A Hierarchical Bayesian Analysis of Neutron-Skin Thicknesses and Implications for the Symmetry-Energy Slope

TL;DR

The paper tackles the challenge of extracting reliable information about the symmetry-energy slope $L$ from heterogeneous neutron-skin measurements by adopting a hierarchical Bayesian framework. It models the neutron-skin thickness as a latent function of isospin asymmetry $I=(N-Z)/A$ and nuclear size $A^{1/3}$, with method-specific biases and intrinsic scatters to account for diverse experimental and theoretical systematics. The global fit to 57 measurements across hadronic, electromagnetic, mesonic, and astrophysical probes yields a smooth latent Sn-band for $ abla r_{np}$, from which an EDF-based mapping to nuclear-matter parameters $(J,L)$ is performed, revealing a pronounced compression of $L$ while $J$ remains less constrained. The approach demonstrates robust, transparent constraints on sub-saturation isovector physics and strengthens the finite-nucleus–neutron-star bridge, with clear potential for extension to future data and other isotopic chains.

Abstract

Neutron-skin thicknesses provide a sensitive probe of the isovector sector of the nuclear equation of state and its density dependence, commonly characterized by the symmetry-energy slope parameter L. A wide variety of experimental and observational methods have been used to extract neutron skins, ranging from hadronic and electromagnetic probes of finite nuclei to inferences from neutron-star observations. Each approach carries distinct theoretical and systematic uncertainties, complicating global interpretations and obscuring genuine physical trends. In this work we present a hierarchical Bayesian framework for the statistically consistent synthesis of heterogeneous neutron-skin constraints. The neutron-skin thickness is modeled as a smooth latent function of isospin asymmetry and nuclear size, while method-dependent bias parameters and intrinsic nuisance widths are introduced to account for unmodeled experimental and theoretical systematics. Focusing on the tin isotopes, we infer probabilistic neutron-skin trends from 100Sn to 140Sn, finding minimal uncertainties near stability and increasing uncertainties toward the proton-rich and neutron-rich extremes. We assess the consistency of nuclear energy-density functionals and obtain conditional constraints on the symmetry-energy parameters. The resulting posterior exhibits a pronounced compression of the symmetry-energy slope parameter L, reflecting the dominant sensitivity of neutron skins to sub-saturation symmetry pressure. We demonstrate that our hierarchical Bayesian framework provides robust and transparent constraints on the sub-saturation isovector sector of the nuclear equation of state.

Figures (4)

• Figure 1: Neutron skin data collected from several recent sources, including antiproton annihilation, proton elastic scattering, PVES, pionic atoms, PDR, GDR, AGDR, coherent pion production, and neutron stars observations. See text for details.
• Figure 2: Posterior-predictive neutron-skin thickness $\Delta r_{np}$ as a function of neutron number $N$ along the tin isotopic chain. The solid line denotes the posterior median, while the shaded bands indicate 68% and 90% credible intervals.
• Figure 3: The solid curve and shaded band show the inferred latent neutron-skin systematics along the Sn isotopic chain (same as figure \ref{['fig:sn_chain']}). The gray envelopes represent the posterior-weighted EDF predictive distribution.
• Figure 4: Highest-posterior-density (HPD) constraints in the $(J,L)$ plane obtained from the latent Sn neutron-skin systematics. Gray dashed contours show the unweighted EDF prior density in $(J,L)$ space. Blue shaded regions denote the 90% (light) and 68% (dark) HPD posterior regions obtained after weighting each EDF by its likelihood against the latent Sn constraint. Black points indicate individual EDFs, with marker size proportional to their posterior weight. The red star marks the posterior median.