Abstract
The finite-nuclear size correction to the fine structure of muonic atoms is considered. The procedure for the analytical calculation of the energies and wave functions has been derived in a homogeneously charged sphere nuclear charge distribution approximation. The finite-nuclear size effect was calculated in a first few orders of the perturbation energy, with the accurate estimations of the convergence. Finally, we present energies of the low-lying electronic and muonic states with the finite-nuclear size correction, calculated analytically, for 75185Re ion.Graphical abstract
Highlights
One of the simplest and at the same time exotic atomic system is the highly charged hydrogen-like muonic atom, where a negative muon μ− is bound to an atomic nucleus
Muonic orbits are closer to the nucleus than that of electron, making muonic systems a suitable probe to investigate and extract nuclear parameters, i.e., nuclear size, charge distribution and moments [1]
For the light end of the periodic system, the most important and interesting is muonic hydrogen, where the prediction for the proton radius from the muonic spectroscopy disagree with the prediction based on the spectroscopy of the electronic hydrogen
Summary
One of the simplest and at the same time exotic atomic system is the highly charged hydrogen-like muonic atom, where a negative muon μ− is bound to an atomic nucleus. Having the spin of 1/2 as an electron does, a muon has a much larger mass, mμ ≈ 207me. Due to this fact, muonic orbits are closer to the nucleus than that of electron, making muonic systems a suitable probe to investigate and extract nuclear parameters, i.e., nuclear size, charge distribution and moments [1]. We incorporate muonic systems into a procedure for analytical calculation of the finite nuclear size (FNS) effect developed for electronic states [5].
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