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Abstract

In this work, the relativistic recoil correction to the energies of heavy muonic
atoms has been considered, based on the formalism suggested by Borie and
Rinker.
Muonic atoms are atoms, which have a bound muon instead of an electron.
The lifetime of a muon is long enough so it can be considered stable on
the atomic scale. Additionally, an atom with a single bound muon can be
considered as a hydrogen-like system. As muons are about 200 times heavier
than electrons, they orbit the nucleus 200 times closer. This leads to a larger
contribution of all kinds of nuclear effects to the energy levels of the muon.
We calculated the recoil effect for the shell, sphere and Fermi nuclear
models and studied model and nuclear parameters dependence. Additionally,
we compared the results with previous studies. Going forward, the results
can be used for high-precision theoretical predictions of the spectra of heavy
muonic atoms, and in further comparison with experimental data, aiming at
the extraction of nuclear properties and parameters. In the future, a more
rigorous quantum electrodynamics formalism can be applied to enhance the
accuracy of the relativistic recoil effect.