Microscopic determination of the nuclear incompressibility within the nonrelativistic framework

The nuclear incompressibility K_∞ is deduced from measurements of the isoscalar giant monopole resonance (ISGMR) in medium-heavy nuclei, and the resulting value turns out to be model dependent. Since the considered nuclei have neutron excess, it has been suggested that the model dependence is due to the different behavior of the symmetry energy in different models. To clarify this issue, we make a systematic and careful analysis based on new Skyrme forces, which span a wide range of values for K_∞, for the value of the symmetry energy at saturation and for its density dependence. By calculating, in a fully self-consistent fashion, the ISGMR centroid energy in ²⁰⁸Pb, we reach three important conclusions: (i) the monopole energy, and consequently the deduced value of K_∞, depend on a well-defined parameter related to the shape of the symmetry energy curve and called Ksym; (ii) Skyrme forces of the type of SLy4 predict K_∞ around 2300.3em0exMeV, in agreement with the Gogny force (previous estimates using Skyrme interactions having been plagued by a lack of full self-consistency); (iii) it is possible to build forces which predict K_∞ around 2500.3em0exMeV, although part of this increase is due to our poor knowledge of the density dependence and effective mass.