Modern energy density functional for nuclei and the nuclear matter equation of state

We discuss a method of determining a modern energy density functional (EDF) in nuclei. We adopt a Skyrme type EDF and fit the Skyrme parameters to an extensive set of experimental data on the ground-state binding energies, radii, and the breathing mode energies of a wide range of nuclei. We further constrain the values of the Skyrme parameters by requiring positive values for the slope of the symmetry energy S, the enhancement factor κ, associated with the isovector giant dipole resonance, and the Landau parameter G ₀^′. This is done within the approaches of Hartree-Fock (HF) and HF with the inclusion of correlation effects, using a simulated-annealing based algorithm forminimizing χ ².We also present results of HF based random phase approximation for the excitation strength function of the breathing mode and discuss the current status of the nuclear matter incompressibility coefficient.