Separate shared missing physics from experimental element-dependent structure

Determine how to separate, within the common residual component of the WS* and HFB-25 charge-radius residual fields, the nuclear-structure physics missed by both models from element-dependent structure originating in the experimental charge-radius compilation.

Background

The paper finds a strong correlation between the residual fields of the phenomenological Weizsäcker–Skyrme formula (WS*) and the microscopic Hartree–Fock–Bogoliubov model HFB-25. A common-component decomposition attributes a substantial fraction of the residual variance to a component shared by both theoretical descriptions, while the difference field shows that the models also diverge in an element-structured way.

Because the residuals are computed using common experimental charge radii, the shared element-dependent pattern could reflect either nuclear-structure effects absent from both models or systematic structure in the experimental compilation itself. The authors explicitly state that their analyses do not resolve this attribution, leaving the separation of these contributions as an unresolved problem.

References

We cannot, however, separate within $c$ the physics both models miss from any element-dependent structure in the experimental compilation itself.

— Directional correlations in nuclear charge-radius model residuals enable extrapolation with calibrated uncertainties  (2608.25624 - Kar et al., 26 Aug 2026) in Supplementary Material, Section S2, subsection “Model independence”