Decoding the Density Dependence of the Nuclear Symmetry Energy

TL;DR

This paper refines the understanding of how the nuclear symmetry energy varies with density by analyzing experimental data across a range of densities, leading to more precise constraints relevant for neutron star physics.

Contribution

It demonstrates that experimental observables probe a range of densities, not just saturation density, and provides a detailed density-dependent symmetry energy profile from 0.25 to 1.5 times saturation density.

Findings

Determined the slope parameter L at 0.10 fm^{-3} as 53.1±6.1 MeV.

Estimated neutron skin thickness of 0.23±0.04 fm for 208Pb.

Predicted neutron star radius of 13.1±0.6 km for 1.4 solar masses.

Abstract

The large imbalance in the neutron and proton densities in very neutron rich systems increases the nuclear symmetry energy so that it governs many aspects of neutron stars and their mergers. Extracting the density dependence of the symmetry energy therefore constitutes an important scientific objective. Many analyses have been limited to extracting values for the symmetry energy, $S_0$, and its ``derivative'', $L$, at saturation density $\rho_0 \approx 2.6 \times 10^{14}~\mathrm{g/cm^3}$ $\approx 0.16~\mathrm{nucleons/fm^{3}}$, resulting in constraints that appear contradictory. We show that most experimental observables actually probe the symmetry energy at densities far from $\rho_0$, making the extracted values of $S_0$ or $L$ imprecise. By focusing on the densities these observables actually probe, we obtain a detailed picture of the density dependence of the symmetry energy from $0.25\rho_0$ to $1.5\rho_0$. From this experimentally derived density functional, we extract $L_{01}=53.1\pm6.1 MeV$ at $\rho \approx 0.10~\mathrm{fm^{-3}}$, a neutron skin thickness for $^{208}Pb$ of $R_{np} =$ $0.23\pm0.04$ fm, a symmetry pressure at saturation density of $P_0=3.2\pm1.2 MeV/fm^3$ and suggests a radius for a 1.4 solar mass neutron star of $13.1\pm0.6$ km.