# g Factor of Few-Electron Highly Charged Ions

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## Abstract

**:**

## 1. Introduction

## 2. Li-like Silicon and Calcium

## 3. B-like Argon

## 4. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

- Häffner, H.; Beier, T.; Hermanspahn, N.; Kluge, H.J.; Quint, W.; Stahl, S.; Verdú, J.; Werth, G. High-Accuracy Measurement of the Magnetic Moment Anomaly of the Electron Bound in Hydrogenlike Carbon. Phys. Rev. Lett.
**2000**, 85, 5308. [Google Scholar] [CrossRef] [PubMed] - Verdú, J.; Djekić, S.; Stahl, S.; Valenzuela, T.; Vogel, M.; Werth, G.; Beier, T.; Kluge, H.J.; Quint, W. Electronic g Factor of Hydrogenlike Oxygen
^{16}O^{7+}. Phys. Rev. Lett.**2004**, 92, 093002. [Google Scholar] [CrossRef] [PubMed] - Sturm, S.; Wagner, A.; Schabinger, B.; Zatorski, J.; Harman, Z.; Quint, W.; Werth, G.; Keitel, C.H.; Blaum, K. g Factor of Hydrogenlike
^{28}Si^{13+}. Phys. Rev. Lett.**2011**, 107, 023002. [Google Scholar] [CrossRef] [PubMed] - Sturm, S.; Wagner, A.; Kretzschmar, M.; Quint, W.; Werth, G.; Blaum, K. g-factor measurement of hydrogenlike
^{28}Si^{13+}as a challenge to QED calculations. Phys. Rev. A**2013**, 87, 030501. [Google Scholar] [CrossRef] - Sturm, S.; Köhler, F.; Zatorski, J.; Wagner, A.; Harman, Z.; Werth, G.; Quint, W.; Keitel, C.H.; Blaum, K. High-precision measurement of the atomic mass of the electron. Nature
**2014**, 506, 467. [Google Scholar] [CrossRef] - Shabaev, V.M.; Glazov, D.A.; Plunien, G.; Volotka, A.V. Theory of Bound-Electron g Factor in Highly Charged Ions. J. Phys. Chem. Ref. Data
**2015**, 44, 031205. [Google Scholar] [CrossRef] - Harman, Z.; Sikora, B.; Yerokhin, V.A.; Cakir, H.; Debierre, V.; Michel, N.; Oreshkina, N.S.; Belov, N.A.; Zatorski, J.; Keitel, C.H. The g factor of highly charged ions. J. Phys. Conf. Ser.
**2018**, 1138, 012002. [Google Scholar] [CrossRef] - Indelicato, P. QED Tests with Highly Charged Ions. J. Phys. B
**2019**, 52, 232001. [Google Scholar] [CrossRef] - Czarnecki, A.; Dowling, M.; Piclum, J.; Szafron, R. Two-Loop Binding Corrections to the Electron Gyromagnetic Factor. Phys. Rev. Lett.
**2018**, 120, 043203. [Google Scholar] [CrossRef] - Sikora, B.; Yerokhin, V.A.; Oreshkina, N.S.; Cakir, H.; Keitel, C.H.; Harman, Z. Theory of the two-loop self-energy correction to the g factor in nonperturbative Coulomb fields. Phys. Rev. Res.
**2020**, 2, 012002. [Google Scholar] [CrossRef] - Czarnecki, A.; Piclum, J.; Szafron, R. Logarithmically enhanced Euler-Heisenberg Lagrangian contribution to the electron gyromagnetic factor. Phys. Rev. A
**2020**, 102, 050801. [Google Scholar] [CrossRef] - Debierre, V.; Sikora, B.; Cakir, H.; Oreshkina, N.S.; Yerokhin, V.A.; Keitel, C.H.; Harman, Z. Two-loop virtual light-by-light scattering corrections to the bound-electron g factor. Phys. Rev. A
**2021**, 103, L030802. [Google Scholar] [CrossRef] - Karshenboim, S.G. Non-relativistic calculations of the g-factor of a bound electron. Phys. Lett. A
**2000**, 266, 380. [Google Scholar] [CrossRef] - Glazov, D.A.; Shabaev, V.M. Finite nuclear size correction to the bound-electron g factor in a hydrogenlike atom. Phys. Lett. A
**2002**, 297, 408. [Google Scholar] [CrossRef] - Shabaev, V.M.; Yerokhin, V.A. Recoil Correction to the Bound-Electron g Factor in H-Like Atoms to All Orders in αZ. Phys. Rev. Lett.
