Effects of vacuum polarization modify the energy levels in atoms with anorbiting particle heavier than an electron. The dominant effect is due to theUehling potential. In this paper we consider the relativistic corrections tothe energy levels caused by the Uehling potential and in particular the finestructure in muonic and antiprotonic atoms. We derive general expressions andconsider in detail specific regions of parameters which allow simple asymptoticexpansion. We take into account the recoil effects and anomalous magneticmoment in the case of an antiproton as the orbiting particle.
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