Directional correlations in nuclear charge-radius model residuals enable extrapolation with calibrated uncertainties

Abstract

We identify a pronounced directional anisotropy in the residuals between measured nuclear charge radii and two structurally distinct global models: the phenomenological Weizsäcker--Skyrme formula (WS*) and the microscopic Hartree--Fock--Bogoliubov model (HFB-25). In both cases, the residuals remain correlated over several neutron steps along isotopic chains but decorrelate almost completely after a single proton step along isotonic chains. This common pattern, reinforced by a strong correlation between the two residual fields ($r\simeq0.73$), points to a shared deficiency of both global descriptions rather than a model-specific artefact. Motivated by this geometry, we introduce ARCUS (Anisotropic Residual Calibration with Uncertainty Scaling), which applies an anisotropic kernel-regression correction with empirically calibrated prediction intervals. In out-of-fold cross-validation, ARCUS reduces the root-mean-square errors of both WS* and HFB-25 by approximately a factor of two. On an independent, temporally blind test set of 129 nuclei, its prediction intervals retain coverage close to nominal under extrapolation. An isotropic kernel matched to the same cross-validation coverage instead substantially overestimates uncertainties on the blind set, showing that reliable calibration transfer depends on encoding the directional residual structure. In regions with anomalous structure, such as around $^{52}$Ca, ARCUS keeps its prediction intervals wide enough to cover the increased errors, rather than yielding overconfident point predictions. We also extend these calibrated predictions to 1008 unmeasured nuclei near known isotopic chains, ranked by uncertainty to support the future charge-radius measurements.