Incompressibility in finite nuclei and nuclear matter

Abstract

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 re-analysis of recent data on GMR energies in even-even 112−124 Sn and 106,100−116 Cd 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 K vol , K surf , Kτ and K coul . 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 K vol is identified with K0, the K coul = -(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 = K surf /K vol to be between -2.4 and -1.6 and Kτ between -840 and -350 MeV. In addition, estimation of the volume and surface parts of the isospin coefficient Kτ , Kτ,v and Kτ,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 K surf /K vol and yields predictions consistent with our findings.

Vlasov formalism for extended relativistic mean field models: The crust-core transition and the stellar matter equation of state

“…However, the incompressibility of these models is within the range 250 < K < 315 MeV predicted in Ref. [69,70]. Therefore, we consider that the K constraint is satisfied.…”

“…[55], except the one in K τ , the constraints from neutron matter calculations and those from Refs. [69,70]. Models NL3ωρ6 and NL3σρ6 only fail the flow and KaoS experiments.…”

“…[55], the ones from Refs. [69,70], the microscopic neutron matter calculations [33,34], and the 2M observational constraint [39,40]. We note that the Z271σρ5-6 models fail this last constraint; however, by using the procedure of Ref.…”

Van der Waals equation of state with Fermi statistics for nuclear matter

“…Different theoretical models and their comparison with experimental estimates of the nuclear matter properties have been widely discussed in the literature (see, e.g., Refs. [28][29][30]). In the present paper we do not attempt to make any detail comparison of the developed VDW quantum model with existing data for nuclear matter.…”

Finite Nuclei in the Quark-Meson Coupling Model

“…Recently, Stone et al [18] analyzed all GMR data available to date, in a way independent of the choice of nuclear interaction, showing that the limits on K 0 are 250 < K 0 < 315 MeV. As an additional comment we note that the relativistic version [19] of the QMC EDF, previously applied to cold uniform matter, showed that the contribution of a long-range Yukawa single pion exchange lowered the incompressibility from 340 MeV to ∼300 MeV, compatible with results in [18]. We intend to include the explicit pion exchange in the future development of the nonrelativistic QMC model used in the present study.…”