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

TL;DR

This paper develops a formalism to map the Dirac--Hartree--Fock approach onto a relativistic mean-field model, incorporating density dependence from Fock exchange and nonlinear self-interactions, enhancing the understanding of nuclear matter energy density.

Contribution

It introduces a parameter-free method to express the exchange energy density as a density functional and extends it to include nonlinear self-couplings in the DHF model.

Findings

Exchange energy density expressed as a density functional.

Relativistic mean-field model recovered with density-dependent couplings.

Nonlinear self-interactions induce medium modifications of effective couplings.

Abstract

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 form and expressed as density functional. After the rearranging terms the relativistic mean-field approach with density-dependent couplings may be recovered with density dependence coming from the Fock exchange. The formalism developed, is then extended to the nonlinear DHF approximation with field self-couplings allowed. The nonlinear self--interactions result in essential density dependence (medium modification) of effective couplings that are decoupled from the Fock ones.