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The reduced-mass dependence of relativistic and radiative effects in simplemuonic bound systems is investigated. The spin-dependent nuclear recoilcorrection of order (Zalpha)^4 mu^3/m_N^2 is evaluated for muonic hydrogen anddeuterium, and muonic helium ions (mu is the reduced mass and m_N is thenuclear mass). Relativistic corrections to vacuum polarization of order alpha(Zalpha)^4 mu are calculated, with a full account of the reduced-massdependence. The results shift theoretical predictions. The radiative-recoilcorrection to vacuum polarization of order alpha (Z\alpha)^5 ln^2(Zalpha)mu^2/m_N is obtained in leading logarithmic approximation. The resultsemphasize the need for a unified treatment of relativistic corrections tovacuum polarization in muonic hydrogen, muonic deuterium and muonic heliumions, where the mass ratio of the orbiting particle to the nuclear mass islarger than the fine-structure constant.

Relativistic Reduced-Mass and Recoil Corrections to Vacuum Polarization in Muonic Hydrogen, Muonic Deuterium and Muonic Helium Ions