Relativistic and recoil corrections to light-fermion vacuum polarization for bound systems of spin-0, spin- 1 / 2 , and spin-1 particles

In bound systems whose constituent particles are heavier than the electron, the dominant radiative correction to energy levels is given by light-fermion (electronic) vacuum polarization. In consequence, relativistic and recoil corrections to the one-loop vacuum-polarization correction are phenomenologically relevant. Here, we generalize the treatment, previously accomplished for systems with orbiting muons, to bound systems of constituents with more general spins: spin-0, spin- 1 / 2 , and spin-1. We discuss the application of our more general expressions to various systems of interest, including spinless systems (pionium), muonic hydrogen and deuterium, and devote special attention to the excited non- S states of deuteronium, the bound system of a deuteron and its antiparticle. The obtained energy corrections are of order α 5 m r , where α is the fine-structure constant and m r is the reduced mass.