Hartree Fock Calculations in the Density Matrix Expansion Approach

The density matrix expansion is used to derive a local energy density functional for finite range interactions with a realistic meson exchange structure. Exchange contributions are treated in a local momentum approximation. A generalized Slater approximation is used for the density matrix where an effective local Fermi momentum is chosen such that the next to leading order off-diagonal term is canceled. Hartree–Fock equations are derived incorporating the momentum structure of the underlying finite range interaction. For applications a density dependent effective interaction is determined from a G-matrix which is renormalized such that the saturation properties of symmetric nuclear matter are reproduced. Intending applications to systems far off stability special attention is paid to the low density regime and asymmetric nuclear matter. Results are compared to predictions obtained from Skyrme interactions. The ground state properties of stable nuclei are well reproduced without further adjustments of parameters. The potential of the approach is further exemplified in calculations for A=100. . .140 tin isotopes. Rather extended neutron skins are found beyond Sn corresponding to solid layers of neutron matter surrounding a core of normal composition.