Accurate vacuum-polarization calculations

Persson, Hans; Lindgren, Ingvar; Salomonson, Sten; Sunnergren, Per

doi:10.1103/physreva.48.2772

Cited by 122 publications

(65 citation statements)

References 25 publications

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“…(19) and (20). Comparison of the numerical results obtained in this work for the Wichmann-Kroll correction with those reported in previous calculations [15,25] is presented in Table V.…”

Section: Ns Correction To Vacuum Polarizationmentioning

confidence: 71%

“…Our result for hydrogen is G h.o. NSE (Z = 1) = 0.075 (25). The Uehling part of the NVP correction is calculated directly, with the result (for the Gaussian model) G NVP,Ue (Z = 1) = 2.5835 α.…”

Section: Results For Hydrogenmentioning

confidence: 99%

“…(19) and (20). Comparison of the numerical results obtained in this work for the Wichmann-Kroll correction with those reported in previous calculations [15,25] is presented in Table V.The nuclear-size vacuum-polarization (NVP) correction is defined as the difference between the oneloop vacuum-polarization corrections evaluated with the point-Coulomb potential and the potential of the extended-charge nucleus. The NVP correction can be parameterized in the same way as the one-loop radiative corrections,…”

mentioning

confidence: 88%

“…We note that Eq. (19) is valid both for the point-nucleus and the extended-nucleus binding potentials.Calculations of the Wichmann-Kroll part of the oneloop vacuum polarization were extensively discussed in the literature over past decades [7,[24][25][26]. In the present work, we perform calculations of the vacuum polarization, evaluating the integrations and the summation over κ in the order specified by Eqs.…”

mentioning

confidence: 99%

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Nuclear-size correction to the Lamb shift of one-electron atoms

Yerokhin

2011

Phys. Rev. A

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The nuclear size effect on the one-loop self energy and vacuum polarization is evaluated for the 1s, 2s, 3s, 2p 1/2 , and 2p 3/2 states of hydrogen-like ions. The calculation is performed to all orders in the binding nuclear strength parameter Zα. Detailed comparison is made with previous all-order calculations and calculations based on the expansion in the parameter Zα. Extrapolation of the all-order numerical results obtained towards Z = 1 provides results for the radiative nuclear size effect on the hydrogen Lamb shift.PACS numbers: 31.30.jf, 12.20.Ds, 31.15.A- IntroductionThe distribution of charge of the nucleus influences the Dirac energies of atomic systems as well as the quantum electrodynamical corrections to the energy levels. This effect, termed as the nuclear size (NS) correction, is important for comparison of theoretical predictions with experimental data for the whole range of the nuclear charges Z, from hydrogen (Z = 1) up to uranium (Z = 92). The NS corrections to the one-loop self energy and vacuum polarization have been previously investigated both within the approach based on the expansion in the nuclear binding strength parameter Zα [1][2][3][4][5][6] (where α is the fine structure constant) and within the numerical approach that accounts the parameter Zα to all orders [7,8]. In the high-Z region, the numerical allorder approach provides accurate predictions for the NS effect on the radiative corrections. For lower Z, however, the NS effect diminishes and becomes increasingly more difficult to identify in a numerical calculation. On the contrary, the Zα-expansion approach provides accurate predictions for the low-Z ions and only the qualitative estimates in the high-Z region. A quantitative cross-check of the two complementary approaches is not simple and has not been accomplished up to now.The NS corrections became of particular interest recently, after the results of the muonic hydrogen Lambshift experiment were announced [9]. It turned out that the value for the proton charge radius r p deduced from the muonic hydrogen differs by five standard deviations from the spectroscopic value of r p derived from the hydrogen atom. This unexplained disagreement stimulates the scientific community to double-check all contributions originating from the nuclear charge distribution, both for the muonic and normal atoms.The aim of the present investigation is to perform an accurate numerical all-order calculation of the NS correction to the one-loop self energy and vacuum polarization and to make a detailed comparison with the Zα-expansion results available.The relativistic units (m = = c = 1) and the charge units α = e 2 /(4π) are used in this paper. I. NS CORRECTION TO DIRAC ENERGYThe leading-order NS correction to the energy levels of a hydrogen-like atom is defined as the difference of the corresponding eigenvalues of the Dirac equation with the point-Coulomb and the extended-nucleus potentials. The two most commonly used models of the nuclear charge distribution are the uniformly charged sphere ("sp...

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“…(19) and (20). Comparison of the numerical results obtained in this work for the Wichmann-Kroll correction with those reported in previous calculations [15,25] is presented in Table V.…”

Section: Ns Correction To Vacuum Polarizationmentioning

confidence: 71%

Section: Results For Hydrogenmentioning

confidence: 99%

mentioning

confidence: 88%

mentioning

confidence: 99%

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Nuclear-size correction to the Lamb shift of one-electron atoms

Yerokhin

2011

Phys. Rev. A

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“…Calculations of the WK contribution in a wide range of Z were performed first by Soff and Mohr [17] for the extended nucleus case and by Manakov et al [18] for the point nucleus case. The most accurate results for some specific ions were obtained by Persson et al [19].…”

Section: H-like Ionsmentioning

confidence: 54%

QED Effects in Heavy Few-Electron Ions

Shabaev

Yerokhin

Zherebtsov

et al. 2001

Atomic Physics at Accelerators: Mass Spectrometry

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Accurate calculations of the binding energies, the hyperfine splitting, the bound-electron g-factor, and the parity nonconservation effects in heavy few-electron ions are considered. The calculations include the relativistic, quantum electrodynamic (QED), electron-correlation, and nuclear effects. The theoretical results are compared with available experimental data. A special attention is focused on tests of QED in a strong Coulomb field.

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Relativistic many-body and QED calculations on atomic systems

Lindgren

1996

Int. J. Quantum Chem.

Self Cite

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mA review is given of many-body perturbation methods, particularly in the all-order and coupled-cluster forms. Relativistic many-body schemes are analyzed in terms of one-and two-photon potentials, derived by means of QED. A complete second-order (nonradiative) calculation for He-like ions is presented, including repeated Breit interactions as well as the effects of retardation and of negative-energy states, but omitting the Lamb shift. Numerical results of some Lamb-shift calculations are also given. From the analysis, conclusions can be drawn concerning the accuracy of certain relativistic many-body approaches.

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Accurate vacuum-polarization calculations

Cited by 122 publications

References 25 publications

Nuclear-size correction to the Lamb shift of one-electron atoms

Nuclear-size correction to the Lamb shift of one-electron atoms

QED Effects in Heavy Few-Electron Ions

Relativistic many-body and QED calculations on atomic systems

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