Brueckner-Hartree-Fock calculations in the Density Matrix Expansion approach

Recently, a microscopically based nuclear energy density functional was derived by applying the Density Matrix Expansion to the Hartree-Fock energy obtained from long-range chiral effective field theory two- and three-nucleon interactions. The Hartree-Fock approach cannot contain the full many-body correlations. Brueckner-Hartree-Fock theory gives an improved definition of the one-body potential U by replacing the interaction by a reaction matrix G. The central result of modern renormalization theory is that a general RG decoupling generates an infinite series of counterterms consistent with the input interaction. Then we can apply the DME at Hartree-Fock level with long-range $\chi$EFT interactions and zero-range contact interactions to model BHF correlations.