent measurements of the 1s2s ³S₁ ionization energy without the need for a quantum defect (QD) extrapolation to the series limit. The averaged result of 1152 842 742.728(6) MHz agrees with but is larger than the experimental QD value by 14 ± 17 kHz. Both values confirm a much larger 9σ discrepancy of 0.468 ± 0.055 MHz with the theoretical ionization energy.