We present a calculation of the two-electron Bethe logarithm, the main part of the theoretical expression for the Lamb shift of the atomic ground state. The basic method uses Hylleraas pseudostates to approximate the intermediate states in the slowly convergent sum defining the quantity of interest. Three tricks improve the convergence in our method. First, we choose the nonlinear parameters of the pseudostates by a variational method. Second, we extend the energy sum analytically, beyond the last pseudoenergy. Finally, we extrapolate the result using a physically reasonable parameter as the independent variable. The extrapolation proves to be remarkably linear. Results are given for helium and several two-electron ions and compared with previous calculations. The hydrogen system is also considered.

• Received 21 October 1997

DOI:https://doi.org/10.1103/PhysRevA.57.4301