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Physical Review Letters

New variational techniques for the 1sndstates of helium

G. W. F. Drake

Published Oct 5, 1987• 81 citations
Publisher

Abstract

New variational techniques are described which yield a factor of 1000 improvement in accuracy for the energies of the 1snd $^{1}\mathrm{D}$ and $^{3}\mathrm{D}$ states of helium up to n=8. Convergence to better than \ifmmode\pm\else\textpm\fi{}10 kHz is obtained, making possible high-precision comparisons with experiment for fine structure and singlet-triplet splittings. The comparisons are sensitive to QED, relativistic recoil, and second-order mass-polarization corrections.

DOI
10.1103/physrevlett.59.1549

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New variational techniques are described which yield a factor of 1000 improvement in accuracy for the energies of the 1snd 1D^{1}\mathrm{D}1D and 3D^{3}\mathrm{D}3D states of helium up to n=8. Convergence to better than \ifmmode\pm\else\textpm\fi{}10 kHz is obtained, making possible high-precision comparisons with experiment for fine structure and singlet-triplet splittings. The comparisons are sensitive to QED, relativistic recoil, and second-order mass-polarization corrections.
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We present a combined application of perturbation and configuration-interaction calculation for the nonrelativistic electrostatic energy for the He 1s4f 1^{1}1,3F multiplets with particular emphasis given to the contributions beyond the second order from perturbation calculation. The numerical efficiency and the quantitative accuracy of our ab initio calculation are greatly improved with the use of a finite basis set constructed from the B splines. The calculated fine-structure level splittings for the 1s4f 1^{1}1,3F multiplets compare very well with the result from the most recent rf electric-resonance experiment.