Patterns in Isotopic Compositions, Nucleon Numbers, and Magic Numbers

Abstract This paper identifies a distinct pattern in the nuclear stability of isotopes with a nucleon number A = S(S+1)-2. It posits that S represents an ordinal number corresponding to a shell, with the maximum observed value of S being 16. The relation A=S(S+1) lies in a close packed hexagonal arrangement pattern. In this configuration, as neutrons fill certain shells to form closed loops, and each neutron couples with one or more protons in adjacent shells, the total number of neutrons or protons corresponds to magic numbers. This deduction leads to the elucidation of the nucleon arrangement patterns for each nuclide. The paper presents the nucleon arrangement schemes for 20 key nuclides and traces the evolution of shell structures. Regularities in the nucleon numbers of isotopes with the highest relative abundance, magic number phenomena, and the inversion of elemental atomic masses serve as evidence supporting these nucleon arrangement patterns. The proposed regularities and patterns unexpectedly emerge through an intriguing toroidal helix model. This study requires reference to the concept of an “electron cloud,” assuming nucleons as a toroidal helical “nucleon cloud” to explore the interaction mechanisms among nucleons. The structural model is novel, and further research must comprehensively cover a wide range of nuclear characteristics.