The SSS Symmetric Skeleton Structure Approach to Nuclear Structure: A Spatial Interpretation of Symmetry and Harmonic Distribution Principles

The explanation of the internal structure of the atomic nucleus is one of the fundamental problems of modern nuclear physics. Existing theoretical models — the liquid drop model, the shell model, and collective models — explain various features of nuclear stability and energy levels; however, the visual and structural interpretation of the spatial arrangement of protons and neutrons remains insufficiently clear. In this work, a new interpretative approach to the spatial organization of the atomic nucleus is presented — the SSS (Symmetric Skeleton Structure) approach. This approach is not proposed as an alternative nuclear model, but rather as a spatial interpretation of the results obtained from existing theories in terms of symmetry. The main principle of the SSS approach is that nuclear stability is related to the formation of a symmetric skeleton structure created by protons and neutrons within the nucleus. This structure is based on two fundamental symmetry principles: radial symmetry and mirror symmetry. Radial symmetry manifests itself in certain light elements as analogues of regular polyhedral structures. In this case, protons correspond to the vertices of geometric polyhedra located at equal distances from the center of the nucleus. Structures of this type are observed in elements such as beryllium, carbon, oxygen, magnesium, and calcium. In heavier nuclei, however, the dominant symmetry principle is equatorial mirror symmetry. In this case, protons are arranged in layers within the nucleus, forming a symmetric distribution relative to the equatorial plane. This distribution follows harmonic regularities. The study shows that the distribution of protons across layers may form fully harmonic, partially harmonic, or non-harmonic structures. These structures exhibit different stability properties depending on whether the number of protons is even or odd. The work also demonstrates that there are six types of harmonic symmetry, and each type includes four categories of systems. These categories are based on the division rule of protons across layers: triple, quadruple, quintuple, and sextuple harmonic systems. Structural analyses performed for various elements — including tin, mercury, silver, gold, and lead — show that wide intervals of nuclear stability are associated with these harmonic symmetry principles. The article also presents graphical models of nuclear skeleton structures and provides their classification in terms of harmonic type, category, and variant. The results show that the SSS approach allows the structural causes of nuclear stability to be explained in a visual and conceptual manner and expands the spatial interpretation of existing nuclear models.