**2002**, 88, 091801. [Google Scholar] [CrossRef] - Nefiodov, A.V.; Plunien, G.; Soff, G. Nuclear-Polarization Correction to the Bound-Electron g Factor in Heavy Hydrogenlike Ions. Phys. Rev. Lett.
**2002**, 89, 081802. [Google Scholar] [CrossRef] - Yerokhin, V.A.; Indelicato, P.; Shabaev, V.M. Self-Energy Correction to the Bound-Electron g Factor in H-like Ions. Phys. Rev. Lett.
**2002**, 89, 143001. [Google Scholar] [CrossRef] - Pachucki, K.; Czarnecki, A.; Jentschura, U.D.; Yerokhin, V.A. Complete two-loop correction to the bound-electron g factor. Phys. Rev. A
**2005**, 72, 022108. [Google Scholar] [CrossRef] - Jentschura, U.D. Binding two-loop vacuum-polarization corrections to the bound-electron g factor. Phys. Rev. A
**2009**, 79, 044501. [Google Scholar] [CrossRef] - Yerokhin, V.A.; Harman, Z. Two-loop QED corrections with closed fermion loops for the bound-electron g factor. Phys. Rev. A
**2013**, 88, 042502. [Google Scholar] [CrossRef] - Tiesinga, E.; Mohr, P.J.; Newell, D.B.; Taylor, B.N. CODATA recommended values of the fundamental physical constants: 2018. Rev. Mod. Phys.
**2021**, 93, 025010. [Google Scholar] [CrossRef] - Köhler, F.; Sturm, S.; Kracke, A.; Werth, G.; Quint, W.; Blaum, K. The electron mass from g-factor measurements on hydrogen-like carbon
^{12}C^{5+}. J. Phys. B**2015**, 48, 144032. [Google Scholar] [CrossRef] - Zatorski, J.; Sikora, B.; Karshenboim, S.G.; Sturm, S.; Köhler-Langes, F.; Blaum, K.; Keitel, C.H.; Harman, Z. Extraction of the electron mass from g-factor measurements on light hydrogenlike ions. Phys. Rev. A
**2017**, 96, 012502. [Google Scholar] [CrossRef] - Shabaev, V.M.; Glazov, D.A.; Shabaeva, M.B.; Yerokhin, V.A.; Plunien, G.; Soff, G. g factor of high-Z lithiumlike ions. Phys. Rev. A
**2002**, 65, 062104. [Google Scholar] [CrossRef] - Shabaev, V.M.; Glazov, D.A.; Oreshkina, N.S.; Volotka, A.V.; Plunien, G.; Kluge, H.J.; Quint, W. g-Factor of Heavy Ions: A New Access to the Fine Structure Constant. Phys. Rev. Lett.
**2006**, 96, 253002. [Google Scholar] [CrossRef] - Volotka, A.V.; Plunien, G. Nuclear polarization study: New frontiers for tests of QED in heavy highly charged ions. Phys. Rev. Lett.
**2014**, 113, 023002. [Google Scholar] [CrossRef] - Yerokhin, V.A.; Berseneva, E.; Harman, Z.; Tupitsyn, I.I.; Keitel, C.H. g Factor of Light Ions for an Improved Determination of the Fine-Structure Constant. Phys. Rev. Lett.
**2016**, 116, 100801. [Google Scholar] [CrossRef] - Malyshev, A.V.; Shabaev, V.M.; Glazov, D.A.; Tupitsyn, I.I. Nuclear recoil effect on g-factor of heavy ions: Prospects for tests of quantum electrodynamics in a new region. JETP Lett.
