Energy density functional and sensitivity of energies of giant resonances to bulk nuclear matter properties

We provide a short review of the current status of the nuclear energy density functional (EDF) and the theoretical results obtained for properties of nuclei and nuclear matter. We will first describe a method for determining the parameters of the EDF, associated with the Skyrme type effective interaction, by carrying out a Hartree - Fock (HF)-based fit to the extensive set of data of ground-state properties and constraints. Next, we will describe the fully self-consistent HF-based random-phase-approximation (RPA) theory for calculating the strength functions S(E) and centroid energies E_CEN of giant resonances and the folding model (FM) distorted wave Born approximation (DWBA) to calculate the excitation cross-section of giant resonances by α scattering. Then we will provide results for: (i) the Skyrme parameters of the KDE0v1 EDF; (ii) consequences of violation of self-consistency in HF-based RPA; (iii) FM-DWBA calculation of excitation cross-section; (iv) values of the E_CEN of isoscalar and isovector giant resonances of multipolarities L = 0-3 for a wide range of spherical nuclei, using 33 EDFs associated with the standard form of the Skyrme type interactions, commonly employed in the literature; and (v) the sensitivities E_CEN of the giant resonances to bulk properties of nuclear matter (NM). We also determine constraints on NM properties, such as the incompressibility coefficient and effective mass, by comparing with experimental data on E_CEN of giant resonances. (author)