Theory of the Lamb shift in muonic helium ions

Krutov, A. A.; Martynenko, A. P.; Martynenko, G. A.; Фаустов, Р. Н.

doi:10.1134/s1063776115010033

Cited by 34 publications

(81 citation statements)

References 35 publications

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“…There was also analyzed a number of relatively subtle effects in the fine and hyperfine structure, which however did not lead to any considerable change in the results (see, for example, [27][28][29][30]). The aim of the present work is to extend our previous calculations of the Lamb shift in muonic helium ions [31] on other muonic ions such as muonic lithium, muonic beryllium and muonic boron. We consistently calculate the contributions of orders α 3 ÷ α 6 within the framework of the quasipotential method in quantum electrodynamics [32][33][34][35].…”

Section: Introductionmentioning

confidence: 99%

“…An estimate of their contribution to the Lamb shift is included in Tables I-III. Finally, there exists another one-loop vacuum polarization correction of order α(Zα) 4 in the Lamb shift known as the Wichmann-Kroll correction [42,43]. Its calculation was discussed repeatedly in [15,31], so we restrict ourselves here by including numerical results in the final Tables as well as the whole light-by-light contribution (see detailed calculation in [44]). Almost all of the corrections presented in this section are written in the integral form, and are therefore specific character for each muon atom.…”

Section: Effects Of Vacuum Polarization In the One-photon Interacmentioning

confidence: 99%

“…Corresponding numerical values which have the order α(Zα) 4 are included in Tables I,II,III. The two-loop vacuum polarization effects in the one-photon interaction can be divided into two parts: loop-after-loop correction (vp-vp) and two-loop vacuum polarization operator correction which we denote further as the "2-loop vp" correction. The potential of loopafter-loop VP effect has the form [10,31]:…”

Section: Effects Of Vacuum Polarization In the One-photon Interacmentioning

confidence: 99%

“…Significantly smaller size are the radiative-recoil corrections of orders α(Zα) 5 and (Z 2 α)(Zα) 4 from the Tables 8-9 [15] (see their explicit form in [31]). Their numerical values we have included in the summary Tables I-III. On the basis of obtained in [54,55] expressions we give an estimate of the nuclear structure corrections of orders (Zα) 6 and α(Zα) 5 to the lamb shift in muonic ions.…”

Section: Recoil Corrections Muon Self-energy and Vacuum Polarizatmentioning

confidence: 99%

“…For the calculation of the Lamb shift contributions we use a representation of the RCGF for 2S− and 2P − states obtained in [47] (see exact expressions forG 2S ,G 2P , g 2S and g 2P in [31]). In the case of the two-loop corrections shown in Fig.1(c), we get the integral expressions for 2S and 2P states…”

Section: Relativistic Corrections With the Account Of Vacuum Polmentioning

confidence: 99%

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Lamb shift in muonic ions of lithium, beryllium, and boron

Krutov

Martynenko

et al. 2016

Phys. Rev. A

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We present a precise calculation of the Lamb shift (2P 1/2 − 2S 1/2 ) in muonic ions (µ 6 3 Li) 2+ , (µ 7 3 Li) 2+ , (µ 9 4 Be) 3+ , (µ 10 4 Be) 3+ , (µ 10 5 B) 4+ , (µ 11 5 B) 4+ . The contributions of orders α 3 ÷α 6 to the vacuum polarization, nuclear structure and recoil, relativistic effects are taken into account. Our numerical results are consistent with previous calculations and improve them due to account of new corrections. The obtained results can be used for the comparison with future experimental data, and extraction more accurate values of nuclear charge radii.

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Section: Introductionmentioning

confidence: 99%

Section: Effects Of Vacuum Polarization In the One-photon Interacmentioning

confidence: 99%

Section: Effects Of Vacuum Polarization In the One-photon Interacmentioning

confidence: 99%

Section: Recoil Corrections Muon Self-energy and Vacuum Polarizatmentioning

confidence: 99%

Section: Relativistic Corrections With the Account Of Vacuum Polmentioning

confidence: 99%

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Lamb shift in muonic ions of lithium, beryllium, and boron

Krutov

Martynenko

et al. 2016

Phys. Rev. A

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Theory of the n=2 levels in muonic deuterium

et al. 2016

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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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Theory of the Lamb shift in muonic helium ions

Cited by 34 publications

References 35 publications

Lamb shift in muonic ions of lithium, beryllium, and boron

Lamb shift in muonic ions of lithium, beryllium, and boron

Theory of the n=2 levels in muonic deuterium

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

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