Determination of the density dependence of the nuclear incompressibility

Background: The determination of the density dependence of the nuclear incompressibility can be investigated using the isoscalar giant monopole resonance. Purpose: The importance of the so-called crossing density at subsaturation density is underlined. Methods: The measurements of the isoscalar giant monopole resonance (GMR), also called the breathing mode, are analyzed with respect to their constraints on the quantity M-c, e.g., the density dependence of the nuclear incompressibility around the so-called crossing density rho(c) = 0.1 fm(-3). Results: The correlation between the centroid of the GMR, E-GMR, and M-c is shown to be more accurate than the one between E-GMR and the incompressibility modulus at saturation density, K-infinity, giving rise to an improved determination on the nuclear equation of state. The relationship between M-c and K-infinity is given as a function of the skewness parameter Q(infinity) associated with the density dependence of the equation of state. The large variation of Q(infinity) among different energy density functionals directly impacts the knowledge of K-infinity: A better knowledge of Q(infinity) is required to deduce more accurately K-infinity. Using the local density approximation, a simple and accurate expression relating E-GMR and the quantity M-c is derived and successfully compared to the fully microscopic predictions. Conclusions: The measurement of the GMR constrains the slope of the incompressibility M-c at the crossing density rather than the incompressibility modulus at the saturation density.