We study relationships between the neutron-rich skin of a heavy nucleus and the properties of neutron-star crusts. Relativistic effective field theories with a thicker neutron skin in 208 Pb have a larger electron fraction and a lower liquid-to-solid transition density for neutron-rich matter. These properties are determined by the density dependence of the symmetry energy which we vary by adding nonlinear couplings between isoscalar and isovector mesons. An accurate measurement of the neutron radius in 208 Pb-via parity violating electron scattering-may have important implications for the structure of neutron stars.It is an extrapolation of 18 orders of magnitude from the neutron radius of a heavy nucleus-such as 208 Pb with R n ≈ 5.5 fm-to the approximately 10 km radius of a neutron star. Yet both radii depend on our incomplete knowledge of the equation of state of neutron-rich matter. Therefore, an accurate measurement of the neutron radius in 208 Pb may have important implications for the structure of neutron stars.Heavy nuclei are expected to have a neutron-rich skin. This important feature of nuclear structure arises because of the large neutron excess and because the Coulomb barrier reduces the proton density at the surface. The thickness of the neutron skin depends on the pressure of neutron-rich matter: the greater the pressure, the thicker the skin as neutrons are pushed out against surface tension. The same pressure supports a neutron star against gravity [1]. Thus models with thicker neutron skins often produce neutron stars with larger radii.Neutron stars are expected to have a solid crust of nonuniform neutron-rich matter above a liquid mantle. The phase transition from solid to liquid depends on the properties of neutron-rich matter. Indeed, a high pressure implies a rapid rise of the energy with density making it energetically unfavorable to separate uniform matter into regions of high and low densities. Thus a high pressure typically implies a low transition density from a solid crust to a liquid mantle. This suggests an inverse relationship: the thicker the neutron-rich skin of a heavy nucleus, the thinner the solid crust of a neutron star.In this letter we study possible "data-to-data" relations between the neutron-rich skin of a heavy nucleus and the crust of a neutron star. These relations may impact neutron star observables. Indeed, properties of the crust are important for models of glitches in the rotational period of pulsars [2,3], for the shape and gravitational radiation of non-spherical rotating stars [4] and for neutron-star cooling [5]. Note that the skin of a heavy nucleus and the crust of a neutron star are composed of the same material: neutron-rich matter at similar densities.The Parity Radius Experiment (PREX) at the Jefferson Laboratory aims to measure the neutron radius in 208 Pb via parity violating electron scattering [6,7]. Parity violation is sensitive to the neutron density because the Z 0 boson couples primarily to neutrons. The result of this purely electroweak experim...

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The symmetry energy contribution to the nuclear equation of state impacts various phenomena in nuclear astrophysics, nuclear structure, and nuclear reactions. Its determination is a key objective of contemporary nuclear physics, with consequences for the understanding of dense matter within neutron stars. We examine the results of laboratory experiments that have provided initial constraints on the nuclear symmetry energy and on its density dependence at and somewhat below normal nuclear matter density. Even though some of these constraints have been derived from properties of nuclei while others have been derived from the nuclear response to electroweak and hadronic probes, within experimental uncertainties-they are consistent with each other. We also examine the most frequently used theoretical models that predict the symmetry energy and its slope parameter. By comparing existing constraints on the symmetry pressure to theories, we demonstrate how contributions of three-body forces, which are essential ingredients in neutron matter models, can be determined.

The historical first detection of a binary neutron star merger by the LIGO-Virgo Collaboration [B. P. Abbott et al., Phys. Rev. Lett. 119, 161101 (2017)PRLTAO0031-900710.1103/PhysRevLett.119.161101] is providing fundamental new insights into the astrophysical site for the r process and on the nature of dense matter. A set of realistic models of the equation of state (EOS) that yield an accurate description of the properties of finite nuclei, support neutron stars of two solar masses, and provide a Lorentz covariant extrapolation to dense matter are used to confront its predictions against tidal polarizabilities extracted from the gravitational-wave data. Given the sensitivity of the gravitational-wave signal to the underlying EOS, limits on the tidal polarizability inferred from the observation translate into constraints on the neutron-star radius. Based on these constraints, models that predict a stiff symmetry energy, and thus large stellar radii, can be ruled out. Indeed, we deduce an upper limit on the radius of a 1.4M_{⊙} neutron star of R_{⋆}^{1.4}<13.76  km. Given the sensitivity of the neutron-skin thickness of ^{208}Pb to the symmetry energy, albeit at a lower density, we infer a corresponding upper limit of about R_{skin}^{208}≲0.25  fm. However, if the upcoming PREX-II experiment measures a significantly thicker skin, this may be evidence of a softening of the symmetry energy at high densities-likely indicative of a phase transition in the interior of neutron stars.

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