Variational calculations for He I4 : Improved energies for singlet and triplet n D and n F levels (n=3–8)

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Abstract
Hylleraas method variational calculations with up to 458 expansion terms are reported for the n D1, n D3 terms and for the n F1, n F3 terms (n=4–8) of neutral helium. Convergence arguments are presented to obtain new estimates of the exact nonrelativistic energies of these terms. The reliability of the estimates ranges from 3×10−10 a.u. in the worst case to 10−11 a.u. in the best case. The nonrelativistic singlet and triplet energies are combined with previously calculated values for relativistic and other small energy contributions to evaluate the total ionization energies for the n D and n F levels. Comparisons of the n D1 and n D3 energies with other calculations and available data yield improved values for relativistic contributions. The calculated relativistic n F ionization energies agree with values based on core-polarization theoretical n G and n H energies within deviations of 3 MHz (5×10−11 a.u.) for n=5 to 1 MHz (1.5×10−11 a.u.) for n=7,8. The calculated n F fine-structure separations generally agree with experiment for n=5–8 within uncertainties of the order of 1 to 0.1 MHz. Predicted values given for the 4 F fine-structure separations and the 41F ionization energy are probably accurate within a few MHz.