Calculation of Hydrogenic Bethe Logarithms for Rydberg States

Abstract

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. 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.

10 pages, RevTeX

References in corpus (10)

• Ultra-precise measurement of optical frequency ratios
• Absolute frequency measurement of the 171Yb+ clock transition with a Kerr-lens mode-locked femtosecond laser
• Higher-order binding corrections to the Lamb shift of 2P states
• Two-Loop Bethe Logarithms
• Convergence Acceleration via Combined Nonlinear-Condensation Transformations
• Lamb Shift of 3P and 4P states and the determination of $\alpha$
• Radiative energy shifts induced by local potentials
• Implementation of the Combined--Nonlinear Condensation Transformation
• Two-Loop Bethe Logarithms for Higher Excited S Levels
• Relativistic and Radiative Energy Shifts for Rydberg States

Cited by in corpus (13)

• QED tests with highly-charged ions
• Lamb Shift in Muonic Hydrogen. I. Verification and Update of Theoretical Predictions
• Mass Measurements and the Bound--Electron g Factor
• Fundamental constants and tests of theory in Rydberg states of one-electron ions
• Two-Loop Bethe Logarithms for non-S Levels
• Metrology of Rydberg states of the hydrogen atom
• Relativistic Ritz approach to hydrogen-like atoms I: theoretical considerations
• From First Principles of QED to an Application: Hyperfine Structure of P States of Muonic Hydrogen
• Defect Theory of Positronium and Nontrivial QED Relations
• Calculations of Bethe logarithms for Hydrogen and Helium atoms using B-splines in different gauges
• Precision Rydberg State Spectroscopy with Slow Electrons and Proton Radius Puzzle
• Bound and Resonant States of Muonic Few-Body Coulomb Systems: Extended Stochastic Variational Approach
• Fitting for the energy levels of hydrogen