Further analysis of the complete Breit interaction

In a recent paper [Phys. Rev. A 37, 1087 (1988)] Gorceix and Indelicato study the difference between the multiconfiguration Dirac-Fock (MCDF) expectation value of the Lorentz and Coulomb gauge forms for the Breit interaction. After a slight rearrangement of their expressions, we have found that the difference can be written as a commutator with the full Hamiltonian. This commutator is nonvanishing due to projection operators onto positive energy states implicit in the MCDF approach and gives contributions O($Z^2$ ${\alpha }^2$). It is shown that the diagram involving the excitation of a single virtual electron-positron pair, which removes the discrepancy if the low-frequency limit is used also where it is not valid, does not do so for the proper frequency-dependent form and that a more detailed analysis is required.