Symmetry energy systematics and its high density behavior

We explore the systematics of the density dependence of nuclear matter symmetry energy in the ambit of microscopic calculations with various energy density functionals, and find that the symmetry energy from subsaturation density to supra-saturation density can be well determined by three characteristic parameters of the symmetry energy at saturation density $\rho_0$, i.e., the magnitude $E_{\text{sym}}({\rho_0 })$, the density slope $L$ and the density curvature $K_{\text{sym}}$. This finding opens a new window to constrain the supra-saturation density behavior of the symmetry energy from its (sub-)saturation density behavior. In particular, we obtain $L=46.7 \pm 12.8$ MeV and $K_{\text{sym}}=-166.9 \pm 168.3$ MeV as well as $E_{\text{sym}}({2\rho _{0}}) \approx 40.2 \pm 12.8$ MeV and $L({2\rho _{0}}) \approx 8.9 \pm 108.7$ MeV based on the present knowledge of $E_{\text{sym}}({\rho_{0}}) = 32.5 \pm 0.5$ MeV, $E_{\text{sym}}({\rho_c}) = 26.65 \pm 0.2$ MeV and $L({\rho_c}) = 46.0 \pm 4.5$ MeV at $\rho_{\rm{c}}= 0.11$ fm$^{-3}$ extracted from nuclear mass and the neutron skin thickness of Sn isotopes. Our results indicate that the symmetry energy cannot be stiffer than a linear density dependence.In addition, we also discuss the quark matter symmetry energy since the deconfined quarks could be the right degree of freedom in dense matter at high baryon densities.Comment: 10 pages, 5 figures. Contribution to International Workshop on Multi facets of Eos and Clustering (IWM-EC 2014), May 6-9, 2014, Catania, Ital

Recent progress on the determination of the symmetry Energy

We summarize the current status on constraining the density dependence of the symmetry energy from terrestrial laboratory measurements and astrophysical observations. While the value $E_{sym}({\rho_{0}})$ and density slope $L$ of the symmetry energy at saturation density $\rho_{0}$ can vary largely depending on the data or methods, all the existing constraints are essentially consistent with $E_{sym}({\rho_{0}}) = 31 \pm 2$ MeV and $L = 50 \pm 20$ MeV. The determination of the supra-saturation density behavior of the symmetry energy remains a big challenge.Comment: 12 pages, 2 figures. Plenary talk at 14th National Conference on Nuclear Structure in China, Huzhou, Zhejiang, 12-16 April, 201

Empirical information on nuclear matter fourth-order symmetry energy from an extended nuclear mass formula

We establish a relation between the equation of state (EOS) of nuclear matter and the fourth-order symmetry energy $a_{\rm{sym,4}}(A)$ of finite nuclei in a semi-empirical nuclear mass formula by self-consistently considering the bulk, surface and Coulomb contributions to the nuclear mass. Such a relation allows us to extract information on nuclear matter fourth-order symmetry energy $E_{\rm{sym,4}}(\rho_0)$ at normal nuclear density $\rho_0$ from analyzing nuclear mass data. Based on the recent precise extraction of $a_{\rm{sym,4}}(A)$ via the double difference of the "experimental" symmetry energy extracted from nuclear masses, for the first time, we estimate a value of $E_{\rm{sym,4}}(\rho_0) = 20.0\pm4.6$ MeV. Such a value of $E_{\rm{sym,4}}(\rho_0)$ is significantly larger than the predictions from mean-field models and thus suggests the importance of considering the effects of beyond the mean-field approximation in nuclear matter calculations.Comment: 7 pages, 1 figure. Presentation improved and discussions added. Accepted version to appear in PL