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The results of an extended series of high-precision variational calculations for all states of helium up to n=10 and L=7 (excluding S states above n=2) are presented. Convergence of the nonrelativistic eigenvalues ranges from five parts in 10^15 for the 2P states to four parts in 10^19 for the 10K states. Relativistic and quantum electrodynamic corrections of order ^2, ^3, ^2/M, ^2 (/M) ^2, and ^3/M are included and the required matrix elements listed for each state. For the 1s2p ^3P₉ states, the lowest-order spin-dependent matrix elements of the Breit interaction are determined to an accuracy of three parts in 10^9, which, together with higher-order corrections, would be sufficient to allow an improved measurement of the fine-structure constant. Methods of asymptotic analysis are extended to provide improved precision for the relativistic and relativistic-recoil corrections. A comparison with the variational results for the high-angular-momentum states shows that the ``standard-atomic-theory'' and ``long-range-interaction'' pictures discussed by Hessels et al. Phys. Rev. Lett. 65, 2765 (1990) come into agreement, thereby resolving what appeared to be a discrepancy. The comparison shows that the asymptotic expansions for the total energies are accurate to better than 100 Hz for L>7, and results are presented for the 9L, 10L, and 10M states (i. e. , angular momentum L=8 and 9). Significant discrepancies with experiment persist for transitions among the n=10 states, which cannot be easily accommodated by supposed higher-order corrections or additional terms. Finally, the asymptotic analysis indicates that a revision to the quantum-defect method is required for the analysis of high-precision data.
Drake et al. (Tue,) studied this question.