Physical Review A
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 1015 for the 2P states to four parts in 1019 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 3PJ states, the lowest-order spin-dependent matrix elements of the Breit interaction are determined to an accuracy of three parts in 109, 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. © 1992 The American Physical Society.
Drake, Gordon W. F. and Yan, Z. C.. (1992). Energies and relativistic corrections for the Rydberg states of helium: Variational results and asymptotic analysis. Physical Review A, 46 (5), 2378-2409.