Self-Energy Correction to the Two-Photon Decay Width in Hydrogenlike Atoms

Abstract

We investigate the gauge invariance of the leading logarithmic radiative correction to the two-photon decay width in hydrogenlike atoms. It is shown that an effective treatment of the correction using a Lamb-shift "potential" leads to equivalent results in both the length as well as the velocity gauges provided all relevant correction terms are taken into account. Specifically, the relevant radiative corrections are related to the energies that enter into the propagator denominators, to the Hamiltonian, to the wave functions, and to the energy conservation condition that holds between the two photons; the form of all of these effects is different in the two gauges, but the final result is shown to be gauge invariant, as it should be. Although the actual calculation only involves integrations over nonrelativistic hydrogenic Green functions, the derivation of the leading logarithmic correction can be regarded as slightly more complex than that of other typical logarithmic terms. The dominant radiative correction to the 2S two-photon decay width is found to be -2.020536 (alpha/pi) (Zalpha)^2 ln[(Zalpha)^-2] in units of the leading nonrelativistic expression. This result is in agreement with a length-gauge calculation [S. G. Karshenboim and V. G. Ivanov, e-print physics/9702027], where the coefficient was given as -2.025(1).

9 pages, RevTeX

References in corpus (8)

• Radiative Corrections to the Muonium Hyperfine Structure. I. The ${\alpha }^2(Z\alpha )$ Correction
• Higher-order binding corrections to the Lamb shift of 2P states
• Logarithmic two-loop corrections to the Lamb shift in hydrogen
• Radiative Corrections to the Muonium Hyperfine Structure. II. The $\alpha (Z\alpha {)}^2$ Correction
• Radiative energy shifts induced by local potentials
• Radiative Corrections to One-Photon Decays of Hydrogenic Ions
• Double-Logarithmic Two-Loop Self-Energy Corrections to the Lamb Shift
• Radiative Corrections to the 2E1 Decay Rate of the 2s-State in Hydrogen-Like Atoms

Cited by in corpus (16)

• Relativistic calculation of the two-photon decay rate of highly-excited ionic states
• Non-uniform convergence of two-photon decay rates for excited atomic states
• Long-range interactions of hydrogen atoms in excited states. I. 2S-1S interactions and Dirac-delta perturbations
• Influence of external electric fields on multi-photon transitions between the 2s, 2p and 1s levels for hydrogen and anti-hydrogen atoms and hydrogen-like ions
• Functional Form of the Imaginary Part of the Atomic Polarizability
• Theory of the multiphoton cascade transitions with two photon links: comparison of Quantum Electrodynamical and Quantum Mechanical approaches
• Separation of Transitions with Two Quantum Jumps from Cascades
• Vacuum polarization and finite nuclear size effects in the two-photon decay of hydrogen-like ions
• Two-photon approximation in the theory of the electron recombination in hydrogen
• Relativistic and Radiative Corrections to the Dynamic Stark Shift: Gauge Invariance and Transition Currents in the Velocity Gauge
• Relativistic (Z alpha)^2-Corrections and Leading Quantum Electrodynamic Corrections to the Two-Photon Decay Rate of Ionic States
• Investigation of two-photon 2s -> 1s decay in one-electron and one-muon ions
• QED model of the radiation escape from the matter
• Gauge dependence of spontaneous radiation spectrum in a time-dependent relativistic non-perturbative Coulomb field
• Quasi-analytical lineshape for the 1S-2S laser spectroscopy of antihydrogen and hydrogen
• Radiative corrections to the level width in the presence of magnetic field