Evaluation of the screened QED corrections to the<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mi>g</mml:mi></mml:mrow></mml:math>factor and the hyperfine splitting of lithiumlike ions

Glazov, D. A.; Volotka, A. V.; Shabaev, V. M.; Tupitsyn, I. I.; Plunien, G.

doi:10.1103/physreva.81.062112

Cited by 48 publications

(84 citation statements)

References 70 publications

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“…Theoretical results for various effects were taken from the literature, Refs. [9,[23][24][25][26][27][28]. The total theoretical value is compared to the experimental result [2,29,30].…”

Section: The Weighted Difference Of the 2s And 1s G Factorsmentioning

confidence: 99%

Weighted difference ofgfactors of light Li-like and H-like ions for an improved determination of the fine-structure constant

et al. 2016

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A weighted difference of the g-factors of the Li-and H-like ion of the same element is studied and optimized in order to maximize the cancellation of nuclear effects. To this end, a detailed theoretical investigation is performed for the finite nuclear size correction to the one-electron g-factor, the one-and two-photon exchange effects, and the QED effects. The coefficients of the Zα expansion of these corrections are determined, which allows us to set up the optimal definition of the weighted difference. It is demonstrated that, for moderately light elements, such weighted difference is nearly free from uncertainties associated with nuclear effects and can be utilized to extract the fine-structure constant from bound-electron g-factor experiments with an accuracy competitive with or better than its current literature value.

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“…Theoretical results for various effects were taken from the literature, Refs. [9,[23][24][25][26][27][28]. The total theoretical value is compared to the experimental result [2,29,30].…”

Section: The Weighted Difference Of the 2s And 1s G Factorsmentioning

confidence: 99%

Weighted difference ofgfactors of light Li-like and H-like ions for an improved determination of the fine-structure constant

et al. 2016

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“…This stimulated significant efforts in calculations of the g factor of Li-like ions [51][52][53][54][55][56] .…”

Section: The G Factor Of Li-like Ionsmentioning

confidence: 99%

“…53,54,56 . As in the case of the two-photon exchange diagrams, the calculations were accomplished starting with an effective local potential.…”

Section: The G Factor Of Li-like Ionsmentioning

confidence: 99%

Theory of Bound-Electron g Factor in Highly Charged Ions

Shabaev

Glazov

Plunien

et al. 2015

Journal of Physical and Chemical Reference Data

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The paper presents the current status of the theory of bound-electron g factor in highly charged ions. The calculations of the relativistic, QED, nuclear recoil, nuclear structure, and interelectronic-interaction corrections to the g factor are reviewed. Special attention is paid to tests of QED effects at strong coupling regime and determinations of the fundamental constants. a) Invited paper published as part of the Proceedings of the Fundamental Constants Meeting, Eltville, Germany, February, 1-6, 2015.

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“…Corrections due to the oneand two-electron QED effects were taken from Refs. [8,[18][19][20][21][22]30]. Theoretical results are compared with the experimental value [10,11,24].…”

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confidence: 99%

“…The first one is NRQED (used, e.g., in [28]) that accounts for the nonrelativistic electron-electron interactions to all orders but expands the QED and relativistic effects in α and Zα. The second method (used, e.g., in [19,21,22,30]) accounts for the relativistic effects to all orders in Zα but uses perturbation expansions for QED effects (in α) and for the electron-electron interaction (in 1/Z). Matching the coefficients of Zα and 1/Z expansions of these two methods allows one to merge them together, as it was done for the energy levels in [27].…”

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gFactor of Light Ions for an Improved Determination of the Fine-Structure Constant

et al. 2016

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A weighted difference of the g-factors of the H-and Li-like ions of the same element is theoretically studied and optimized in order to maximize the cancelation of nuclear effects between the two charge states. We show that this weighted difference and its combination for two different elements can be used to extract a value for the fine-structure constant from near-future bound-electron g-factor experiments with an accuracy competitive with or better than the present literature value. PACS numbers: 06.20.Jr, 21.10.Ky, 31.30.jn, 31.15.ac, 32.10.Dk Precision measurements of the free-electron g-factor have enabled determination of the fine-structure constant α to a high accuracy [1, 2]. An independent value of α may be extracted from the measurement of the g-factor of an electron bound in an H-like ion. This can be accomplished by identifying the leading relativistic (Dirac) contribution g D = 2 /3 1 + 2 1 − (Zα) 2 , with Z being the nuclear charge number, after subtracting corrections induced by quantum electrodynamics (QED) and nuclear effects from the measured value. The sensitivity of g D to α is largest for heavy ions. For these ions, however, nuclear effects (charge distributions, polarizabilities etc.) are not well understood and set a limitation on the ultimate accuracy of such determination.In Ref.[3], it was suggested to use a weighted difference of the g-factors of the H-and Li-like charge states of the same element in order to reduce the nuclear size effect by about two orders of magnitude for high-Z ions. In Ref.[4] (see also [5]), a specific weighted difference of the g-factors of heavy H-and B-like ions with the same Z was put forward. It was demonstrated that the theoretical uncertainty of the nuclear size effect in this difference can be brought down to 4 × 10 −10 for heavy ions around Pb, which was several times smaller than the uncertainty due to α at that time. Since then, however, the uncertainty of α was reduced by an order of magnitude [6][7][8], making it more difficult to access α in such experiments. In this Letter we propose a weighted difference of the g-factors of low-Z ions, for which a much stronger cancelation of nuclear effects can be achieved. The low-Z region also seems favorable from the experimental point of view, since experiments so far concentrated in this regime [9][10][11].Measurements of the g-factor of H-like ions have reached the fractional level of accuracy of 3 × 10 −11 [9]. Experiments have also been performed for Li-like ions [10]. In the future, it should be possible to perform experiments not only with a single ion in the trap, but also with several ions simultaneously. Such a setup will directly access differences of g-factors of different ions, greatly reducing systematic uncertainties and possibly gaining two orders of magnitude in accuracy [12]. Such experiments, complemented by corresponding improvements in the theoretical description, would become sensitive to the uncertainty of α.In the present Letter we put forward a method to extract α to higher accura...

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Evaluation of the screened QED corrections to thegfactor and the hyperfine splitting of lithiumlike ions

Cited by 48 publications

References 70 publications

Weighted difference ofgfactors of light Li-like and H-like ions for an improved determination of the fine-structure constant

Weighted difference ofgfactors of light Li-like and H-like ions for an improved determination of the fine-structure constant

Theory of Bound-Electron g Factor in Highly Charged Ions

gFactor of Light Ions for an Improved Determination of the Fine-Structure Constant

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