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An exact method is suggested to treat the nonlinear self-interactions (NLSI)in the relativistic Hartree-Fock (RHF) approach for nuclear systems. Weconsider here the NLSI constructed from the relativistic scalar nucleondensities and including products of six and eight fermion fields. This type ofNLSI corresponds to the zero range limit of the standard cubic and quarticself-interactions of the scalar field. The method to treat the NLSI uses theFierz transformation, which enables one to express the exchange (Fock)components in terms of the direct (Hartree) ones. The method is applied tonuclear matter and finite nuclei. It is shown that, in the RHF formalism, theNLSI, which are explicitly isovector-independent, generate scalar, vector andtensor nucleon self-energies strongly density-dependent. This strong isovectorstructure of the self-energies is due to the exchange terms of the RHF method.Calculations are carried out with a parametrization containing five freeparameters. The model allows a description of both types of systems compatiblewith experimental data.Comment: 23 pages, 14 figures (v2: major quantitative changes

Description of nuclear systems within the relativistic Hartree–Fock method with zero-range self-interactions of the scalar field