Nuclear recoil corrections to the Lamb shift of hydrogen and light hydrogenlike ions

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

doi:10.1103/physreva.93.062514

Cited by 21 publications

(18 citation statements)

References 36 publications

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“…where G rec (1S, Z = 1) = 9.720 (3), G rec (2S, Z = 1) = 14.899 (3), δ fns P (nS, H) = −0.000 184 (1) in the case of hydrogen and δ fns P (nS, D) = −0.000 786 (6) for deuteron [28,30]. In the result, the updated contribution is…”

Section: Results and Summarymentioning

confidence: 99%

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Three-photon-exchange nuclear structure correction in hydrogenic systems

2018

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The complete relativistic O(α 2 ) nuclear structure correction to the energy levels of ordinary (electronic) and muonic hydrogen-like atoms is investigated. The elastic part of the nuclear structure correction is derived analytically. The resulting formula is valid for an arbitrary hydrogenic system and is much simpler than analogous expressions previously reported in the literature. The analytical result is verified by high-precision numerical calculations. The inelastic O(α 2 ) nuclear structure correction is derived for the electronic and muonic deuterium atoms. The correction comes from a three-photon exchange between the nucleus and the bound lepton and has not been considered in the literature so far. We demonstrate that in the case of deuterium, the inelastic three-photon exchange contribution is of a similar size and of the opposite sign to the corresponding elastic part and, moreover, cancels exactly the model dependence of the elastic part. The obtained results affect the determination of nuclear charge radii from the Lamb shift in ordinary and muonic atoms.

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Section: Results and Summarymentioning

confidence: 99%

“…(33) of Ref. [21]) is replaced by the complete all-order (in Zα) result by Yerokhin and Shabaev [28,30]. The corresponding correction to the energy is δE(nS) = m 2 M (Zα) 5 πn 3 Zα 4 ln 2 − 7 2 π + (Zα) 2 G rec + δ fns P ,…”

Section: Results and Summarymentioning

confidence: 99%

Three-photon-exchange nuclear structure correction in hydrogenic systems

2018

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“…The higher‐order remainder G REC has an expansion of the form

G_{REC} false(Z α false) = D_{72} {prefixln}^{2} {(Z α)}^{- 2} + D_{71} {prefixln}^{2} false(Z α false) + D_{70} + \dots

where

D_{72} = - 11 / 60 δ_{ℓ 0}

and the next two coefficients were obtained by fitting numerical results in refs. []

D_{71} false(1 S false) = 2.919 false(10 false), D_{70} false(1 S false) = - 1.32 false(10 false)

D_{71} false(2 S false) = 3.335 false(10 false), D_{70} false(2 S false) = - 0.26 false(6 false)

D_{71} false(2 P_{1 / 2} false) = 0.149 false(5 false), D_{70} false(2 P_{1 / 2} false) = - 0.035 false(15 false)

Numerical, all‐order in

Z α

results for the higher‐order remainder G REC are obtained in refs. [] and summarized in Table .…”

Section: Nuclear Recoilmentioning

confidence: 99%

Theory of the Lamb Shift in Hydrogen and Light Hydrogen‐Like Ions

2018

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Theoretical calculations of the Lamb shift provide the basis required for the determination of the Rydberg constant from spectroscopic measurements in hydrogen. The recent high-precision determination of the proton charge radius drastically reduces the uncertainty in the hydrogen Lamb shift originating from the proton size. As a result, the dominant theoretical uncertainty now comes from the two-and three-loop QED effects, which calls for further advances in their calculations. The present status of theoretical calculations of the Lamb shift in hydrogen and light hydrogen-like ions with the nuclear charge number up to Z = 5 is reviewed. Theoretical errors due to various effects are critically examined and estimated. Binding EnergyWe consider the binding energy E njl of an electronic state with quantum numbers n, j , and l in a light hydrogen-like atom. If the atomic nucleus has a nonzero spin I, the energy level |nj l is splitted by the interaction with the nuclear magnetic moment according to values of the total angular momentum F , |nj l F . In

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“…F) for hydrogen and has later been given by Borie [3] for µd, (µ 3 He) + , and (µ 4 He) + . We discard item #18 because it is considered to be included in the elastic TPE [64,65].…”

Section: Qed Lamb Shift In (µ 4 He) +mentioning

confidence: 99%

Theory of the Lamb Shift and fine structure in muonic 4He ions and the muonic 3He– 4He Isotope Shift

et al. 2018

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We provide an up to date summary of the theory contributions to the 2S → 2P Lamb shift and the fine structure of the 2P state in the muonic helium ion (µ 4 He) + . This summary serves as the basis for the extraction of the alpha particle charge radius from the muonic helium Lamb shift measurements at the Paul Scherrer Institute, Switzerland. Individual theory contributions needed for a charge radius extraction are compared and compiled into a consistent summary. The influence of the alpha particle charge distribution on the elastic two-photon exchange is studied to take into account possible model-dependencies of the energy levels on the electric form factor of the nucleus. We also discuss the theory uncertainty which enters the extraction of the 3 He-4 He isotope shift from the muonic measurements. The theory uncertainty of the extraction is much smaller than a present discrepancy between previous isotope shift measurements. This work completes our series of n = 2 theory compilations in light muonic atoms which we have performed already for muonic hydrogen, deuterium, and helium-3 ions.

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Nuclear recoil corrections to the Lamb shift of hydrogen and light hydrogenlike ions

Cited by 21 publications

References 36 publications

Three-photon-exchange nuclear structure correction in hydrogenic systems

Three-photon-exchange nuclear structure correction in hydrogenic systems

Theory of the Lamb Shift in Hydrogen and Light Hydrogen‐Like Ions

Theory of the Lamb Shift and fine structure in muonic 4He ions and the muonic 3He– 4He Isotope Shift

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