How tightly is the nuclear symmetry energy constrained by a unitary Fermi gas?

Abstract

We examine critically how tightly the density dependence of nuclear symmetry energy Esym(ρ) is constrained by the universal equation of state (EOS) of the unitary Fermi gas EUG(ρ) considering currently known uncertainties of higher order parameters describing the density dependence of the Equation of State of isospin-asymmetric nuclear matter. We found that EUG(ρ) does provide a useful lower boundary for the Esym(ρ) . However, it does not tightly constrain the correlation between the magnitude Esym(ρ0) and slope L unless the curvature Ksym of the symmetry energy at saturation density ρ0 is more precisely known. The large uncertainty in the skewness parameters affects the Esym(ρ0) versus L correlation by the same almost as significantly as the uncertainty in Ksym.PACS numbers: 24.30. Cz, 21.65.+f, 21.30.Fe, 24.10.Lx Introduction: To understand the nature of neutron-rich nucleonic matter has been a major scientific goal in both nuclear physics and astrophysics. The density dependence of nuclear symmetry energy E sym (ρ) has been a major uncertain part of the equation of state (EOS) of neutron-rich matter especially at high densities, see, e.g., collections in [1]. Reliable knowledge about the E sym (ρ) has significant ramifications in answering many interesting questions regarding the structure of rare isotopes and neutron stars, dynamics of heavy-ion collisions and supernova explosions as well as the frequency and strain amplitude of gravitational waves from deformed pulsars and/or cosmic collisions involving neutron stars. During the last two decades, significant efforts have been devoted to exploring the E sym (ρ) using both terrestrial laboratory experiments [2][3][4][5][6][7][8][9][10][11][12] and astrophysical observations [13][14][15][16][17][18][19][20]. Extensive surveys of the extracted constraints on the E sym (ρ) around the saturation density ρ 0 indicate that the central values of the E sym (ρ 0 ) and its slope L = [3ρ(∂E sym /∂ρ)] ρ0 scatter around 31.6 MeV and 58.9 MeV, respectively [14,21,22]. At densities away from ρ 0 , however, the E sym (ρ) remains rather unconstrained especially at supra-saturation densities [12].

Progress in Constraining Nuclear Symmetry Energy Using Neutron Star Observables Since GW170817

“…Their correlations have significant effects on a number of neutron star properties [11]. While the individual values of L and K sym shown in Figures 1 and 2 are useful, future constraints on their correlations will also be important [82,[90][91][92].…”

A Modern View of the Equation of State in Nuclear and Neutron Star Matter

“…Experimental information on the symmetry energy at saturation S 0 and its first derivative L can be obtained from the analysis of giant [80] and pygmy [81,82] dipole resonances, isospin diffusion measurements [83], isobaric analog states [84], measure-ments of the neutron skin thickness in heavy nuclei [85][86][87][88] and the meson production in HICs [89]. However, whereas S 0 is more or less well established (≈ 3 MeV), the values of L (30 MeV < L < 87 MeV), and especially those of K sym (−400 MeV < K sym < 100 MeV) are still quite uncertain and poorly constrained [90,91], and therefore we disregard them in our analysis.…”

The Equation of State of Nuclear Matter: From Finite Nuclei to Neutron Stars

“…Experimental information on the symmetry energy at saturation S 0 and its derivative L can be obtained from several sources such as the analysis of giant [83] and pygmy [84,85] dipole resonances, isospin diffusion measurements [86], isobaric analog states [87], measurements of the neutron-skin thickness in heavy nuclei [88][89][90][91][92] and meson production in heavy-ion collisions [93]. However, whereas S 0 is more or less well established (≈30 MeV), the values of L (30 MeV < L < 87 MeV), and especially those of K sym (−400 MeV < K sym < 100 MeV) are still quite uncertain and poorly constrained [94,95]. The reason why the isospin dependent part of the nuclear EoS is so uncertain is still an open question, very likely related to our limited knowledge of the nuclear forces and, in particular, to its spin and isospin dependence.…”