**2017**, 106, 765. [Google Scholar] [CrossRef] - Cakir, H.; Oreshkina, N.S.; Valuev, I.A.; Debierre, V.; Yerokhin, V.A.; Keitel, C.H.; Harman, Z. Improved access to the fine-structure constant with the simplest atomic systems. arXiv
**2020**, arXiv:2006.14261. [Google Scholar] - Köhler, F.; Blaum, K.; Block, M.; Chenmarev, S.; Eliseev, S.; Glazov, D.A.; Goncharov, M.; Hou, J.; Kracke, A.; Nesterenko, D.A.; et al. Isotope dependence of the Zeeman effect in lithium-like calcium. Nat. Commun.
**2016**, 7, 10246. [Google Scholar] [CrossRef] - Shabaev, V.M.; Glazov, D.A.; Malyshev, A.V.; Tupitsyn, I.I. Recoil Effect on the g Factor of Li-Like Ions. Phys. Rev. Lett.
**2017**, 119, 263001. [Google Scholar] [CrossRef] [PubMed] - Shabaev, V.M.; Glazov, D.A.; Malyshev, A.V.; Tupitsyn, I.I. Nuclear recoil effect on the g factor of highly charged Li-like ions. Phys. Rev. A
**2018**, 98, 032512. [Google Scholar] [CrossRef] - Sailer, T.; Debierre, V.; Harman, Z.; Heiße, F.; König, C.; Morgner, J.; Tu, B.; Volotka, A.V.; Keitel, C.H.; Blaum, K.; et al. Measurement of the bound-electron g-factor difference in coupled ions. Nature
**2022**, 606, 479. [Google Scholar] [CrossRef] [PubMed] - Debierre, V.; Keitel, C.; Harman, Z. Fifth-force search with the bound-electron g factor. Phys. Lett. B
**2020**, 807, 135527. [Google Scholar] [CrossRef] - Debierre, V.; Oreshkina, N.S.; Valuev, I.A.; Harman, Z.; Keitel, C.H. Testing standard-model extensions with isotope shifts in few-electron ions. Phys. Rev. A
**2022**, 106, 062801. [Google Scholar] [CrossRef] - Wagner, A.; Sturm, S.; Köhler, F.; Glazov, D.A.; Volotka, A.V.; Plunien, G.; Quint, W.; Werth, G.; Shabaev, V.M.; Blaum, K. g factor of lithiumlike silicon
^{28}Si^{11+}. Phys. Rev. Lett.**2013**, 110, 033003. [Google Scholar] [CrossRef] - Glazov, D.A.; Köhler-Langes, F.; Volotka, A.V.; Blaum, K.; Heiße, F.; Plunien, G.; Quint, W.; Rau, S.; Shabaev, V.M.; Sturm, S.; et al. g Factor of Lithiumlike Silicon: New Challenge to Bound-State QED. Phys. Rev. Lett.
**2019**, 123, 173001. [Google Scholar] [CrossRef] - Arapoglou, I.; Egl, A.; Höcker, M.; Sailer, T.; Tu, B.; Weigel, A.; Wolf, R.; Cakir, H.; Yerokhin, V.A.; Oreshkina, N.S.; et al. The g-factor of Boronlike Argon
^{40}Ar^{13+}. Phys. Rev. Lett.**2019**, 122, 253001. [Google Scholar] [CrossRef] - Egl, A.; Arapoglou, I.; Höcker, M.; König, K.; Ratajczyk, T.; Sailer, T.; Tu, B.; Weigel, A.; Blaum, K.; Nörtershäuser, W.; et al. Application of the Continuous Stern-Gerlach Effect for Laser Spectroscopy of the
^{40}Ar^{13+}Fine Structure in a Penning Trap. Phys. Rev. Lett.**2019**, 123, 123001. [Google Scholar] [CrossRef] - Micke, P.; Leopold, T.; King, S.A.; Benkler, E.; Spieß, L.J.; Schmöger, L.; Schwarz, M.; López-Urrutia, J.R.C.; Schmidt, P.O. Coherent laser spectroscopy of highly charged ions using quantum logic. Nature
