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Bethe logarithms for the 1 singlet S, 2 singlet S and 2 triplet S states of helium and helium-like ions

Jonathan D. Baker·Robert C. Forrey·Malgorzata Jeziorska·John D. Morgan III
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Abstract

We have computed the Bethe logarithms for the 1 singlet S, 2 singlet S and 2 triplet S states of the helium atom to about seven figure-accuracy using a generalization of a method first developed by Charles Schwartz. We have also calculated the Bethe logarithms for the helium-like ions of Li, Be, O and S for all three states to study the 1/Z behavior of the results. The Bethe logarithm of H minus was also calculated with somewhat less accuracy. The use of our Bethe logarithms for the excited states of neutral helium, instead of those from Goldman and Drake's first-order 1/Z-expansion, reduces by several orders of magnitude the discrepancies between the theoretically calculated and experimentally measured ionization potentials of these states.

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Jonathan D. Baker, Robert C. Forrey, Malgorzata Jeziorska, John D. Morgan III. 2000-02-03. Bethe logarithms for the 1 singlet S, 2 singlet S and 2 triplet S states of helium and helium-like ions. https://arxiv.org/abs/physics/0002005

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