Radiative Corrections and Parity Nonconservation in Heavy Atoms

Milstein, A. I.; Sushkov, O. P.; Terekhov, I. S.

doi:10.1103/physrevlett.89.283003

Cited by 96 publications

(136 citation statements)

References 40 publications

(68 reference statements)

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“…This way of argument was used in calculating radiative corrections to the PNC amplitude in cesium [9,10,11,12]. Moreover, it was assumed in [10] that to find radiative correction it is sufficient to consider only corrections to the weak matrix elements. Radiative corrections to E1 transition amplitudes and energies were not considered because it was believed that corresponding contritions to the PNC amplitude are small and can be neglected.…”

Section: Resultsmentioning

confidence: 99%

Breit interaction and parity nonconservation in many-electron atoms

2006

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We present accurate ab initio non-perturbative calculations of the Breit correction to the parity non-conserving (PNC) amplitudes of the 6s−7s and 6s−5d 3/2 transitions in Cs, 7s−8s and 7s−6d 3/2 transitions in Fr, 6s − 5d 3/2 transition in Ba + , 7s − 6d 3/2 transition in Ra + , and 6p 1/2 − 6p 3/2 transition in Tl. The results for the 6s − 7s transition in Cs and 7s − 8s transition in Fr are in good agreement with other calculations while calculations for other atoms/transitions are presented for the first time. We demonstrate that higher-orders many-body corrections to the Breit interaction are especially important for the s − d PNC amplitudes. We confirm good agreement of the PNC measurements for cesium and thallium with the standard model .

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Section: Resultsmentioning

confidence: 99%

Breit interaction and parity nonconservation in many-electron atoms

2006

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“…It is interesting to note that for the 2p 3/2 state and high nuclear charges, the correction coming from the Wichmann-Kroll part of the vacuum polarization dominates over the Uehling part. The leading dependence of the NVP correction on R and Zα can be conveniently factorized out in terms of the first-order NS contribution ∆E N [6,22],…”

Section: Ns Correction To Vacuum Polarizationmentioning

confidence: 99%

“…(4) and (5). An important feature of this parametrization [6,22] is that it involves the full NS correction, rather than only the leading term of its Zα expansion. With such choice of normalization, G NSE is a slowly-varying function of Z and its dependence on R is more tractable.…”

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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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“…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 PNC matrix element only, they do not include other SE diagrams which contribute to the 6s-7s transition amplitude. For instance, these calculations do not account for diagrams in which the virtual photon embraces both the weak interaction and the absorbed photon.…”

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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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Radiative Corrections and Parity Nonconservation in Heavy Atoms

Cited by 96 publications

References 40 publications

Breit interaction and parity nonconservation in many-electron atoms

Breit interaction and parity nonconservation in many-electron atoms

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

QED Corrections to the Parity-Nonconserving6s−7sAmplitude inCs133

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