Incompressibility of neutron-rich matter

Abstract

The saturation properties of neutron-rich matter are investigated in a relativistic mean-field formalism using two accurately calibrated models: NL3 and FSUGold. The saturation properties-density, binding energy per nucleon, and incompressibility coefficient-are calculated as a function of the neutron-proton asymmetry α ≡ (N − Z)/A to all orders in α. Good agreement (at the 10% level or better) is found between these numerical calculations and analytic expansions that are given in terms of a handful of bulk parameters determined at saturation density. Using insights developed from the analytic approach and a general expression for the incompressibility coefficient of infinite neutron-rich matter, i.e., K 0 (α) = K 0 + K τ α 2 + · · ·, we construct a hybrid model with values for K 0 and K τ as suggested by recent experimental findings. Whereas the hybrid model provides a better description of the measured distribution of isoscalar monopole strength in the Sn isotopes relative to both NL3 and FSUGold, it significantly underestimates the distribution of strength in 208 Pb. Thus, we conclude that the incompressibility coefficient of neutron-rich matter remains an important open problem.

Higher-order effects on the incompressibility of isospin asymmetric nuclear matter

“…Again, we note that the conclusions obtained here from the MDI interaction are also valid for the SHF approach and the MSL model. Our results are further consistent with the very recent study based on the RMF model [118].…”

“…As pointed out in Ref. [118], these features suggest that the K τ = −550 ± 100 MeV value obtained in Refs. [22,23] may suffer from the same ambiguities already encountered in earlier attempts to extract the K 0 and K sat,2 values of infinite nuclear matter from finite-nuclei extrapolations.…”

“…[22,23] from recent measurements of the isotopic dependence of the GMR in even-A Sn isotopes, its magnitude is significantly smaller than that of the constrained K τ . Recently, there have been several studies [118,135,136] on extracting the value of the K sat,2 parameter based on the idea initiated by Blaizot and collaborators that the values of both K 0 and K sat,2 should be extracted from the same consistent theoretical model that successfully reproduces the experimental GMR energies of a variety of nuclei. These studies show that no single model (interaction) can simultaneously describe correctly the recent measurements of the isotopic dependence of the GMR in even-A Sn isotopes and the GMR data of 90 Zr and 208 Pb nuclei, and this makes it difficult to accurately determine the value of K sat,2 from these experimental data.…”

Neutron skin thickness in the droplet model with surface width dependence: Indications of softness of the nuclear symmetry energy

“…One has c sym (ρ 0 ) = J . The DM coefficients L and K sym are, respectively, proportional to the slope and the curvature of the symmetry energy coefficient c sym (ρ) at saturation density: (5) is often a reliable representation of the actual value of the c sym (ρ) coefficient at densities roughly between ρ 0 /2 and 2ρ 0 [61]. For instance, in the case of a typical subsaturation density value ρ = 0.10 fm −3 , one finds that the above quadratic expansion of c sym (ρ) differs from the exact c sym (ρ) by less than 1% in many different nuclear mean field forces [51].…”

Isoscalar giant resonances inCa48

“…Systematic studies of the ISGMR energy E 0 in various nuclei lead to the value of K NM = 231±5 MeV [4] for the incompressibility coefficient of symmetric NM . This property of the ISGMR and the variation of the incompressibility coefficient with neutron number can also be used to extract the asymmetry coefficient K sym in the EOS of asymmetric NM [5]. In the analysis of experimental data on E 0 it is common to employ two approaches: (i) Adopting a semiclassical model to relate E 0 to an incompressibility coefficient K A of the nucleus and carry out a Leptodermous (A -1/3 ) expansion of K A , similar to a mass formula, to parameterize K A into volume, surface, symmetry and Coulomb terms [6,7]; and (ii) Carrying out microscopic calculations of the strength function S(E) of the ISGMR, within a fully self consistent mean-field based random phase approximation (RPA), with specific interactions (see the review [8]) and comparing with the experimental data.…”