Incompressibility in finite nuclei and nuclear matter

The incompressibility (compression modulus) K₀ of infinite symmetric nuclear matter at saturation density has become one of the major constraints on mean-field models of nuclear many-body systems as well as of models of high density matter in astrophysical objects and heavy-ion collisions. It is usually extracted from data on the giant monopole resonance (GMR) or calculated using theoretical models. We present a comprehensive reanalysis of recent data on GMR energies in even-even ¹¹²⁻⁻¹²⁴Sn and 106,100--116Cd and earlier data on 58≤A≤208 nuclei. The incompressibility of finite nuclei KA is calculated from experimental GMR energies and expressed in terms of A^-1/3 and the asymmetry parameter β=(N-Z)/A as a leptodermous expansion with volume, surface, isospin, and Coulomb coefficients Kᵥₒₗ, Ksurf, K_τ, and KCoul. Only data consistent with the scaling approximation, leading to a fast converging leptodermous expansion, with negligible higher-order-term contributions to KA, were used in the present analysis. Assuming that the volume coefficient Kᵥₒₗ is identified with K₀, the KCoul=-(5.2±0.7) MeV and the contribution from the curvature term KcurvA^-2/3 in the expansion is neglected, compelling evidence is found for K₀ to be in the range 250 <K₀< 315 MeV, the ratio of the surface and volume coefficients c=Ksurf/Kᵥₒₗ to be between -2.4 and -1.6 and K_τ between -840 and -350 MeV. In addition, estimation of the volume and surface parts of the isospin coefficient K_τ, K_τ,v, and K_τ,s, is presented. We show that the generally accepted value of K₀ = (240 ± 20) MeV can be obtained from the fits provided c~-1, as predicted by the majority of mean-field models. However, the fits are significantly improved if c is allowed to vary, leading to a range of K₀, extended to higher values. The results demonstrate the importance of nuclear surface properties in determination of K₀ from fits to the leptodermous expansion of KA. A self-consistent simple (toy) model has been developed, which shows that the density dependence of the surface diffuseness of a vibrating nucleus plays a major role in determination of the ratio Ksurf/Kᵥₒₗ and yields predictions consistent with our findings.