Ядерное магнитное экранирование и квадратичный эффект Зеемана в ионах, подобных гелию

Авторы

  • Валентин Александрович Агабабаев Университет ИТМО https://orcid.org/0000-0003-3400-5910
  • Дмитрий Алексеевич Глазов Университет ИТМО; «Петербургский институт ядерной физики имени Б. П. Константинова» Национального исследовательского центра «Курчатовский институт» https://orcid.org/0000-0002-4158-6963
  • Матвей Максимович Осипцов Университет ИТМО
  • Андрей Викторович Волотка Университет ИТМО https://orcid.org/0000-0001-8439-1472
  • Владимир Моисеевич Шабаев Санкт-Петербургский государственный университет https://orcid.org/0000-0002-2769-6891

DOI:

https://doi.org/10.33910/2687-153X-2026-7-2-84-91

Ключевые слова:

эффект Зеемана, g-фактор, многозарядные ионы, КЭД связанных состояний, ядерное магнитное экранирование, сверхтонкая структура

Аннотация

Квадратичный эффект Зеемана и сверхтонкое магнитное экранирование рас­считаны в гелиеподобных ионах в основном (1s)2 состоянии с помощью теории возмущений. Численные значения получены для диапазона зарядов ядра Z = 6 – 32. Зеемановское расщепле­ние оценивается путем решения уравнения Дирака в кулоновском поле с конечным ядром с использованием B-сплайнов, построенных в рамках метода ДКБ. Вклады ведущего порядка, а также однофотонные обменные поправки рассматриваются в рамках строгого подхода КЭД. Рассчитанные константы ядерного магнитного экранирования могут быть использованы для определения ядерных магнитных моментов, в то время как квадратичный эффект Зеемана имеет значение для прецизионных измерений энергий переходов в гелиеподобных ионах в ло­вушках Пеннинга.

Библиографические ссылки

Agababaev, V. A., Volchkova, A. M., Varentsova, A. S. et al. (2017) Quadratic Zeeman effect in boronlike argon. Nuclear Instruments and Methods in Physics Research Section B: Beam Interactions with Materials and Atoms, 408, 70–73. https://doi.org/10.1016/j.nimb.2017.03.130 (In English)

Arapoglou, I., Egl, A., Höcker, M. et al. (2019) g factor of boronlike argon 40Ar13+. Physical Review Letters, 122 (25), article 253001. https://doi.org/10.1103/PhysRevLett.122.253001 (In English)

Beiersdorfer, P., Brown, G. V. (2015) Experimental study of the x-ray transitions in the heliumlike isoelectronic sequence: Updated results. Physical Review A, 91 (3), article 032514. https://doi.org/10.1103/PhysRevA.91.032514 (In English)

Egl, A., Arapoglou, I., Höcker, M. et al. (2019) Application of the continuous Stern-Gerlach effect for laser spectroscopy of the 40Ar13+ fine structure in a Penning trap. Physical Review Letters, 123 (12), article 123001. https://doi.org/10.1103/PhysRevLett.123.123001 (In English)

Epp, S. W., Steinbrügge, R., Bernitt, S. et al. (2015) Single-photon excitation of K α in heliumlike Kr34+: Results supporting quantum electrodynamics predictions. Physical Review A, 92 (2), article 020502. https://doi.org/10.1103/PhysRevA.92.020502 (In English)

Feinberg, G., Rich, A., Sucher, J. (1990) Quadratic Zeeman effect in positronium. Physical Review A, 41 (7), 3478–3480. https://doi.org/10.1103/PhysRevA.41.3478 (In English)

Fella, V., Skripnikov, L. V., Nörtershäuser, W. et al. (2020) Magnetic moment of 207Pb and the hyperfine splitting of 207Pb81+. Physical Review Research, 2 (1), article 013368. https://doi.org/10.1103/PhysRevResearch.2.013368 (In English)

Glazov, D. A., Köhler-Langes, F., Volotka, A. V. et al. (2019) g factor of lithiumlike silicon: New challenge to bound-state QED. Physical Review Letters, 123 (17), article 173001. (In English)

Glazov, D. A., Volotka, A. V., Schepetnov, A. A. et al. (2013) g factor of boron-like ions: Ground and excited states. Physica Scripta, T156, article 014014. https://doi.org/10.1088/0031-8949/2013/T156/014014 (In English)

Grozdanov, T. P., Taylor, H. S. (1986) Second-order perturbation calculations for the hydrogenic Zeeman effect. Journal of Physics B: Atomic and Molecular Physics, 19 (24), 4075–4085. (In English)

Harman, Z., Sikora, B., Yerokhin, V. A. et al. (2018) The g factor of highly charged ions. Journal of Physics: Conference Series, 1138 (1), article 012002. (In English)

Kozhedub, Y. S., Malyshev, A. V., Glazov, D. A. et al. (2019) QED calculation of electron-electron correlation effects in heliumlike ions. Physical Review A, 100 (6), article 062506. https://doi.org/10.1103/PhysRevA.100.062506 (In English)

