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