The radiative potential method for calculations of QED radiative corrections to energy levels and electromagnetic amplitudes in many-electron atoms

Abstract

We derive an approximate expression for a "radiative potential" which can be used to calculate QED strong Coulomb field radiative corrections to energies and electric dipole (E1) transition amplitudes in many-electron atoms with an accuracy of a few percent. The expectation value of the radiative potential gives radiative corrections to the energies. Radiative corrections to E1 amplitudes can be expressed in terms of the radiative potential and its energy derivative (the low-energy theorem): the relative magnitude of the radiative potential contribution is ~alpha^3 Z^2 ln(1/(alpha^2 Z^2)), while the sum of other QED contributions is ~alpha^3 (Z_i+1)^2, where Z_i is the ion charge; that is, for neutral atoms (Z_i=0) the radiative potential contribution exceeds other contributions ~Z^2 times. The advantage of the radiative potential method is that it is very simple and can be easily incorporated into many-body theory approaches: relativistic Hartree-Fock, configuration interaction, many-body perturbation theory, etc. As an application we have calculated the radiative corrections to the energy levels and E1 amplitudes as well as their contributions (-0.33% and 0.42%, respectively) to the parity non-conserving (PNC) 6s-7s amplitude in neutral cesium (Z=55). Combining these results with the QED correction to the weak matrix elements (-0.41%) we obtain the total QED correction to the PNC 6s-7s amplitude, (-0.32 +/- 0.03)%. The cesium weak charge Q_W=-72.66(29)_{exp}(36)_{theor} agrees with the Standard Model value Q_W^{SM}=-73.19(13), the difference is 0.53(48).

29 pages, 2 figures

References in corpus (23)

• Violations of fundamental symmetries in atoms and tests of unification theories of elementary particles
• Measurement of the 6S-7S transition polarizablility in atomic cesium and an improved test of the standard model
• Precise calculation of parity nonconservation in cesium and test of the standard model
• Reconciliation of the Measurement of Parity-Nonconservation in Cs with the Standard Model
• High accuracy calculation of 6s -> 7s parity nonconserving amplitude in Cs
• Radiative corrections and parity nonconservation in heavy atoms
• Measurement of the 6s - 7p transition probabilities in atomic cesium and a revised value for the weak charge Q_W
• QED corrections to the parity-nonconserving 6s-7s amplitude in ${}^{133}$Cs
• Off-Diagonal Hyperfine Interaction and Parity Non-conservation in Cesium
• QED radiative corrections to parity nonconservation in heavy atoms
• Role of Present and Future Atomic Parity Violation Experiments in Precision Electroweak Tests
• Quantum Münchhausen effect in tunneling
• Radiative Corrections to One-Photon Decays of Hydrogenic Ions
• Calculation of radiative corrections to the effect of parity nonconservation in heavy atoms
• Breit interaction correction to the hyperfine constant of an external s-electron in many-electron atom
• Parity nonconservation in heavy atoms: The radiative correction enhanced by the strong electric field of the nucleus
• Vacuum polarization calculations for hydrogenlike and alkalilike ions
• Radiative Corrections to Parity Nonconserving Transitions in Atoms
• Calculation of Radiative Corrections to E1 matrix elements in the Neutral Alkalis
• Relaxation effect and radiative corrections in many-electron atoms
• Influence of perturbations on the electron wave function inside the nucleus
• Z alpha expansion for self-energy radiative corrections to parity nonconservation in atoms
• Vacuum-polarization corrections to the parity-nonconserving 6s-7p transition amplitude in 133Cs

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