Loetzsch, R., Beyer, H. F., Duval, L. et al. (2024) Testing quantum electrodynamics in extreme fields using helium-like uranium. Nature, 625 (7996), 673–678. https://doi.org/10.1038/s41586-023-06910-y (In English)

Machado, J., Szabo, C. I., Santos, J. P. et al. (2018) High-precision measurements of n = 2 → n = 1 transition energies and level widths in He- and Be-like argon ions. Physical Review A, 97 (3), article 032517. https://doi.org/10.1103/PhysRevA.97.032517 (In English)

Malyshev, A. V., Kozhedub, Y. S., Glazov, D. A. et al. (2019) QED calculations of the n = 2 to n = 1 x-ray transition energies in middle-Z heliumlike ions. Physical Review A, 99 (1), article 010501. https://doi.org/10.1103/PhysRevA.99.010501 (In English)

Malyshev, A. V., Kozhedub, Y. S., Shabaev, V. M. (2023) Ab initio calculations of the 2p3/2 → 2s transition in He-, Li-, and Be-like uranium. Physical Review A, 107 (4), article 042806. https://doi.org/10.1103/PhysRevA.107.042806 (In English)

Manakov, N. L., Rapoport, L. P., Zapryagaev, S. A. (1974) Relativistic electromagnetic susceptibilities of hydrogen-like atoms. Journal of Physics B: Atomic and Molecular Physics, 7 (9), article 1076. https://doi.org/10.1088/0022-3700/7/9/019 (In English)

Manakov, N. L., Zapryagaev, S. A. (1976) A reduced Green function of the Dirac equation with a Coulomb potential. Second order Zeeman effect. Physics Letters A, 58 (1), 23–25. (In English)

Micke, P., Leopold, T., King, S. A. et al. (2020) Coherent laser spectroscopy of highly charged ions using quantum logic. Nature, 578 (7793), 60–65. https://doi.org/10.1038/s41586-020-1959-8 (In English)

Moore, E. A. (1999) Relativistic chemical shielding: Formally exact solutions for one-electron atoms of maximum total angular momentum for any principal quantum number. Molecular Physics, 97 (3), 375–380. https://doi.org/10.1080/00268979909482838 (In English)

Morgner, J., Tu, B., Moretti, M. et al. (2025) g factor of boronlike tin. Physical Review Letters, 134 (12), article 123201. https://doi.org/10.1103/PhysRevLett.134.123201 (In English)

Moskovkin, D. L., Oreshkina, N. S., Shabaev, V. M. et al. (2004) g factor of hydrogenlike ions with nonzero nuclear spin. Physical Review A, 70 (30), article 032105. https://doi.org/10.1103/PhysRevA.70.032105 (In English)

Moskovkin, D. L., Shabaev, V. M. (2006) Zeeman effect of the hyperfine-structure levels in hydrogenlike ions. Physical Review A, 73 (5), article 052506. https://doi.org/10.1103/PhysRevA.73.052506 (In English)

Moskovkin, D. L., Shabaev, V. M., Quint, W. (2008a) g factor of Li-like ions with a nonzero nuclear spin. Optics and Spectroscopy, 104 (5), 637–649. https://doi.org/10.1134/S0030400X08050019 (In English)

Moskovkin, D. L., Shabaev, V. M., Quint, W. (2008b) Zeeman effect of the hyperfine-structure levels in lithiumlike ions. Physical Review A, 77 (6), article 063421. https://doi.org/10.1103/PhysRevA.77.063421 (In English)

Pyper, N. C. (1999) Relativistic theory of nuclear shielding in one-electron atoms 1. Theoretical foundations and first-order terms. Molecular Physics, 97 (3), 381–390. https://doi.org/10.1080/00268979909482839 (In English)

Pyper, N. C., Zhang, Z. C. (1999) Relativistic theory of nuclear shielding in one-electron atoms 2. Analytical and numerical results. Molecular Physics, 97 (3), 391–413. https://doi.org/10.1080/00268979909482840 (In English)

Quint, W., Moskovkhin, D. L., Shabaev, V. M., Vogel, M. (2008) Laser-microwave double-resonance technique for g-factor measurements in highly charged ions. Physical Review A, 78 (3), article 032517. https://doi.org/10.1103/PhysRevA.78.032517 (In English)

Shabaev, V. M. (1994) Hyperfine structure of hydrogen-like ions. Journal of Physics B: Atomic, Molecular and Optical Physics, 27 (24), 5825–5832. https://doi.org/10.1088/0953-4075/27/24/006 (In English)

Shabaev, V. M., Glazov, D. A., Plunien, G., Volotka, A. V. (2015) Theory of bound-electron g factor in highly charged ions. Journal of Physical and Chemical Reference Data, 44 (3), article 031205. https://doi.org/10.1063/1.4921299 (In English)

Shabaev, V. M., Tupitsyn, I. I., Yerokhin, V. A. et al. (2004) Dual kinetic balance approach to basis-set expansions for the Dirac equation. Physical Review Letters, 93 (13), article 130405. https://doi.org/10.1103/PhysRevLett.93.130405 (In English)

