The Neutron Skin — a parameter-free ratio against PREX and CREX

A neutron-rich heavy nucleus carries its excess neutrons in a surface layer: the neutron skin, the thin region where the neutron density distribution extends beyond the proton density distribution. Its thickness is the difference of the neutron and proton root-mean-square radii. Two parity-violating electron-scattering experiments have measured it with minimal nuclear-structure model input: PREX-2 places the skin of at fm, and CREX places that of at fm (experimental and model errors combined in quadrature). The two results are difficult to reconcile: leading energy-density functionals that reproduce one tend to miss the other, and the associated spread in the density-dependence of the symmetry energy remains an open problem in nuclear structure. This paper reports a single parameter-free geometric prediction for these two nuclei. Model the nucleus as a uniform sphere of radius with fm, and require the neutron excess to occupy the outermost spherical shell. The shell thickness is then fixed by volume conservation alone: By construction this is an upper bound on the skin: mixing any of the excess into the interior can only reduce the shell thickness. From it, three predictions follow, and all three were tested. The bound is satisfied for both nuclei. The parameter-free ratio of the two skin thicknesses lies from the measured ratio (a magnitude; §3 reports the signed pull as , predicted below measured). The fraction of the bound realized by each measurement (the shell occupancy) agrees between the two nuclei within errors. The model bounds the absolute skin rather than predicting it — a restriction imposed by the geometry. This record holds one paper on its own and is refreshed every couple of months. The complete deposit, 10.5281/zenodo.21788037, holds every paper with its code and data and is updated first; for the newest version of this paper, go there.