  An exact method is suggested to treat the nonlinear self-interactions (NLSI)
in the relativistic Hartree-Fock (RHF) approach for nuclear systems. We
consider here the NLSI constructed from the relativistic scalar nucleon
densities and including products of six and eight fermion fields. This type of
NLSI corresponds to the zero range limit of the standard cubic and quartic
self-interactions of the scalar field. The method to treat the NLSI uses the
Fierz transformation, which enables one to express the exchange (Fock)
components in terms of the direct (Hartree) ones. The method is applied to
nuclear matter and finite nuclei. It is shown that, in the RHF formalism, the
NLSI, which are explicitly isovector-independent, generate scalar, vector and
tensor nucleon self-energies strongly density-dependent. This strong isovector
structure of the self-energies is due to the exchange terms of the RHF method.
Calculations are carried out with a parametrization containing five free
parameters. The model allows a description of both types of systems compatible
with experimental data.