**2020**, 578, 60–65. [Google Scholar] [CrossRef] - Volotka, A.V.; Glazov, D.A.; Shabaev, V.M.; Tupitsyn, I.I.; Plunien, G. Many-Electron QED Corrections to the g Factor of Lithiumlike Ions. Phys. Rev. Lett.
**2014**, 112, 253004. [Google Scholar] [CrossRef] - Yerokhin, V.A.; Keitel, C.H.; Harman, Z. Two-photon-exchange corrections to the g factor of Li-like ions. Phys. Rev. A
**2021**, 104, 022814. [Google Scholar] [CrossRef] - Kosheleva, V.P.; Volotka, A.V.; Glazov, D.A.; Zinenko, D.V.; Fritzsche, S. g Factor of Lithiumlike Silicon and Calcium: Resolving the Disagreement between Theory and Experiment. Phys. Rev. Lett.
**2022**, 128, 103001. [Google Scholar] [CrossRef] [PubMed] - Zinenko, D.V.; Glazov, D.A.; Kosheleva, V.P.; Volotka, A.V.; Fritzsche, S. Electron correlation effects on the g factor of lithiumlike ions. Phys. Rev. A
**2023**, 107, 032815. [Google Scholar] [CrossRef] - Volotka, A.V.; Glazov, D.A.; Shabaev, V.M.; Tupitsyn, I.I.; Plunien, G. Screened QED corrections in lithiumlike heavy ions in the presence of magnetic fields. Phys. Rev. Lett.
**2009**, 103, 033005. [Google Scholar] [CrossRef] [PubMed] - Glazov, D.A.; Volotka, A.V.; Shabaev, V.M.; Tupitsyn, I.I.; Plunien, G. Evaluation of the screened QED corrections to the g factor and the hyperfine splitting of lithiumlike ions. Phys. Rev. A
**2010**, 81, 062112. [Google Scholar] [CrossRef] - Volotka, A.V.; Glazov, D.A.; Andreev, O.V.; Shabaev, V.M.; Tupitsyn, I.I.; Plunien, G. Test of Many-Electron QED Effects in the Hyperfine Splitting of Heavy High-Z Ions. Phys. Rev. Lett.
**2012**, 108, 073001. [Google Scholar] [CrossRef] - Andreev, O.V.; Glazov, D.A.; Volotka, A.V.; Shabaev, V.M.; Plunien, G. Evaluation of the screened vacuum-polarization corrections to the hyperfine splitting of Li-like bismuth. Phys. Rev. A
**2012**, 85, 022510. [Google Scholar] [CrossRef] - Cakir, H.; Yerokhin, V.A.; Oreshkina, N.S.; Sikora, B.; Tupitsyn, I.I.; Keitel, C.H.; Harman, Z. QED corrections to the g factor of Li- and B-like ions. Phys. Rev. A
**2020**, 101, 062513. [Google Scholar] [CrossRef] - Yerokhin, V.A.; Pachucki, K.; Puchalski, M.; Keitel, C.H.; Harman, Z. Self-energy screening effects in the g factor of Li-like ions. Phys. Rev. A
**2020**, 102, 022815. [Google Scholar] [CrossRef] - Glazov, D.A.; Volotka, A.V.; Schepetnov, A.A.; Sokolov, M.M.; Shabaev, V.M.; Tupitsyn, I.I.; Plunien, G. g factor of boron-like ions: Ground and excited states. Phys. Scr.
**2013**, T156, 014014. [Google Scholar] [CrossRef] - Verdebout, S.; Nazé, C.; Jönsson, P.; Rynkun, P.; Godefroid, M.; Gaigalas, G. Hyperfine structures and Landé g
_{J}-factors for n = 2 states in beryllium-, boron-, carbon-, and nitrogen-like ions from relativistic configuration interaction calculations. At. Data Nucl. Data Tables**2014**, 100, 1111. [Google Scholar] [CrossRef] - Shchepetnov, A.A.; Glazov, D.A.; Volotka, A.V.; Shabaev, V.M.; Tupitsyn, I.I.; Plunien, G. Nuclear recoil correction to the g factor of boron-like argon. J. Phys. Conf. Ser.
