Nuclear incompressibility and speed of sound in uniform matter and finite nuclei

We have extended the compressible liquid-drop model with a density-dependent surface term which allows for a unified description of both the nuclear ground-state energies and the incompressibility modulus in finite nuclei KA. We analyze the role of the nuclear empirical parameters, e.g., Ksat, Qsat, Lsym, and Ksym, which contribute to the bulk properties, as well as the role of the finite-size contributions. For the bulk properties, the density and isospin dependencies of the nuclear incompressibility in infinite matter are characterized by introducing new empirical parameters, and two new constraints for the value of Ksym are suggested. For finite nuclei, we employ a Bayesian approach coupled to a Markov-Chain Monte Carlo exploration of the parameter space to confront the model predictions of KA in Zr, Sn, and Pb isotopes to the experimental data. We show that Qsat ti -950 +/- 200 MeV describes the experimental measurements of KA in these isotopes. This value is different from those deduced from phenomenological nuclear energy density functionals, suggesting a possible explanation of their difficulty to accurately describe Zr, Sn, and Pb data all together. In addition we explore the impact of a fictitious measurement of the giant monopole resonance energy in 132Sn. We show that this measurement, provided it is accurate enough, will allow us to better determine Ksym and Kr. Finally we explore the properties of the speed of sound around saturation density and show the important role of finite-size terms in finite nuclei since they reduce the speed of sound to approximately half compared with nuclear matter.