Determination of the density dependence of the nuclear incompressibility

Abstract

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 ${\ensuremath{\rho}}_{c}=0.1$ fm${}^{\ensuremath{-}3}$.Results: The correlation between the centroid of the GMR, ${E}_{\mathrm{GMR}}$, and ${M}_{c}$ is shown to be more accurate than the one between ${E}_{\mathrm{GMR}}$ and the incompressibility modulus at saturation density, ${K}_{\ensuremath{\infty}}$, giving rise to an improved determination on the nuclear equation of state. The relationship between ${M}_{c}$ and ${K}_{\ensuremath{\infty}}$ is given as a function of the skewness parameter ${Q}_{\ensuremath{\infty}}$ associated with the density dependence of the equation of state. The large variation of ${Q}_{\ensuremath{\infty}}$ among different energy density functionals directly impacts the knowledge of ${K}_{\ensuremath{\infty}}$: A better knowledge of ${Q}_{\ensuremath{\infty}}$ is required to deduce more accurately ${K}_{\ensuremath{\infty}}$. Using the local density approximation, a simple and accurate expression relating ${E}_{\mathrm{GMR}}$ 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.