Symmetric Skeleton Structure (SSS) Approach to Atomic Nuclei: A Comparative Analysis of Symmetry, Harmonicity, and Stability in Molybdenum, Technetium, Promethium, and Samarium Isotopes

This paper presents and applies the Symmetric Skeleton Structure (SSS) approach as a novel framework for interpreting the spatial structure of atomic nuclei. The primary objective of the study is to identify the structural basis of fundamental nuclear properties such as stability and radioactivity.

Within this framework, a comparative analysis is carried out for the isotopes of four chemical elements: molybdenum (Z = 42), technetium (Z = 43), promethium (Z = 61), and samarium (Z = 62).

The selection of these elements is justified by their distinct stability characteristics. Technetium and promethium are the only elements that do not possess stable isotopes in nature, whereas molybdenum and samarium exhibit multiple stable isotopes. This contrast is interpreted within the SSS framework in terms of the symmetry and harmonic organization of the proton skeleton.

According to the SSS model, all atomic nuclei possess an intrinsic symmetric structure, which manifests in two principal forms: central radial symmetry and mirror symmetry with respect to the equatorial plane. Nuclear stability is not determined solely by the presence of symmetry, but rather by the degree of its harmonic organization. In particular, it is demonstrated that an odd number of protons in the equatorial layer disrupts radial symmetry, leading to nuclear instability.

The results of this study indicate that nuclei with fully harmonic and radially symmetric proton skeletons exhibit high stability, whereas partially harmonic structures with broken radial symmetry tend to be radioactive and evolve toward more stable neighboring nuclei. This framework provides a unified structural explanation for the absence of stable isotopes in technetium and promethium.