Bethe logarithms for the 1 singlet S, 2 singlet S and 2 triplet S states   of helium and helium-like ions
  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. 
Jonathan D. Baker (NIST), Robert C. Forrey (Penn State University),   Malgorzata Jeziorska (University of Warsaw) and John D...