Hartree-Fock calculations in the density matrix expansion approach

The density matrix expansion is used to obtain a local energy density functional for interactions with a realistic meson exchange structure. Hartree-Fock (HF) equations are derived and applications to infinite matter and finite nuclei are discussed. Using a generalized Slater approximation for the density matrix the HF equations still incorporate the momentum structure of the underlying finite range interaction. For applications a density dependent effective interaction is determined from a $G$ matrix where the density dependence is adjusted to the saturation properties of symmetric nuclear matter. Intending applications to systems far off stability special attention is paid to the low density regime and asymmetric nuclear matter. Results are compared to Skyrme HF calculations. The ground state properties of stable nuclei are well reproduced. The potential of the approach is further exemplified in calculations for $A=100\mathrm{}-140$ tin isotopes. Extended neutron skins are found beyond ${}^{130}\mathrm{Sn}$ corresponding to solid layers of neutron matter surrounding a core of normal composition.