Recoil Corrections to the Energy Levels of Hydrogenic Atoms

We have completed the calculation of pure-recoil corrections of order (Z alpha)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 (Z alpha)7 corrections.

Automated summary

We have calculated the pure-recoil corrections of order (Z alpha)6 for Coulombic bound states of two spin-1/2 fermions without approximation in the particle masses. Our results apply to systems with arbitrary mass ratios, including muonium, positronium, hydrogen, and muonic hydrogen (neglecting proton structure effects). We have also demonstrated a method for analytically computing the two-loop master integrals that occur in the relativistic region, and suggest that the same approach can be used for the calculation of three-loop integrals in order (Z alpha)7 corrections.