Spatial Interpretation of the Principle of Energy Minimum: Natural Central Symmetry and Complete Harmonic Mirror Symmetry (Even-Proton Nuclei)

The problem of nuclear stability is one of the central topics of nuclear physics, and the fundamental mechanism underlying this stability is explained by the principle of energy minimum. Existing theoretical models—particularly the shell model, the liquid drop model, and collective approaches—have interpreted the energetic structure of the nucleus from various perspectives [1–4]. However, the spatial–structural symmetry interpretation of the results obtained within these models has not been systematically presented as a distinct classification framework. In this article, a spatial interpretation of the principle of energy minimum is proposed, and two principal forms of structural symmetry underlying nuclear stability are investigated: Natural central (radial) symmetry Complete harmonic mirror symmetry (for even-proton nuclei) The purpose of this work is not to introduce an alternative mechanism to existing nuclear models, but rather to provide a symmetry-based structural interpretation of their results. It is shown that, in the minimum-energy state, nucleon density distribution tends toward maximal symmetry, and this tendency may be classified through specific harmonic symmetry classes. As examples of central symmetry, the nuclei Be-9, C-12, O-16, Mg-24, and Ca-40 are analyzed. Complete harmonic mirror symmetry is examined in Fe-56, Sr-80, Ru-102, Sn-116, Ba-132, Sm-158, W-161, Hg-202, Pb-206, and U-238. The analyses indicate that complete harmonic structures with even proton numbers correspond to broad stability intervals. The proposed approach does not contradict the shell model or the pairing effect; rather, it serves as a spatial-structural interpretative complement to their results.