Calculation of Hydrogenic Bethe Logarithms for Rydberg States
U Jentschura, Peter J. Mohr
We describe the calculation of hydrogenic (one-loop) Bethe logarithms for all states with principal quantum numbers n 200. While the calculation of the Bethe logarithm is a rather easy computational problem involving only the nonrelativistic a (Schr'dinger) theory of the hydrogen atom, certain calculational problems affect highly excited states, and in particular states for which the principal quantum number is much larger than the orbital angular momentum 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 Schr'dinger-Coulomb propagator. Selected numerical results are presented. The full set of values is available at physics.nist.gov/hdel.
Physical Review A (Atomic, Molecular and Optical Physics)