Correlations between the behavior of the nuclear symmetry energy, the neutron skins, and the percentage of energy-weighted sum rule (EWSR) exhausted by the Pygmy Dipole Resonance (PDR) in 68 Ni and 132 Sn have been investigated by using different Random Phase Approximation (RPA) models for the dipole response, based on a representative set of Skyrme effective forces plus meson-exchange effective Lagrangians. A comparison with the experimental data has allowed us to constrain the value of the derivative of the symmetry energy at saturation. The neutron skin radius is deduced under this constraint.

Effects of medium polarization are studied for 1 S0 pairing in neutron and nuclear matter. The screening potential is calculated in the RPA limit, suitably renormalized to cure the low density mechanical instability of nuclear matter. The selfenergy corrections are consistently included resulting in a strong depletion of the Fermi surface. All medium effects are calculated based on the Brueckner theory. The 1 S0 gap is determined from the generalized gap equation. The selfenergy corrections always lead to a quenching of the gap, which is enhanced by the screening effect of the pairing potential in neutron matter, whereas it is almost completely compensated by the antiscreening effect in nuclear matter.

The isospin splitting of the nucleon mean field is derived from the Brueckner theory extended to asymmetric nuclear matter. The Argonne V18 has been adopted as bare interaction in combination with a microscopic three body force. The isospin splitting of the effective mass is determined from the Brueckner-Hartree-Fock self-energy: It is linear acording to the Lane ansatz and such that $m^*_n > m^*_p$ for neutron-rich matter. The symmetry potential is also determined and a comparison is made with the predictions of the Dirac-Brueckner approach and the phenomenological interactions. The theoretical predictions are also compared with the empirical parametrizations of neutron and proton optical-model potentials based on the experimental nucleon-nucleus scattering and the phenomenological ones adopted in transport-model simulations of heavy-ion collisions. The direct contribution of the rearrangement term due to three-body forces to the single particle potential and symmetry potential is discussed.Comment: 8 pages, 10 figure