The tunneling ionization of exotic atoms such as muonic hydrogen, muonium and positronium in a strong laser field of circular polarization is investigated taking into account the impact of the motion of the center of mass on the the tunneling ionization dynamics. The momentum partition between the ionization products is deduced. The effect of the center of mass motion for the momentum distribution of the ionization components is determined. The effect scales with the ratio of the electron (muon) to the atomic core masses and is nonnegligible for exotic atoms, while being insignificant for common atoms. It is shown that the electron (muon) momentum shift during the under-the-barrier motion due to the magnetically induced Lorentz force has a significant impact on the momentum distribution of the atomic core and depends on the ratio of the electron to the atomic core masses.
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