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Bound state properties, hyperfine structure, field shifts and vacuum polarization in the bound 1sμnse-states of the helium-muonic atoms.

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Title: Bound state properties, hyperfine structure, field shifts and vacuum polarization in the bound 1sμnse-states of the helium-muonic atoms.
Authors: Frolov, Alexei M.1 (AUTHOR) alex1975frol@gmail.com
Source: European Physical Journal D (EPJ D). Jun2026, Vol. 80 Issue 6, p1-21. 21p.
Subjects: Hyperfine structure, Vacuum polarization, Excited state energies, Nuclear size (Physics), Bound states, Ions, Helium atom
Abstract: The hyperfine structure splittings in the bound 1 s μ n s e states (where n = 1, 2, 3) in the helium-muonic 3 He μ e and 4 He μ e atoms are determined to high numerical accuracy. Corrections on the finite nuclear size are also investigated and evaluated numerically for these helium-muonic atoms. We also analyze the lowest-order correction on vacuum polarization, which is often called the Uehling correction, for the bound 1 s μ n s e states in both the helium-muonic 3 He μ e and 4 He μ e atoms. Rotationally excited, bound states with L = 1 and L = 2 in the helium-muonic 3 He μ e and 4 He μ e atoms are briefly discussed. It is also shown that the four-body, negatively charged, two-electron 3 He μ e 2 and 4 He μ e 2 ions have no actual 'atomic' hyperfine structure. The ordinary, second-order differential equation for the Uehling potentia [ABSTRACT FROM AUTHOR]
Copyright of European Physical Journal D (EPJ D) is the property of Springer Nature and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
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  Data: Bound state properties, hyperfine structure, field shifts and vacuum polarization in the bound 1sμnse-states of the helium-muonic atoms.
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  Data: <searchLink fieldCode="AR" term="%22Frolov%2C+Alexei+M%2E%22">Frolov, Alexei M.</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> alex1975frol@gmail.com</i>
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  Data: <searchLink fieldCode="JN" term="%22European+Physical+Journal+D+%28EPJ+D%29%22">European Physical Journal D (EPJ D)</searchLink>. Jun2026, Vol. 80 Issue 6, p1-21. 21p.
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  Data: <searchLink fieldCode="DE" term="%22Hyperfine+structure%22">Hyperfine structure</searchLink><br /><searchLink fieldCode="DE" term="%22Vacuum+polarization%22">Vacuum polarization</searchLink><br /><searchLink fieldCode="DE" term="%22Excited+state+energies%22">Excited state energies</searchLink><br /><searchLink fieldCode="DE" term="%22Nuclear+size+%28Physics%29%22">Nuclear size (Physics)</searchLink><br /><searchLink fieldCode="DE" term="%22Bound+states%22">Bound states</searchLink><br /><searchLink fieldCode="DE" term="%22Ions%22">Ions</searchLink><br /><searchLink fieldCode="DE" term="%22Helium+atom%22">Helium atom</searchLink>
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  Data: The hyperfine structure splittings in the bound 1 s μ n s e states (where n = 1, 2, 3) in the helium-muonic 3 He μ e and 4 He μ e atoms are determined to high numerical accuracy. Corrections on the finite nuclear size are also investigated and evaluated numerically for these helium-muonic atoms. We also analyze the lowest-order correction on vacuum polarization, which is often called the Uehling correction, for the bound 1 s μ n s e states in both the helium-muonic 3 He μ e and 4 He μ e atoms. Rotationally excited, bound states with L = 1 and L = 2 in the helium-muonic 3 He μ e and 4 He μ e atoms are briefly discussed. It is also shown that the four-body, negatively charged, two-electron 3 He μ e 2 and 4 He μ e 2 ions have no actual 'atomic' hyperfine structure. The ordinary, second-order differential equation for the Uehling potentia [ABSTRACT FROM AUTHOR]
– Name: AbstractSuppliedCopyright
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  Group: Ab
  Data: <i>Copyright of European Physical Journal D (EPJ D) is the property of Springer Nature and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.)
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        Value: 10.1140/epjd/s10053-026-01192-1
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      – Code: eng
        Text: English
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        PageCount: 21
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    Subjects:
      – SubjectFull: Hyperfine structure
        Type: general
      – SubjectFull: Vacuum polarization
        Type: general
      – SubjectFull: Excited state energies
        Type: general
      – SubjectFull: Nuclear size (Physics)
        Type: general
      – SubjectFull: Bound states
        Type: general
      – SubjectFull: Ions
        Type: general
      – SubjectFull: Helium atom
        Type: general
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      – TitleFull: Bound state properties, hyperfine structure, field shifts and vacuum polarization in the bound 1sμnse-states of the helium-muonic atoms.
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              M: 06
              Text: Jun2026
              Type: published
              Y: 2026
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