Density-Matrix Expansion for an Effective Nuclear Hamiltonian

An expansion for the nuclear wave-function density matrix in relative and c.m. coordinates is developed such that the leading term is the corresponding nuclear-matter density matrix at the local neutron and proton density. Truncation of all derivatives beyond second order yields an extremely simple form for the energy density which retains all the computational simplicity of the modified δ interaction and the Skyrme force, while maintaining contact with nuclear-matter theory based on a realistic interaction and reproducing the results of more-complicated density-dependent Hartree-Fock calculations.