**2015**, 583, 012001. [Google Scholar] [CrossRef] - Marques, J.P.; Indelicato, P.; Parente, F.; Sampaio, J.M.; Santos, J.P. Ground-state Landé g factors for selected ions along the boron isoelectronic sequence. Phys. Rev. A
**2016**, 94, 042504. [Google Scholar] [CrossRef] - Agababaev, V.A.; Glazov, D.A.; Volotka, A.V.; Zinenko, D.V.; Shabaev, V.M.; Plunien, G. Ground-state g factor of middle-Z boronlike ions. J. Phys. Conf. Ser.
**2018**, 1138, 012003. [Google Scholar] [CrossRef] - Maison, D.E.; Skripnikov, L.V.; Glazov, D.A. Many-body study of the g factor in boronlike argon. Phys. Rev. A
**2019**, 99, 042506. [Google Scholar] [CrossRef] - Agababaev, V.A.; Glazov, D.A.; Volotka, A.V.; Zinenko, D.V.; Shabaev, V.M.; Plunien, G. G Factor of the [(1 s)
^{2}(2 s)^{2}2 p]^{2}P_{3/2}State of Middle- Z Boronlike Ions. X-ray Spectrom.**2020**, 49, 143. [Google Scholar] [CrossRef] - Hegstrom, R.A. Magnetic moment of atomic lithium. Phys. Rev. A
**1975**, 11, 421–426. [Google Scholar] [CrossRef] - Yan, Z.C. Calculations of Magnetic Moments for Three-Electron Atomic Systems. Phys. Rev. Lett.
**2001**, 86, 5683. [Google Scholar] [CrossRef] - Yan, Z.C. Calculations of magnetic moments for lithium-like ions. J. Phys. B
**2002**, 35, 1885. [Google Scholar] [CrossRef] - Yerokhin, V.A.; Pachucki, K.; Puchalski, M.; Harman, Z.; Keitel, C.H. Electron-correlation effects in the g factor of light Li-like ions. Phys. Rev. A
**2017**, 95, 062511. [Google Scholar] [CrossRef] - Yerokhin, V.A.; Indelicato, P.; Shabaev, V.M. Evaluation of the self-energy correction to the g factor of S states in H-like ions. Phys. Rev. A
**2004**, 69, 052503. [Google Scholar] [CrossRef] - Glazov, D.A.; Shabaev, V.M.; Tupitsyn, I.I.; Volotka, A.V.; Yerokhin, V.A.; Plunien, G.; Soff, G. Relativistic and QED corrections to the g factor of Li-like ions. Phys. Rev. A
**2004**, 70, 062104. [Google Scholar] [CrossRef] - Glazov, D.A.; Volotka, A.V.; Shabaev, V.M.; Tupitsyn, I.I.; Plunien, G. Screened QED corrections to the g factor of Li-like ions. Phys. Lett. A
**2006**, 357, 330. [Google Scholar] [CrossRef] - Yerokhin, V.A.; Harman, Z. One-loop electron self-energy for the bound-electron g factor. Phys. Rev. A
**2017**, 95, 060501(R). [Google Scholar] [CrossRef] - Glazov, D.; Malyshev, A.; Volotka, A.; Shabaev, V.; Tupitsyn, I.; Plunien, G. Higher-order perturbative relativistic calculations for few-electron atoms and ions. Nucl. Instr. Meth. Phys. Res. B
**2017**, 408, 46. [Google Scholar] [CrossRef] - Yerokhin, V.A.; Glazov, D.A.; Volotka, A.V. to be published.
- Tryapitsyna, E.V.; et al. to be published.
- Grotch, H.; Kashuba, R. Magnetic Interactions of One-Electron Atoms and of Positronium. Phys. Rev. A
**1973**, 7, 78. [Google Scholar] [CrossRef] - Glazov, D.A.; Malyshev, A.V.; Shabaev, V.M.; Tupitsyn, I.I. Interelectronic-interaction contribution to the nuclear recoil effect on the g factor of boronlike ions. Phys. Rev. A
**2020**, 101, 012515. [Google Scholar] [CrossRef] - Malyshev, A.V.; Glazov, D.A.; Aleksandrov, I.A.; Tupitsyn, I.I.; Shabaev, V.M. Relativistic Calculation of the Nuclear Recoil Effect on the g Factor of the
^{2}P_{3/2}State in Highly Charged B-like Ions. Opt. Spectrosc.**2020**, 128, 297. [Google Scholar] [CrossRef] - Angeli, I.; Marinova, K.P. Table of Experimental Nuclear Ground State Charge Radii: An Update. At. Data Nucl. Data Tables
**2013**, 99, 69. [Google Scholar] [CrossRef]

