A Grape-Cluster Atomic Model Based on Proton–electron–Neutron (PeN) Units and Helium Structures

We propose the grape-cluster atomic model, in which proton–electron–neutron (PeN) units serve as universal building blocks of atoms beyond hydrogen. Unlike conventional orbital models, which treat quantum numbers as abstract postulates, this framework derives them directly from the geometric arrangement of PeN shells. The model reproduces several key experimental trends: the proportional increase of inert-gas radii with period number, the linear variation of reciprocal atomic radius with atomic number within periods, and the slope branching observed in heavier periods. It also explains the empirical rule that stable atomic masses are approximately twice the atomic number, and interprets the additional neutrons in heavy nuclei as a structural consequence of PeN substitutions, providing insight into isotope stability and the special role of helium-4. These results show that many features of atomic and nuclear organization can be consistently interpreted within a single structural paradigm. Although still phenomenological, the grape-cluster model offers a unified alternative to orbital-based descriptions, linking periodicity, isotopic diversity, and electronic properties through PeN-based clustering.