Skripnikov, L. V., Schmidt, S., Ullmann, J. et al. (2018) New nuclear magnetic moment of 209Bi: Resolving the bismuth hyperfine puzzle. Physical Review Letters, 120 (9), article 093001. https://doi.org/10.1103/PhysRevLett.120.093001 (In English)

Sturm, S., Köhler, F., Zatorski, J. et al. (2014) High-precision measurement of the atomic mass of the electron. Nature, 506 (7489), 467–470. https://doi.org/10.1038/nature13026 (In English)

Sturm, S., Vogel, M., Köhler-Langes, F. et al. (2017) High-precision measurements of the bound electron’s magnetic moment. Atoms, 5 (1), article 4. (In English)

Szmytkowski, R. (2002a) Magnetizability of the relativistic hydrogen-like atom: Application of the Sturmian expansion of the first-order Dirac-Coulomb Green function. Journal of Physics B: Atomic, Molecular and Optical Physics, 35 (5), 1379–1391. https://doi.org/10.1088/0953-4075/35/5/319 (In English)

Szmytkowski, R. (2002b) Larmor diamagnetism and Van Vleck paramagnetism in relativistic quantum theory: The Gordon decomposition approach. Physical Review A, 65 (3), article 032112. https://doi.org/10.1103/PhysRevA.65.032112 (In English)

Ullmann, J., Andelkovic, Z., Brandau, C. et al. (2017) High precision hyperfine measurements in bismuth challenge bound-state strong-field QED. Nature Communications, 8 (1), article 15484. (In English)

Varentsova, A. S., Agababaev, V. A., Glazov, D. A. et al. (2018) Interelectronic-interaction contribution to the nonlinear Zeeman effect in boronlike ions. Physical Review A, 97 (4), article 043402. (In English)

Varentsova, A. S., Agababaev, V. A., Volchkova, A. M. et al. (2017) Third-order Zeeman effect in highly charged ions. Nuclear Instruments and Methods in Physics Research Section B: Beam Interactions with Materials and Atoms, 408, 80–83. https://doi.org/10.1016/j.nimb.2017.05.040 (In English)

Volchkova, A. M., Varentsova, A. S., Zubova, N. A. et al. (2017) Nuclear magnetic shielding in boronlike ions. Nuclear Instruments and Methods in Physics Research Section B: Beam Interactions with Materials and Atoms, 408, 89–92. https://doi.org/10.1016/j.nimb.2017.04.086 (In English)

Volotka, A. V., Glazov, D. A., Andreev, O. V. et al. (2012) Test of many-electron QED effects in the hyperfine splitting of heavy high-Z ions. Physical Review Letters, 108 (7), article 073001. https://doi.org/10.1103/PhysRevLett.108.073001 (In English)

Volotka, A. V., Glazov, D. A., Tupitsyn, I. I. et al. (2008) Ground-state hyperfine structure of H-, Li-, and B-like ions in the intermediate-Z region. Physical Review A, 78 (6), article 062507. https://doi.org/10.1103/PhysRevA.78.062507 (In English)

Von Lindenfels, D., Wiesel, M., Glazov, D. A. et al. (2013) Experimental access to higher-order Zeeman effects by precision spectroscopy of highly charged ions in a Penning trap. Physical Review A, 87 (2), article 023412. https://doi.org/10.1103/PhysRevA.87.023412 (In English)

Werth, G., Häffner, H., Hermanspahn, N. et al. (2001) The g factor of hydrogenic ions: A test of bound state QED. In S. G. Karshenboim, F. Bassani, F. Pavone et al. (eds.). The hydrogen atom: Precision physics of simple atomic systems. Berlin; Heidelberg: Springer Publ., pp. 204–220. https://doi.org/10.1007/3-540-45395-4_11 (In English)

Yerokhin, V. A., Pachucki, K., Harman, Z., Keitel, C. H. (2011) QED theory of the nuclear magnetic shielding in hydrogenlike ions. Physical Review Letters, 107 (4), article 043004. https://doi.org/10.1103/PhysRevLett.107.043004 (In English)

Yerokhin, V. A., Pachucki, K., Harman, Z., Keitel, C. H. (2012) QED calculation of the nuclear magnetic shielding for hydrogenlike ions. Physical Review A, 85 (2), article 022512. https://doi.org/10.1103/PhysRevA.85.022512 (In English)

Yerokhin, V. A., Pachucki, K., Harman, Z., Keitel, C. H. (2024) Nuclear magnetic shielding in heliumlike ions. Physical Review A, 109 (3), article 032808. https://doi.org/10.1103/PhysRevA.109.032808 (In English)

Yerokhin, V. A., Patkóš, V., Pachucki, K. (2022) QED calculations of energy levels of heliumlike ions with 5≤z≤30. Physical Review A, 106 (2), article 022815. https://doi.org/10.1103/PhysRevA.106.022815 (In English)

Yerokhin, V. A., Surzhykov, A. (2019) Theoretical energy levels of 1sns and 1snp states of helium-like ions. Journal of Physical and Chemical Reference Data, 48 (3), article 033104. https://doi.org/10.1063/1.5121413 (In English)

Опубликован

2026-06-30

Выпуск

Раздел

Theoretical Physics