One-loop self-energy correction in a strong binding field

Yerokhin, V. A.; Pachucki, Krzysztof; Shabaev, V. M.

doi:10.1103/physreva.72.042502

Cited by 25 publications

(30 citation statements)

References 38 publications

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“…So, our present calculation will be largely based on the previous investigations of the self-energy correction to the Lamb shift [28,30], to the hyperfine structure [31][32][33], and to the g factor [32][33][34]. The double-vertex correction of the kind similar to that in the present work appeared in the evaluation of the self-energy correction to the paritynonconserving transitions in Refs.…”

Section: B Self-energy: Calculationmentioning

confidence: 99%

QED calculation of the nuclear magnetic shielding for hydrogenlike ions

et al. 2012

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We report an ab initio calculation of the shielding of the nuclear magnetic moment by the bound electron in hydrogen-like ions. This investigation takes into account several effects that have not been calculated before (electron self-energy, vacuum polarization, nuclear magnetization distribution), thus bringing the theory to the point where further progress is impeded by the uncertainty due to nuclear-structure effects. The QED corrections are calculated to all orders in the nuclear binding strength parameter and, independently, to the leading order in the expansion in this parameter. The results obtained lay the ground for the high-precision determination of nuclear magnetic dipole moments from measurements of the g-factor of hydrogen-like ions.

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Section: B Self-energy: Calculationmentioning

confidence: 99%

QED calculation of the nuclear magnetic shielding for hydrogenlike ions

et al. 2012

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“…[21] is a fast convergence of the partial-wave expansion of the matrix element (6). In the present work, we calculate the difference between the point-nucleus and extended-nucleus matrix elements.…”

Section: Ns Correction To Self Energymentioning

confidence: 99%

“…Numerical, all-order (in Zα) evaluation of the one-loop self-energy correction have been extensively discussed in the literature over past decades [8,[16][17][18][19][20], both for the case of the point-Coulomb and extended-nucleus potentials. In the present investigation, we employ the method developed in our previous work [21] for the case of the point nucleus. This method can be immediately extended to a general (local and spherically-symmetrical) potential, provided that one can calculate the Green function of the Dirac equation with this potential.…”

Section: Ns Correction To Self Energymentioning

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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“…We did this by performing numerical calculations of the one-loop self-energy matrix elements for the ns, np j , and nd j states for Z = 3 − 9 by the method described in Ref. [25] (extending Tables I -IV of Ref. [23]).…”

Section: Qed Effectsmentioning

confidence: 99%

Relativistic configuration-interaction calculations of the energy levels of the 1s22l and 1s2l2l′
Yerokhin
¹
,
Surzhykov
²
,
Müller
³

2017
Phys. Rev. A
34
10
33
3
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We present systematic calculations of energy levels of the 1s 2 2l and 1s2l2l ′ states of ions along the lithium isoelectronic sequence from carbon till chlorine. The calculations are performed by using the relativisticconfiguration-interaction method adapted to the treatment of autoionizing core-excited states. The relativistic energies are supplemented with the QED energy shifts calculated within the model QED operator approach. A systematic estimation of the theoretical uncertainties is performed for every electronic state and every nuclear charge. The results are in agreement with existing high-precision theoretical and experimental data for the ground and first excited states. For the core-excited states, our theory is much more accurate than the presently available measurements.

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One-loop self-energy correction in a strong binding field

Cited by 25 publications

References 38 publications

QED calculation of the nuclear magnetic shielding for hydrogenlike ions

QED calculation of the nuclear magnetic shielding for hydrogenlike ions

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

Relativistic configuration-interaction calculations of the energy levels of the 1s22l and 1s2l2l′
Yerokhin
¹
,
Surzhykov
²
,
Müller
³

2017
Phys. Rev. A
34
10
33
3
View full text Add to dashboard Cite

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One-loop self-energy correction in a strong binding field

Cited by 25 publications

References 38 publications

QED calculation of the nuclear magnetic shielding for hydrogenlike ions

QED calculation of the nuclear magnetic shielding for hydrogenlike ions

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

Relativistic configuration-interaction calculations of the energy levels of the 1s22l and 1s2l2l′Yerokhin1, Surzhykov2, Müller3 2017Phys. Rev. A3410333View full textAdd to dashboardCite

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Relativistic configuration-interaction calculations of the energy levels of the 1s22l and 1s2l2l′
Yerokhin
¹
,
Surzhykov
²
,
Müller
³

2017
Phys. Rev. A
34
10
33
3
View full text Add to dashboard Cite