Classification of Transuranium Elements in Terms of `Winding' Numbers in the Bohr-Sommerfeld Model

• URL: http://arxiv.org/abs/2510.14289v2
• Date: Sun, 19 Oct 2025 19:28:51 GMT
• Title: Classification of Transuranium Elements in Terms of `Winding' Numbers in the Bohr-Sommerfeld Model
• Authors: Sergei K. Suslov,
• Abstract summary: We revisit the Bohr-Sommerfeld atomic model to explore hydrogen-like ions of Uranium, Oganesson, and hypothetical superheavy elements beyond.<n>Using the Sommerfeld fine structure formula and computer algebra methods, we demonstrate the appearance of self-intersecting orbits in super strong Coulomb fields.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We revisit the Bohr-Sommerfeld atomic model to explore hydrogen-like ions of Uranium ($Z=92$), Oganesson ($Z=118$), and hypothetical superheavy elements beyond. Although superseded by the Dirac equation and modern quantum electrodynamics, the semiclassical approach offers a historically and pedagogically valuable perspective. Using the Sommerfeld fine structure formula and computer algebra methods, we demonstrate the appearance of self-intersecting orbits in super strong Coulomb fields, beginning with Oganesson and hypothetical elements up to $Z\le137$. These orbits can be classified by their `winding' numbers, providing a simple topological description of Coulomb field strength in this framework. Our results highlight a conceptual bridge between early quantum theory and modern superheavy element physics.

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