Exchange potentials in relativistic Hartree-Fock theory of closed-shell nuclei

The relativistic Hartree formalism for nuclei is extended to include the exchange potentials which result from various kinds of one-boson-exchange interactions. A numerical simplification is presented which uncouples the relativistic Hartree-Fock equations and enables local (though state-dependent) single-particle potentials to be defined for the exchange interactions. Calculations are presented for a vector-scalar nucleon-nucleon force model. Comparison of these calculations with Hartree calculations (using the same model) indicates that the exchange terms contribute a net attraction of about 1.5 MeV per particle in light nuclei, while rms radii are reduced by about 0.03 fm. A study is also made of the exchange potentials resulting from the pseudoscalar part (one-pion-exchange) of the nucleon-nucleon interaction. These terms appear to be important, although self-consistent calculations are not possible in the present framework due to numerical instabilities induced by the pseudoscalar term. The instabilities appear to be related to an incorrect enhancement of the effects of virtual $N-\overline{N}$ pair creation which is present in the coordinate space relativistic one-pion-exchange potential.