Constraining the nuclear equation of state at subsaturation densities

Only one third of the nucleons in $^{208}$Pb occupy the saturation density area. Consequently nuclear observables related to average properties of nuclei, such as masses or radii, constrain the equation of state (EOS) not at saturation density but rather around the so-called crossing density, localised close to the mean value of the density of nuclei: $\rho\simeq$0.11 fm$^{-3}$. This provides an explanation for the empirical fact that several EOS quantities calculated with various functionals cross at a density significantly lower than the saturation one. The third derivative M of the energy at the crossing density is constrained by the giant monopole resonance (GMR) measurements in an isotopic chain rather than the incompressibility at saturation density. The GMR measurements provide M=1110 $\pm$ 70 MeV (6% uncertainty), whose extrapolation gives K$_\infty$=230 $\pm$ 40 MeV (17% uncertainty).