Incompressibility in finite nuclei and nuclear matter

The incompressibility (compression modulus) K-0 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 Sn112-124 and Cd-106,Cd-100-116 and earlier data on 58 <= A <= 208 nuclei. The incompressibility of finite nuclei K-A is calculated from experimental GMR energies and expressed in terms of A(-1/3) and the asymmetry parameter beta = (N - Z)/A as a leptodermous expansion with volume, surface, isospin, and Coulomb coefficients K-vol, K-surf, K-t, and K-Coul. Only data consistent with the scaling approximation, leading to a fast converging leptodermous expansion, with negligible higher-order-term contributions to K-A, were used in the present analysis. Assuming that the volume coefficient K-vol is identified with K-0, the K-Coul = -(5.2 +/- 0.7) MeV and the contribution from the curvature term K(curv)A(-2/3) in the expansion is neglected, compelling evidence is found for K-0 to be in the range 250 < K-0 < 315 MeV, the ratio of the surface and volume coefficients c = K-surf/K-vol to be between -2.4 and -1.6 and K-tau between -840 and -350 MeV. In addition, estimation of the volume and surface parts of the isospin coefficient Kt, Kt, v, and Kt, s, is presented. We show that the generally accepted value of K-0 = (240 +/- 20) MeV can be obtained from the fits provided c similar to -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 K-0, extended to higher values. The results demonstrate the importance of nuclear surface properties in determination of K-0 from fits to the leptodermous expansion of K-A. 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 K-surf/K-vol and yields predictions consistent with our findings.