  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.
