Calculation of hydrogenic Bethe logarithms for Rydberg states

Ulrich D. Jentschura, Peter J. Mohr
2005 Physical Review A. Atomic, Molecular, and Optical Physics  
We describe the calculation of hydrogenic (one-loop) Bethe logarithms for all states with principal quantum numbers n <= 200. While, in principle, the calculation of the Bethe logarithm is a rather easy computational problem involving only the nonrelativistic (Schroedinger) theory of the hydrogen atom, certain calculational difficulties affect highly excited states, and in particular states for which the principal quantum number is much larger than the orbital angular momentum quantum number.
more » ... m quantum number. Two evaluation methods are contrasted. One of these is based on the calculation of the principal value of a specific integral over a virtual photon energy. The other method relies directly on the spectral representation of the Schroedinger-Coulomb propagator. Selected numerical results are presented. The full set of values is available at quant-ph/0504002.
doi:10.1103/physreva.72.012110 fatcat:oh57f7ts5jdhhbrkc4y6yrw5fe