Constraining the Symmetry Parameters of the Nuclear Interaction

Abstract

One of the major uncertainties in the dense matter equation of state has been the nuclear symmetry energy. The density dependence of the symmetry energy is important in nuclear astrophysics, as it controls the neutronization of matter in core-collapse supernovae, the radii of neutron stars and the thicknesses of their crusts, the rate of cooling of neutron stars, and the properties of nuclei involved in r-process nucleosynthesis. We show that fits of nuclear masses to experimental masses, combined with other experimental information from neutron skins, heavy ion collisions, giant dipole resonances, and dipole polarizabilities, lead to stringent constraints on parameters that describe the symmetry energy near the nuclear saturation density. These constraints are remarkably consistent with inferences from theoretical calculations of pure neutron matter, and, furthermore, with astrophysical observations of neutron stars. The concordance of experimental, theoretical, and observational analyses suggests that the symmetry parameters S v and L are in the range 29.0-32.7 MeV and 40.5-61.9 MeV, respectively, and that the neutron star radius, for a 1.4 M star, is in the narrow window 10.7 km < R < 13.1 km (90% confidence). We can also set tight limits to the size of neutron star crusts and the fractional moment of inertia they contain, as well as the overall moment of inertia and quadrupole polarizability of 1.4 M stars. Our results also have implications for the disk mass and ejected mass of compact mergers involving neutron stars.

Symmetry Parameter Constraints from a Lower Bound on Neutron-matter Energy

“…Based on these calculations one can obtain constraints on the symmetry energy parameters if one assumes the quadratic expansion to be approximately valid. The extracted symmetry energy parameters are consistent with experimental determinations (Lattimer & Lim 2013;Tews et al 2013). Due to the intimate connection of PNM with the symmetry energy, any additional information about PNM translates into additional constraints on S 0 and L. Establishing a lower limit for the energy of PNM, e.g., would result in general limits to the symmetry energy parameters that so far have not been considered.…”

“…A recent Hartree-Fock study by the UNEDF collaboration (Kortelainen et al 2010) found the confidence ellipse shown in Figure 8, assuming a fiducial fitting error of 2 MeV for the nuclear binding energies. A nearly identical result was found from a liquid-droplet analysis (Lattimer & Lim 2013). This confidence ellipse is essentially compatible with the UG constraint (for positive values of L).…”

“…Other experimental constraints on symmetry energy parameters are reviewed in Lattimer & Lim (2013) and Oertel et al (2017). They indicate that consistency with measurements of nuclear masses, giant dipole resonances and dipole polarizabilities, neutron-skin thicknesses, and flows in heavy-ion collisions is achieved for 30 MeV S 0  32 MeV and 40 MeV L 60 MeV (left panel of Figure 9).…”

“…Excluded regions are shown by shading. Left panel: Experimental constraints are from Lattimer & Lim (2013) and Lattimer & Steiner (2014), supplemented by isobaric analog states and isovector skin (IAS+ΔR) results from Danielewicz et al (2017). The thick dashed curve shows the analytic bound from Equation ( physical correlations between the parameters.…”

Strangeness in Neutron Star Cooling

“…Nuclear structure and symmetry energy are among the main scientific goal of RAON [19]. Symmetry energy is essential for the understanding of the nuclear matter properties beyond normal nuclear matter density [20]. Since central part of neutron star reaches several times of normal nuclear matter density, RAON will be able to provide important information for neutron star equation of state [21].…”