Bethe logarithms for Ps-, H-, and heliumlike atoms

A new method is presented for the calculation of the mean excitation energy (Bethe logarithm) for helium and other two-electron systems. The method requires only a single matrix diagonalization within a correlated Hylleraas basis set extended to contain a wide range of distance scales. High-precision results are obtained for the ground states of Ps(-) and H-, and all the S- and P-states of heliumlike ions up to n = 5, including finite mass corrections. The results are used to calculate revised values for the quantum electrodynamic shifts for helium, and a comparison with experiment is presented.