AI 中文总结
研究发现核电荷半径模型残差的方向相关性，提出ARCUS方法校正WS*和HFB-25的误差，外推时可保持预测区间覆盖率，还扩展了1008个未测量核的预测以支撑未来测量。
AI 中文摘要
我们在测量的核电荷半径与两种结构不同的全局模型的残差中识别出显著的方向各向异性：唯象的魏茨泽克-斯凯姆公式（WS*）和微观的哈特利-福克-博戈留波夫模型（HFB-25）。在两种模型中，残差沿同位素链在多个中子步长上保持相关，但沿同中子素链在单个质子步长后几乎完全去相关。这种共同模式因两个残差场间的强相关性（r≈0.73）而强化，表明其源于两种全局描述的共同缺陷，而非模型特有的人为结果。受此几何特征启发，我们引入ARCUS（各向异性残差校准与不确定性缩放），该方法应用带经验校准预测区间的各向异性核回归校正。在折外交叉验证中，ARCUS将WS*和HFB-25的均方根误差均降低约一半。在包含129个核的独立时间盲测试集上，其预测区间在外推下保持接近标称的覆盖率；而匹配相同交叉验证覆盖率的各向同性核则在盲集上大幅高估不确定性，表明可靠的校准传递依赖于编码残差的方向结构。在具有异常结构的区域，如52Ca附近，ARCUS保持足够宽的预测区间以覆盖增大的误差，而非产生过度自信的点预测。我们还将这些校准后的预测扩展到已知同位素链附近的1008个未测量核，并按不确定性排序以支持未来的电荷半径测量。
英文摘要
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.
