Symmetry energy in dilute matter and the neutron skin

TL;DR

The paper addresses the CREX-PREX-II neutron-skin discrepancy by seeking a unified non-relativistic EDF description that can accommodate both finite nuclei and dilute matter. It extends the KIDS EDF framework by decoupling the dilute-matter EoS from the saturated regime through a low-density exponential term and adjusting isovector gradient and spin-orbit contributions. A broad parameter sweep shows standard functionals cannot fit CREX and PREX-II simultaneously, but certain low-density-modified EDFs can, yielding compatible $R_{np}$ for $^{48}$Ca and $^{208}$Pb while preserving energies and radii within 1%. The mechanism hinges on enhanced symmetry energy at dilute densities increasing surface pressure, which reduces neutron skins, underscoring the role of surface and isovector structure beyond the saturation-density EoS and pointing to the isovector channel as a focus for future work.

Abstract

Energy density functional (EDF) theory provides a unified framework for the description of nuclei and of infinite nuclear matter. In principle, it facilitates direct connections between nuclear data and the nuclear equation of state (EoS). Although in practice traditional nuclear EDF theory has strained to describe finite nuclei and infinite systems at the same time, recently developed extended EDF models overcome many of the limitations of traditional models in that respect. A recent challenge to EDF and EoS studies has come entirely from within nuclear structure, namely how to account both for the relatively thin neutron skin in 48Ca as extracted by the CREX experiment and the relatively thick neutron skin of 208Pb exctracted by the PREX-II experiment. The discrepancy suggests a surface and structure effect. The present study shows that the puzzle can be resolved in a non-relativistic framework by revisiting the nuclear surface tension and diffuseness, as driven in part by the EoS in dilute matter well below the saturation point and in part by the isovector gradient terms and spin-orbit potential. Such effects have no bearing on the EoS near and above saturation.

Figures (4)

• Figure 1: Scatter plots of predictions for the neutron skin thickness of $^{48}$Ca and $^{208}$Pb for various EDF models which reproduce energies and charge radii of closed-shell nuclei within $1\%$ on average and with realistic EoS parameters. The rectangle encloses the CREX and PREX-II results with their reported errorbars. Black: Standard KIDS EoS and EDFs. Red: With modification of the dilute-matter EoS. Yellow: The subset for which the energies and charge radii of $^{48}$Ca and $^{208}$Pb are reproduced within $1\%$ each.
• Figure 2: Symmetry energy as a function of the density. Blue: The regime of dilute-matter EoS explored in this work. Red: EoSs which were found to reproduce both the CREX and PREX-II measurements as well as basic nuclear properties. Black: The example discussed in Sec. \ref{['sec:surf']}.
• Figure 3: Same as fig. \ref{['fig:skin']} but only for the shown values of symmetry-energy parameters.
• Figure 4: Proton (gray lines) and neutron (black lines) density profiles of $^{48}$Ca (left) and $^{208}$Pb (right) in linear (top) and logarithmic scale. The dot-dashed lines, visible for neutrons, correspond to a regular KIDS EoS and EDF with the symmetry-energy parameters $(J,L,K_{\mathrm{sym}},Q_{\mathrm{sym,}}=(32.5,65,-180,1000)$ MeV. The full lines correspond to an EoS with the same standard parameters but including an enhancement at very low densities. The effect is a small change in the neutron-density diffuseness which suffices to reconcile the CREX and PREX-II values.