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The exchange part of energy density of the linear Dirac--Hartree--Fock (DHF)model in symmetric nuclear matter is evaluated in a parameter--free closed formand expressed as density functional. After the rearranging terms therelativistic mean-field approach with density-dependent couplings may berecovered with density dependence coming from the Fock exchange. The formalismdeveloped, is then extended to the nonlinear DHF approximation with fieldself-couplings allowed. The nonlinear self--interactions result in essentialdensity dependence (medium modification) of effective couplings that aredecoupled from the Fock ones.

Mapping Dirac--Hartree--Fock approach onto relativistic mean field model