The development of a modern and more realistic nuclear energy density functional (EDF) for accurate predictions of properties of nuclei is the subject of enhanced activity, since it is very important for the study of properties of rare nuclei with unusual neutron-to-proton ratios that are difficult to produce experimentally and likely to exhibit interesting new phenomena associated with isospin, clusterization and the continuum.
The study of collective modes in nuclei provides very important information on properties of nuclear matter (NM), such as the incompressibility coefficient, K, and the symmetry energy coefficient, J. Accurate values of K and J are needed in order to extend our knowledge of the NM equation of state (EOS) in the vicinity of the saturation point of symmetric NM. The EOS is an important ingredient in the study of various properties of nuclei, heavy ion collisions, supernova and neutron stars.
Adopting the EDF associated with the standard parameterization of Skyrme type interactions within the Hartree Fock approximation, we have developed a more realistic EDF by carrying out, using the simulating annealing method, a fit to an extensive set of experimental data on binding energies, radii, single particle energies, and, in particular, the data on the isoscalar giant monopole resonances (ISGMR) and the isocalar giant dipole resonances (ISGDR) of nuclei. We have also imposed additional constraints, such as the Landau stability constraints on NM and the non-negativity of the slope of the symmetry energy density at high matter density.
We will present results of Hartree-Fock (HF) calculations of properties of nuclei and NM obtained by employing our newly determined EDF. We will then review the current status of the experimental and theoretical methods used to determine the value of K from excitation cross-sections and strength distributions of the ISGMR and ISGDR (compression modes). We will also present and discuss results of our fully self-consistent calculations, obtained within the HF-based random-phase approximation, of excitation cross-sections and strength distributions of the ISGMR and the ISGDR and address, in particular, the issues of:
i) The isospin dependence of the spin-orbit interaction.
ii) The effects of long-range correlations on ground state properties of nuclei.
iii) The current status of K.
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