Electron radiative self-energy of highly stripped heavy atoms

Snyderman, N.J.

doi:10.1016/0003-4916(91)90192-b

Cited by 110 publications

(68 citation statements)

References 23 publications

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“…(27) are UV finite, so that there is no need for any UV regularization. There are, however, IR divergences, which appear when the energy of the intermediate electron states in the electron propagators coincides with the energy of the reference state.…”

Section: Double-vertex Contributionmentioning

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: Double-vertex Contributionmentioning

confidence: 99%

QED calculation of the nuclear magnetic shielding for hydrogenlike ions

et al. 2012

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“…They are removed analytically by calculating these terms in the momentum space (for details, we refer to Refs. [22,23,24]). The many-potential terms are evaluated in configuration space.…”

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confidence: 99%

QED Corrections to the Parity-Nonconserving6s−7sAmplitude inCs133

et al. 2005

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The complete gauge-invariant set of the one-loop QED corrections to the parity-nonconserving 6s-7s amplitude in 133 Cs is evaluated to all orders in αZ using a local version of the Dirac-Hartree-Fock potential. The calculations are peformed in both length and velocity gauges for the absorbed photon. The total binding QED correction is found to be -0.27(3)%, which differs from previous evaluations of this effect. The weak charge of 133 Cs, derived using two most accurate values of the vector transition polarizability β, is QW = −72.57(46) for β = 26.957(51)a 3 B and QW = −73.09(54) for β = 27.15(11)a 3 B . The first value deviates by 1.1σ from the prediction of the Standard Model, while the second one is in perfect agreement with it. PACS numbers: 11.30.Er,31.30.Jv,32.80.Ys Investigations of parity noncoservation (PNC) effects in atomic systems play a prominent role in tests of the Standard Model (SM) and impose constraints on physics beyond it [1,2]. The 6s-7s PNC amplitude in 133 Cs [3] remains one of the most attractive subject for such investigations. The measurement of this amplitude to a 0.3% accuracy [4,5] has stimulated a reanalysis of related theoretical contributions. First, it was found [6,7,8,9] that the role of the Breit interaction had been underestimated in previous evaluations of this effect [10,11]. Then, it was pointed out [12] that the QED corrections may be comparable with the Breit corrections. The numerical evaluation of the vacuum-polarization (VP) correction [13] led to a 0.4% increase of the 6s-7s PNC amplitude in 133 Cs, which resulted in a 2.2σ deviation of the weak charge of 133 Cs from the SM prediction. This has triggered a great interest to calculations of the one-loop QED corrections to the PNC amplitude.While the VP contribution can easily be evaluated to a high accuracy within the Uehling approximation, the calculation of the self-energy (SE) contribution is a much more demanding problem (here and below we imply that the SE term embraces all one-loop vertex diagrams as well). To zeroth order in αZ, it was derived in Refs. [14,15]. This correction, whose relative value equals to −α/(2π), is commonly included in the definition of the nuclear weak charge. The αZ-dependent part of the SE correction to the PNC matrix element between s and p states was evaluated in Refs. [16,17]. These calculations, which are exact to first order in αZ and partially include higher-order binding effects, yield the correction of -0.9(1)% [16, 18] and -0.85% [17]. This restored the agreement with SM.Despite of the close agreement of the results obtained in Refs. [17,18], the status of the QED correction to PNC in 133 Cs cannot be considered as resolved until a complete αZ-dependence calculation of the SE correction to the 6s-7s transition amplitude is accomplished. The reasons for that are the following. First, in case of cesium (Z = 55) the parameter αZ ≈ 0.4 is not small and, therefore, the higher-order corrections can be significant. Second, because the calculations [16,17,18] are performed for the...

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“…In order to isolate the ultraviolet divergencies we have used the dimensional regularization and generalized the procedure of [17] for an external magnetic interaction. The infrared divergencies can explicitly be shown to cancel.…”

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confidence: 99%

Self-Energy Correction to the Hyperfine Structure Splitting of Hydrogenlike Atoms

Persson¹,

Schneider

Greiner

et al. 1996

Phys. Rev. Lett.

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A first testing ground for QED in the combined presence of a strong Coulomb field and a strong magnetic field is provided by the precise measurement of the hyperfine structure splitting of hydrogenlike 209 Bi. We present a complete calculation of the one-loop self-energy correction to the first-order hyperfine interaction for various nuclear charges. In the low-Z regime we almost perfectly agree with the Za expansion, but for medium and high Z there is a substantial deviation.PACS numbers: 31.30. Gs, 31.15.Ar, 31.30.Jv Very recently it was reported that for the first time the hyperfine structure splitting of a hydrogenlike high-Z atom was observed with a high relative accuracy of about 10 24 at the ESR at GSI, Darmstadt. The transition energy of the ground state hyperfine structure splitting of 209 Bi 821 was measured to be DE 5.0840͑8͒ eV [1]. This has challenged theory to perform calculations with comparable accuracy, including also one-loop QED corrections. The new experimental situation opens up a possibility to perform a novel test of QED in a combined strong magnetic field and a strong Coulomb field.The leading QED effects are of two types: vacuum polarization and self-energy corrections. The vacuum polarization correction is relatively straightforward to compute, using an Uehling-like approximation. This contribution was calculated to be DE VP 10.035 eV quite recently [2]. The remaining Wichmann-Kroll contribution is very small. The one-loop self-energy correction, on the other hand, is more difficult to elaborate, and earlier calculations using an Za expansion of the Coulomb field are correct only up to order a͑Za͒ 2 mc 2 [3-7]. For heavy elements such an expansion is not reliable. Therefore it is necessary to calculate the self-energy contribution to all orders in Za. In this Letter we present the first complete calculation of this type for different nuclear charges ranging from Z 1 to Z 92 using similar techniques as published earlier in Refs. [8][9][10][11][12].First we give a brief outline of the computation of the self-energy correction and later we discuss the numerical results. A more detailed analysis of the calculation of QED corrections to the hyperfine interaction will be presented in a forthcoming paper [13].In a previous paper it was shown that the unrenormalized self-energy correction for a bound electron state can be written in Feynman gauge as [9] E bou ͑a͒ 2 awhere a m a m ͑1 2 a ? a͒, C ͓l͔ q is the q component of the spherical angular tensor of order l, j l ͑kr͒ denotes the spherical Bessel function of order l, and ja͘ represents the reference state. There is also a corresponding mass counter term.To calculate the self-energy corrections to the hyperfine structure we treat the magnetic potential A͑r ͒ as a perturbation of the system. This perturbation will affect the binding energy of the bound electron, the wave function, and the bound propagator as already sketched out in Ref. [14]

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Electron radiative self-energy of highly stripped heavy atoms

Cited by 110 publications

References 23 publications

QED calculation of the nuclear magnetic shielding for hydrogenlike ions

QED calculation of the nuclear magnetic shielding for hydrogenlike ions

QED Corrections to the Parity-Nonconserving6s−7sAmplitude inCs133

Self-Energy Correction to the Hyperfine Structure Splitting of Hydrogenlike Atoms

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