Abstract
The muon Lamb shift (2\(P\)–2\(S)\) is calculated in electron–muon helium atom on the basis of stochastic variational method. The basis wave functions of muonic helium are taken in the Gaussian form. The matrix elements of the Hamiltonian are calculated analytically. For numerical calculation a computer code is written in the MATLAB system. The corrections to the nucleus structure, vacuum polarization, relativism and radiative corrections are taken into account by the perturbation theory.
![](http://media.springernature.com/m312/springer-static/image/art%3A10.1134%2FS106377882304021X/MediaObjects/11450_2023_2880_Fig1_HTML.png)
![](http://media.springernature.com/m312/springer-static/image/art%3A10.1134%2FS106377882304021X/MediaObjects/11450_2023_2880_Fig2_HTML.png)
![](http://media.springernature.com/m312/springer-static/image/art%3A10.1134%2FS106377882304021X/MediaObjects/11450_2023_2880_Fig3_HTML.png)
REFERENCES
A. Antognini, F. Kottmann, and R. Pohl, SciPost Phys. Proc. 5, 021 (2021).
J. J. Krauth, K. Schuhmann, M. A. Ahmed, et al., Nature (London, U.K.) 589, 527 (2021).
S. Schmidt, M. Willig, J. Haack, et al., J. Phys.: Conf. Ser. 1138, 012010 (2018).
S. Fukumura et al. (J-PARC Collab.), EPJ Web Conf. 262, 010012 (2022).
C. J. Gardner, A. Badertscher, W. Beer, et al., Phys. Rev. Lett. 48, 1168 (1982).
K. Varga and Y. Suzuki, Comput. Phys. Commun. 106, 157 (1997).
A. V. Eskin, V. I. Korobov, A. P. Martynenko, and V. V. Sorokin, J. Phys.: Conf. Ser. 1690, 012092 (2021).
D. T. Aznabayev, A. K. Bekbaev, and V. I. Korobov, Phys. Part. Nucl. Lett. 15, 236 (2018).
A. A. Krutov, A. P. Martynenko, G. A. Martynenko, and R. N. Faustov, J. Exp. Theor. Phys. 120, 73 (2015).
A. A. Krutov, A. P. Martynenko, F. A. Martynenko, and O. S. Sukhorukova, Phys. Rev. A 94, 062505 (2016).
ACKNOWLEDGMENTS
This work is supported by Russian Science Foundation (grant no. RSF 23-22-00143).
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Eskin, A.V., Korobov, V.I., Martynenko, A.P. et al. Energy Levels of Three-Particle Muon–Electron Helium in Variational Approach. Phys. Atom. Nuclei 86, 583–588 (2023). https://doi.org/10.1134/S106377882304021X
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1134/S106377882304021X