In our previous paper (Can. J. Phys. 91, 715 (2013) doi: 10.1139/cjp-2013-0077 ) we studied a system consisting of a proton, a muon, and an electron; the muon and the electron being in circular states. The study was motivated by numerous applications of muonic atoms and molecules, where one of the electrons is substituted by the heavier lepton μ–. We demonstrated that in such a μpe quasi molecule, the muonic motion can represent a rapid subsystem while the electronic motion can represent a slow subsystem — a result that may seem counterintuitive. In other words, the muon rapidly revolves in a circular orbit about the axis connecting the proton and electron while this axis slowly rotates following a relatively slow electronic motion. We showed that the spectral lines, emitted by the muon in the quasi molecule, μpe, experience a red shift compared to the corresponding spectral lines that would have been emitted by the muon in a muonic hydrogen atom. In the present paper we generalize this study by replacing the proton in the μpe quasi molecule by a fully stripped ion of nuclear charge Z > 1. We show that in this case, just as in the previously studied case of Z = 1, the muonic motion can represent a rapid subsystem while the electronic motion can represent a slow subsystem. For this to be valid, the ratio of the muonic and electronic angular momenta should be slightly greater than in the case of Z = 1. We demonstrate that the binding energies of the muon for Z > 1 are much greater than for Z = 1 at any finite value of the nucleus–electron distance. Finally we show that the red shift of the spectral lines emitted by the muon (compared to the spectral lines of the corresponding muonic hydrogen-like ion of nuclear charge Z) decreases as Z increases. However, the relative red shift remains within the spectral resolution of available spectrometers at least up to Z = 5. Observing this red shift should be one of the ways to detect the formation of the quasi molecules, μZe.
