Universal correlations in the nuclear symmetry energy, slope parameter, and curvature

Abstract

From general Fermi liquid theory arguments, we derive correlations among the symmetry energy (J), its slope parameter (L), and curvature (Ksym) at nuclear matter saturation density. We argue that certain properties of these correlations do not depend on details of the nuclear forces used in the calculation. We derive as well a global parametrization of the density dependence of the symmetry energy that we show is more reliable, especially at low densities, than the usual Taylor series expansion around saturation density. We then benchmark these predictions against explicit results from chiral effective field theory. PACS numbers:The nuclear isospin-asymmetry energy, which characterizes the energy cost of converting protons into neutrons in an interacting many-body system, is an important organizing concept linking the properties of atomic nuclei to the structure and dynamics of neutron stars. In particular the isospin-asymmetry energy governs the proton fraction of dense matter in beta equilibrium, the thickness of neutron star crusts, and the typical radii of neutron stars [1][2][3][4][5][6]. For these reasons the nuclear isospinasymmetry energy is a primary focus of experimental investigations at current and next-generation rare-isotope facilities such as the Radioactive Isotope Beam Factory (RIBF), the Facility for Antiproton and Ion Research (FAIR), and the Facility for Rare Isotope Beams (FRIB).In recent years, theoretical [6-10] and experimental [11][12][13][14][15] studies have reduced the uncertainties on the isospin-asymmetry energy at and below the density scales of normal nuclei, but more challenging is to derive constraints at the higher densities reached in the cores of neutron stars. Given the experimental difficulties of creating and studying high-density, low-temperature matter in the lab, an alternative strategy has been to extract the coefficients in the Taylor series expansion of the isospinasymmetry energy about nuclear matter saturation density. For instance, the slope parameter has been shown to correlate strongly with neutron skin thicknesses in nuclei [13,16,17], nuclear electric dipole polarizabilities [18-23], and the difference in charge radii of mirror nuclei [24,25]. Determining the isospin-asymmetry energy curvature is more challenging [26-28] with larger associated uncertainties.A feature observed in many experimental and theoretical investigations is a nearly linear correlation between the value of the isospin-asymmetry energy at nuclear matter saturation density, its slope, and curvature (for a recent comprehensive analysis, see Ref. [29]). In Ref.[10] it was shown that even chiral nuclear potentials at * Electronic address: holt@physics.tamu.edu † Electronic address: ylim@tamu.edu next-to-leading order (NLO), which are rather simplistic and contain no three-body forces, exhibit a correlation slope consistent with previous microscopic calculations at N2LO and N3LO in the chiral expansion. This suggests that certain aspects of the correlation are ultimately associated with low-ener...

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].…”

Prior probability distributions of neutron star crust models

“…Varying that reference density over a range subject to constraints from chiral-EFT, (Holt and Lim 2018) obtain a 0 = 5.53-6.41 MeV fm 3 and b 12 = 0 to 16 MeV fm 3 (Holt and Lim 2018). This represent a conservative range that encompasses all current PNM EOSs predicted by chiral-EFT and their uncertainties.…”

“…Our second probability distribution is over a conservative range of PNM EOSs allowed by chiral EFT calculations. Holt and Lim (2018) showed that from general arguments about the neutron-neutron interaction from Fermi Liquid theory, there exist correlations between J, L and K sym . The correlations can be written in the following form, in terms of J:…”

“…a 0 and b 12 are related to the Fermi-liquid parameters that characterize the two-neutron interaction at a particular reference density (Holt and Lim 2018;; see also the description in Newton and Crocombe (2020).…”

Analysis of the neutron matter equation of state and the symmetry energy up to fourth order of chiral effective field theory

“…Additional studies that have explored these correlations, using a variety of phenomenological and theoretical models, are provided in Refs. [50][51][52][53][54][55]. Constrains on L vary considerably depending on the methods employed [38,56,57].…”