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

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.