Two-Loop Bethe Logarithms for Higher Excited S Levels

Abstract

Processes mediated by two virtual low-energy photons contribute quite significantly to the energy of hydrogenic S states. The corresponding level shift is of the order of (alpha/pi)^2 (Zalpha)^6 m_e c^2 and may be ascribed to a two-loop generalization of the Bethe logarithm. For 1S and 2S states, the correction has recently been evaluated by Pachucki and Jentschura [Phys. Rev. Lett. vol. 91, 113005 (2003)]. Here, we generalize the approach to higher excited S states, which in contrast to the 1S and 2S states can decay to P states via the electric-dipole (E1) channel. The more complex structure of the excited-state wave functions and the necessity to subtract P-state poles lead to additional calculational problems. In addition to the calculation of the excited-state two-loop energy shift, we investigate the ambiguity in the energy level definition due to squared decay rates.

14 pages, RevTeX, to appear in Phys. Rev. A

References in corpus (30)

• CODATA Recommended Values of the Fundamental Physical Constants: 2010
• Theory of Light Hydrogenlike Atoms
• Two-time Green function method in quantum electrodynamics of high-Z few-electron atoms
• Calculation of the Electron Self Energy for Low Nuclear Charge
• Higher-order binding corrections to the Lamb shift of 2P states
• Self-energy correction to the bound-electron g factor in H-like ions
• CORRECTIONS OF ORDER ${\alpha }^2(Z\alpha {)}^5$ TO HYPERFINE SPLITTING AND LAMB SHIFT
• Two-loop self-energy correction in high-Z hydrogen-like ions
• Two-Loop Bethe Logarithms
• Logarithmic two-loop corrections to the Lamb shift in hydrogen
• Electron Self Energy for the K and L Shell at Low Nuclear Charge
• Nonrelativistic QED approach to the bound-electron g factor
• Next-to-leading-log renormalization-group running in heavy-quarkonium creation and annihilation
• Loop-after-loop contribution to the second-order Lamb shift in hydrogenlike low-Z atoms
• Logarithms of alpha in QED bound states from the renormalization group
• Asymmetry of the natural line profile for the hydrogen atom
• Lamb Shift of 3P and 4P states and the determination of $\alpha$
• Nonresonant effects in one- and two-photon transitions
• Radiative energy shifts induced by local potentials
• Radiative Corrections to One-Photon Decays of Hydrogenic Ions
• Two-Loop Self-Energy Corrections to the Fine-Structure
• Asymptotic properties of self-energy coefficients
• Double-Logarithmic Two-Loop Self-Energy Corrections to the Lamb Shift
• An ${\alpha }^2(Z\alpha {)}^{5}m$ Contribution to the Hydrogen Lamb Shift from Virtual Light by Light Scattering
• Leading logarithmic contribution to the second-order Lamb shift induced by the loop-after-loop diagram
• Three-Loop Reducible Radiative Photon Contributions to Lamb Shift and Hyperfine Splitting
• A Problematic Set of Two-Loop Self-Energy Corrections
• Two-Loop QED Bound-State Calculations and Squared Decay Rates
• Extrapolation of the Zalpha-Expansion and Two--Loop Bound--State Energy Shifts
• QED theory of transition probabilities and line profiles in highly-charged ions

Cited by in corpus (11)

• CODATA Recommended Values of the Fundamental Physical Constants: 2010
• Precision physics of simple atoms: QED tests, nuclear structure and fundamental constants
• QED calculation of the n=1 and n=2 energy levels in He-like ions
• Nonrelativistic QED approach to the Lamb shift
• Calculation of the One- and Two-Loop Lamb Shift for Arbitrary Excited Hydrogenic States
• Calculation of Hydrogenic Bethe Logarithms for Rydberg States
• Two-Loop Bethe Logarithms for non-S Levels
• Two-loop QED corrections in few-electron ions
• Two-Loop Effects and Current Status of the 4He+ Lamb Shift
• Some Recent Advances in Bound-State Quantum Electrodynamics
• Techniques in Analytic Lamb Shift Calculations