Patterns in Isotopic Compositions and Magic Numbers: Insights from a Geometric Model

This paper identifies a regularity in the composition of isotopes and the magic number phenomenon, where nuclei exhibit enhanced stability when the number of nucleons, A, approaches or equals S(S+1) - 2. Using S as the shell number, we derive a nucleon arrangement model consistent with magic numbers and the evolution of shell structure. These patterns emerge from an intriguing torus-helix model with three lobes, resembling Kelvin and Maxwell’s concept of vortex structures, and align with Rutherford’s neutron hypothesis. Furthermore, the proposed toroidal helix nucleon cloud model, which possesses a string-like structure, aligns with the concept of “interactions between strings” insightfully observed in resonance states and Veneziano four-point amplitudes in String Theory.