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]
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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]
ISSN:14346060
DOI:10.1140/epjd/s10053-026-01192-1