A relativistic four-dimensional wave equation, derived previously, for bound states of a two-body system is discussed further. For any "instantaneous" interaction function an exact three-dimensional equation is derived from it, similar to, but not identical with, the Breit equation. A perturbation theory is developed for a small additional non-instantaneous interaction.

Using this covariant method, corrections of relative order $\alpha \left(\frac{m}{M}\right)$ to the fine structure of hydrogen, due to the finite mass of the nucleus, are calculated. No terms of this order were obtained in previous approximate treatments using the Breit equation. Some of the terms obtained contain $log\alpha$ as a factor. It is shown that these special terms can also be derived simply by means of orthodox quantum electrodynamics and perturbation theory.

These corrections to the fine structure are +0.379 Mc/sec for the $2s$ state of hydrogen and -0.017 Mc/sec for the $2p$ state. For hydrogen-like atoms with heavier nuclei the corrections are roughly ($\frac{Z^5}{A}$) times those for hydrogen.

• Received 7 March 1952

DOI:https://doi.org/10.1103/PhysRev.87.328