**Figure 1.**Interelectronic–interaction and QED contributions to the g factor of Li-like silicon and calcium calculated with different binding potentials: Coulomb, core–Hartree, Dirac–Hartree, Kohn–Sham, and Dirac–Slater (see reference [44] for definitions of the potentials).

**Table 1.**Theoretical and experimental values of the ground-state g factor of Li-like silicon and calcium ions.

${}^{28}{\mathbf{Si}}^{11+}$ | ${}^{40}{\mathbf{Ca}}^{17+}$ | |
---|---|---|

${g}_{\mathrm{th}}$ [Wagner et al. (2013) [36]] | 2.000 889 909 (51) | |

${g}_{\mathrm{th}}$ [Volotka et al. (2014) [41]] | 2.000 889 892 (8) | 1.999 202 041 (13) |

${g}_{\mathrm{th}}$ [Köhler et al. (2016) [30]] | 1.999 202 042 (13) | |

${g}_{\mathrm{th}}$ [Glazov et al. (2019) [37]] | 2.000 889 894 4 (34) | |

${g}_{\mathrm{th}}$ [Yerokhin et al. (2020) [50]] | 2.000 889 896 3 (15) | |

${g}_{\mathrm{th}}$ [Yerokhin et al. (2021) [42]] | 2.000 889 893 7 (17) | 1.999 202 052 9 (27) |

${g}_{\mathrm{th}}$ [Kosheleva et al. (2022) [43]] | 2.000 889 892 4 (28) | 1.999 202 042 6 (29) |

${g}_{\mathrm{exp}}$ [Wagner et al. (2013) [36]] | 2.000 889 889 9 (21) | |

${g}_{\mathrm{exp}}$ [Köhler et al. (2016) [30]] | 1.999 202 040 5 (11) | |

${g}_{\mathrm{exp}}$ [Glazov et al. (2019) [37]] | 2.000 889 888 45 (14) |

**Table 2.**Theoretical and experimental values of the g factor of the ground and first excited states of B-like argon ion ${}^{40}{\mathrm{Ar}}^{13+}$.

