Energy levels for S, P, and D states in He through precision variational calculations.

Abstract

Nonrelativistic variational calculations with the relativistic correction to order ${\ensuremath{\alpha}}^{2}$ have been carried out to obtain the energy levels for the n $^{1}$,3S, n $^{1}$,3P, and ${n}^{1}$,3D series in He up to n=8. The calculated term values have converged generally to within an uncertainty of \ensuremath{\sim}${10}^{\mathrm{\ensuremath{-}}4}$ ${\mathrm{cm}}^{\mathrm{\ensuremath{-}}1}$, a value matching the accuracy of recent high-precision wavelength measurements. The results are combined with theoretical Lamb shifts and systematically compared with currently available high-precision experimental data. The consistency between theory and experiment is good, although for some low-lying (n=3--6) S and P states there exist small discrepancies, presumably caused by the estimated Lamb shifts. The calculated term values for high-lying excited states have better accuracies than existing experimental data. Addition of the theoretical term values to the corresponding experimental excitation energies suggests a value of 198 310.7725(5) ${\mathrm{cm}}^{\mathrm{\ensuremath{-}}1}$ for the ground-state ionization energy on the energy scale fixed by the ${2}^{1}$P value of 171 135.0000 ${\mathrm{cm}}^{\mathrm{\ensuremath{-}}1}$.