Recoil Corrections to the Energy Levels of Hydrogenic Atoms.

We have completed the calculation of pure-recoil corrections of order (Zα)^{6} to Coulombic bound states of two spin-1/2 fermions without approximation in the particle masses. Our result applies to systems of arbitrary mass ratio such as muonium and positronium, as well as hydrogen and muonic hydrogen (with the neglect of proton structure effects). We have shown how the two-loop master integrals that occur in the relativistic region can be computed in analytic form and suggest that the same method can be applied to the three-loop integrals that would be present in a calculation of order (Zα)^{7} corrections.

Three-Photon-Annihilation Contributions to Positronium Energies at Order mα^{7}.

Positronium spectroscopy (n=1 hyperfine splitting, n=2 fine structure, and the 2S-1S interval) has reached a precision of order 1 MHz. Vigorous ongoing efforts to improve the experimental results motivate the calculation of the positronium energy levels at order mα^{7}. In this Letter, we present the result for a complete class of such contributions-those involving virtual annihilation of positronium to three photons in an intermediate state.