Empirical Universal Scaling of Neutron-Skin Curvature Across the Nuclear Chart

Abstract

Neutron skins encode essential information about nuclear geometry, surface structure, and isovector response, yet a compact description across the nuclear chart remains elusive. We present an empirical analysis of neutron-excess surface systematics using a mass-normalized, charge-radius-derived proxy ("neutron-skin curvature") built from evaluated experimental charge radii. By normalizing radii to the reduced Compton length $r_B=\hbar/(mc)$, we form a dimensionless curvature ratio that enables comparison across isotopic chains of widely varying mass. When expressed versus normalized neutron excess, data for more than 800 nuclei spanning 88 elements collapse onto a single empirical curve without element-specific rescaling or interaction-model tuning; the curve is used only as a fixed baseline for residual analysis. The collapse accounts for approximately 88% of the variance and is substantially tighter than droplet-style baselines fit to the same dataset. Residuals show structured deviations: three finite-size regimes (skin formation, relaxation toward bulk geometry, and saturation) and a distinct few-body domain for very light nuclei ($Z\le 4$). Stratifying residuals by periodic-table families reveals tighter submanifolds for several groups, suggesting additional geometric constraints layered on the global trend. These results are obtained directly from evaluated experimental data and physical constants, without introducing new interaction terms, and motivate further study of geometric correlations with other nuclear and atomic observables.