A Geometric Approach to Nuclear Cohesion

Standard models of nuclear binding energy rely on phenomenological multi-term decompositions statistically fitted to experimental data. Although highly effective, these models partly obscure the internal collective organization of the nucleus. We propose here a complementary approach based on a minimal geometric hypothesis: dominant nuclear cohesion results from the collective organization of α clusters interpreted as coherent units forming a marginally rigid three-dimensional structure. By imposing the minimal isostatic condition of a 3D network, the number of internal bonds is determined by the topological relation L =3𝑁𝛼 −6 which leads to a deterministic expression for the total binding energy. Starting from a single normalization fixed on the doubly magic oxygen-16 nucleus, the model introduces no additional local adjustments. It captures the dominant trend of binding energies for a wide range of light and intermediate nuclei. A quantitative analysis shows an average accuracy of 97.9% for nuclei with 𝑍 = 0to 40, 92.2% for nuclei with 𝑍 = 40to 92, and an overall accuracy of approximately 94% over the entire set studied. The progressive degradation observed in the region of heavy nuclei is consistent with the expected increase of Coulomb effects, not explicitly taken into account in this minimal formulation.