Radiative-recoil corrections of order<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>α</mml:mi><mml:mo>(</mml:mo><mml:mi>Z</mml:mi><mml:mi>α</mml:mi><mml:mrow><mml:msup><mml:mrow><mml:mo>)</mml:mo></mml:mrow><mml:mrow><mml:mn>5</mml:mn></mml:mrow></mml:msup></mml:mrow><mml:mn /><mml:mo>(</mml:mo><mml:mi>m</mml:mi><mml:mo>/</mml:mo><mml:mi>M</mml:mi><mml:mo>)</mml:mo><mml:mi>m</mml:mi></mml:math>to the Lamb shift revisited

Eides, Michael I.; Grotch, H.; Shelyuto, Valery A.

doi:10.1103/physreva.63.052509

Cited by 47 publications

(53 citation statements)

References 10 publications

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“…In such a case an exact calculation will produce an extra factor 1/(1 + m/M) before the skeleton integral in eq. (280). We have considered above only the nonrecoil contributions, and so we have ignored an extra factor of order m/M, keeping in mind that it would be considered together with other recoil corrections of order α(Zα)E F .…”

Section: Fig 70 Diagrams With Electron-loop Polarization Insertionsmentioning

confidence: 99%

“…Respective contributions once again may be calculated with the help of the skeleton integral in eq. (280) [238,241,242].…”

Section: B Corrections Of Order α 2 (Zα)e Fmentioning

confidence: 99%

“…73 also generate corrections of the previous order in Zα, which would naively induce infrared divergent contributions after substitution in the skeleton integral in eq. (280).…”

Section: B Corrections Of Order α 2 (Zα)e Fmentioning

confidence: 99%

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Theory of light hydrogenlike atoms

2001

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The present status and recent developments in the theory of light hydrogenic atoms, electronic and muonic, are extensively reviewed. The discussion is based on the quantum field theoretical approach to loosely bound composite systems. The basics of the quantum field theoretical approach, which provide the framework needed for a systematic derivation of all higher order corrections to the energy levels, are briefly discussed. The main physical ideas behind the derivation of all binding, recoil, radiative, radiative-recoil, and nonelectromagnetic spin-dependent and spin-independent corrections to energy levels of hydrogenic atoms are discussed and, wherever possible, the fundamental elements of the derivations of these corrections are provided. The emphasis is on new theoretical results which were not available in earlier reviews. An up-to-date set of all theoretical contributions to the energy levels is contained in the paper. The status of modern theory is tested by comparing the theoretical results for the energy levels with the most precise experimental results for the Lamb shifts and gross structure intervals in hydrogen, deuterium, and helium ion He + , and with the experimental data on the hyperfine splitting in muonium, hydrogen and deuterium. *

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Section: Fig 70 Diagrams With Electron-loop Polarization Insertionsmentioning

confidence: 99%

“…Respective contributions once again may be calculated with the help of the skeleton integral in eq. (280) [238,241,242].…”

Section: B Corrections Of Order α 2 (Zα)e Fmentioning

confidence: 99%

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Theory of light hydrogenlike atoms

2001

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“…An insensitive, sterile value is not theoretical, it is rather a mathematical one, and that is the case for the difference ∆(2) and the 2p j energy. Details of theoretical calculations can be found in the review [1]. …”

Section: Hydrogen Lamb Shiftmentioning

confidence: 99%

“…We do not try to review theoretical calculations (if necessary details can be found in Ref. [1]), but present state of art in physics of simple atoms and discuss in detail the theoretical and experimental status of studying such atoms. …”

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Precise physics of simple atoms

Karshenboim¹

2001

AIP Conference Proceedings

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Abstract. We give a review of experimental and theoretical results on the precision study of hydrogen-like atoms with low value of the nuclear charge Z.The simplicity of "simple" atoms has been for a while a challenge to precision theory and experiment. Are the hydrogen-like atomic systems simple enough to be calculated with an accuracy, appropriate to compete with the best experimental results? That is a question, that theorists have tried to answer. The simplest atoms are different two-body bound systems with a low value of the nuclear charge: Z = 1 (hydrogen, deuterium, muonium and positronium) and Z = 2 (ions of helium-3 and helium-4) etc. We do not try to review theoretical calculations (if necessary details can be found in Ref. [1]), but present state of art in physics of simple atoms and discuss in detail the theoretical and experimental status of studying such atoms. LOW-ENERGY TESTS OF QEDThe precise physics of simple atom is the most interesting part of the so-called low-energy tests of Quantum Electrodynamics (QED). Low energy tests of QED offer a number of different options:• A study with free particles provides the possibility of testing the QED Lagrangian for free particles. The most accurate data arise from anomalous magnetic moments of the electron (Kinoshita †2 ) and the muon [2].• However, one knows that the bound problem makes all calculations more complicated. Bound state QED is not a well-established theory. It involves different effective approaches to solve a two-body problem. These approaches can be essentially checked with low Z atomic systems like for e. g. hydrogen 1) Summer address 2) References marked with † correspond to presentations at a satellite meeting to ICAP named Hydrogen atom, 2: Precision physics of simple atomic system and its Proceedings will be published by Springer in 2001.

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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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Radiative-recoil corrections of orderα(Zα)5(m/M)mto the Lamb shift revisited

Cited by 47 publications

References 10 publications

Theory of light hydrogenlike atoms

Theory of light hydrogenlike atoms

Precise physics of simple atoms

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

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