Constraining the density dependence of the symmetry energy with nuclear data and astronomical observations in the Korea-IBS-Daegu-SKKU framework

Abstract

Background: The properties of very neutron rich nuclear systems are largely determined by the density dependence of the nuclear symmetry energy. The KIDS framework for the nuclear equation of state (EoS) and energy density functional (EDF) offers the possibility to explore the symmetryenergy parameters such as J (value at saturation density), L (slope at saturation), Ksym (curvature at saturation) and higher-order ones independently of each other and independently of assumptions about the in-medium effective mass, as previously shown in the cases of closed-shell nuclei and neutron-star properties. Purpose: We examine the performance of EoSs with different symmetry energy parameters on properties of nuclei and observations of neutron stars and gravitational waves in an effort to constrain in particular L and Ksym or the droplet-model counterpart Kτ . Method: Assuming a standard EoS for symmetric nuclear matter, we explore several points on the hyperplane of (J, L, Ksym or Kτ ) values. For each point, the corresponding KIDS functional parameters and a pairing parameter are obtained for applications in spherical even-even nuclei. This is the first application of KIDS energy density functionals with pairing correlations in a spherical HFB computational code. The different EoSs are tested successively on the properties of closed-shell nuclei, along the Sn isotopic chain, and on astronomical observations, in a step-by-step procedure of elimination and correction. Results: A small regime of best-performing parameters is determined and correlations between symmetry-energy parameters are critically discussed. The results strongly suggest that Ksym is negative and no lower than −200 MeV, that Kτ lies between roughly −400 and −300 MeV and that L lies between 40 and 65 MeV, with L 55MeV more likely. For the selected well-performing sets, corresponding predictions for the position of the neutron drip line and the neutron skin thickness of selected nuclei are reported. The results are only weakly affected by the choice of effective mass values. Parts of the drip line can be sensitive to the symmetry energy parameters. Conclusion: Using KIDS EoSs for unpolarized homogeneous matter at zero temperature and KIDS EDFs with pairing correlations in spherical symmetry we have explored the hyperplane of symmetryenergy parameters. Using both nuclear-structure data and astronomical observations as a testing ground, a narrow regime of well-performing parameters has been determined, free of non-physical correlations and decoupled from constraints on the nucleon effective mass. The results underscore the role of Kτ and of precise astronomical observations. More-precise constraints are possible with precise fits to nuclear energies and, in the future, more-precise input from astronomical observations.

Bayesian inference of finite-nuclei observables based on the KIDS model

“…where m s and m v are the isoscalar and isovector nucleon effective mass, respectively. We note that G S and G V are trivially related to the coefficients C 12 and D 12 defined in other studies [55,57], namely G S = −2C 12 , G V = 2D 12 . From Eq.…”

“…It is seen that incorporating K sym as an independent variable can significantly broaden the posterior PDFs of L and K τ . K sym cannot be constrained at all from nu-clear data within the KIDS model, although we should note that it can be constrained from astronomical observations, which probe higher densities, with existing data strongly suggesting −200 MeV < K sym < 0 [55]. A positive K sym − L correlation based on the KIDS model, instead of the negative E 0 sym − L correlation obtained based on the standard SHF model, is observed under the constraint of the neutron-skin thickness.…”

“…Additional constraints from astrophysical observables would further reduce the range of K sym and 3E 0 sym −L as shown in Ref. [55].…”

“…Any set of EOS parameters characterizing, typically, the saturation point and the density dependence of the symmetry energy, is readily transposed to a nuclear EDF for finite nuclei in the highly convenient form of an extended Skyrme functional, with the additional freedom of choosing the values for the effective mass and other interaction parameters which are not active in homogeneous nuclear matter [53,54]. Studies of symmetry-energy parameters based on astronomical observations and bulk nuclear properties were publicized recently [55,56], and a pilot study of the neutron-skin thickness was also conducted [57].…”

“…( 5)), ρ 0 , and the nucleon effective masses (see also Ref. [55]). Under the constraints of ∆r np and IVGDR data for 208 Pb and 120 Sn, the posterior correlated PDFs between K sym and 3E 0 sym − L are displayed in Fig.…”