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.

Figures (14)

• Figure 1: Universal neutron-skin curvature collapse across the nuclear chart. The dimensionless ratio $K_{R,\mathrm{skin}}/K_{R,\mathrm{core}}$ is plotted as a function of normalized neutron excess $N_{\mathrm{excess}}/Z$ for all validated nuclei. Data from 826 isotopes spanning 88 elements collapse onto a single curve without fitted parameters. The solid line shows the fixed empirical baseline $F(x)$ used for residual analysis.
• Figure 2: Radii-only geometric baseline. A skin proxy constructed from experimental charge radii without mass normalization is plotted against $N_{\mathrm{excess}}/Z$. While qualitative growth with neutron excess is evident, no cross-element collapse is observed, and substantial element-dependent scatter remains.
• Figure 3: Comparison of droplet-style isovector scaling to curvature-normalized scaling. The droplet-style baseline (dashed line) is a global linear fit to the radii-only proxy. The solid curve shows the derived curvature baseline for reference. Despite fitted parameters, the droplet-style baseline does not produce a comparable collapse.
• Figure 4: Residual comparison between curvature-normalized scaling and the droplet-style baseline. Residuals relative to the derived baseline exhibit reduced scatter and minimal structure compared to the droplet-style residuals, indicating improved cross-element organization.
• Figure 5: Residual neutron-skin curvature $\Delta K$ as a function of normalized neutron excess. Three finite-size regimes are observed: an initial skin-formation regime at low $N_{\mathrm{excess}}/Z$, a relaxation regime at intermediate values, and a saturation regime at higher neutron excess. The structure indicates physical finite-size effects rather than random scatter.