$2{\mathit{P}}_{1/2}$ | $2{\mathit{P}}_{3/2}$ | |
---|---|---|

${g}_{\mathrm{th}}$ [Glazov et al. (2013) [51]] | 0.663 647 (1) | 1.332 285 (3) |

${g}_{\mathrm{th}}$ [Verdebout et al. (2014) [52]] | 0.663 728 | 1.332 365 |

${g}_{\mathrm{th}}$ [Shchepetnov et al. (2015) [53]] | 0.663 647 7 (7) | 1.332 282 (3) |

${g}_{\mathrm{th}}$ [Marques et al. (2016) [54]] | 0.663 899 (2) | 1.332 372 (1) |

${g}_{\mathrm{th}}$ [Agababaev et al. (2018) [55]] | 0.663 648 8 (12) | |

${g}_{\mathrm{th}}$ [Agababaev et al. (2019) [57]] | 1.332 282 5 (14) | |

${g}_{\mathrm{th}}$ [Maison et al. (2019) [56]] | 0.663 652 (3)(6) | 1.332 286 (3)(6) |

${g}_{\mathrm{th}}$ [Cakir et al. (2020) [49]] | 0.663 648 1 (5) | |

${g}_{\mathrm{exp}}$ [Arapoglou et al. (2019) [38]] | 0.663 648 454 63 (93) | |

${g}_{\mathrm{exp}}$ [Egl et al. (2019) [39]] | 1.332 14 (15) | |

${g}_{\mathrm{exp}}$ [Micke et al. (2020) [40]] | 1.332 289 5 (13)(56) |

**Table 3.**Contributions to the g factor of the ground and first excited states of B-like lead ion ${}_{82}^{208}$Pb${}^{77+}$.

$2{\mathit{P}}_{1/2}$ | $2{\mathit{P}}_{3/2}$ | |
---|---|---|

Dirac value ${g}_{\mathrm{D}}$ | 0.598 669 571 | 1.284 472 641 |

Interelectronic interaction $\Delta {g}_{\mathrm{int}}$ | 0.003 639 3 (23) | 0.002 501 7 (23) |

One-loop QED $\Delta {g}_{\mathrm{QED}}^{\left(1\right)}$ | −0.000 501 6 (66) | 0.000 945 3 (50) |

Two-loop QED $\Delta {g}_{\mathrm{QED}}^{\left(2\right)}$ | 0.000 001 2 (8) | −0.000 001 2 (8) |

Nuclear recoil $\Delta {g}_{\mathrm{rec}}$ | −0.000 001 8 | −0.000 000 7 |

Finite nuclear size $\Delta {g}_{\mathrm{NS}}^{}$ | 0.000 006 8 | 0.000 000 0 |

Total value ${g}_{\mathrm{th}}$ | 0.601 813 5 (70) | 1.287 917 7 (56) |

${g}_{\mathrm{th}}$ [Marques et al. (2016) [54]] | 0.602 860 (33) | 1.288 318 (24) |

${g}_{\mathrm{th}}$ [Cakir et al. (2020) [49]] | 0.601 815 6 (18) |

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Glazov, D.A.; Zinenko, D.V.; Agababaev, V.A.; Moshkin, A.D.; Tryapitsyna, E.V.; Volchkova, A.M.; Volotka, A.V.
*g* Factor of Few-Electron Highly Charged Ions. *Atoms* **2023**, *11*, 119.
https://doi.org/10.3390/atoms11090119

**AMA Style**

Glazov DA, Zinenko DV, Agababaev VA, Moshkin AD, Tryapitsyna EV, Volchkova AM, Volotka AV.
*g* Factor of Few-Electron Highly Charged Ions. *Atoms*. 2023; 11(9):119.
https://doi.org/10.3390/atoms11090119

**Chicago/Turabian Style**

Glazov, Dmitry A., Dmitrii V. Zinenko, Valentin A. Agababaev, Artyom D. Moshkin, Elizaveta V. Tryapitsyna, Anna M. Volchkova, and Andrey V. Volotka.
2023. "*g* Factor of Few-Electron Highly Charged Ions" *Atoms* 11, no. 9: 119.
https://doi.org/10.3390/atoms11090119