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arXiv · 2510.14289

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

Sergei K. Suslov
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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 Although superseded by the Dirac equation and modern quantum electrodynamics, the semiclassical approach offers a historically and pedagogically valuable perspective.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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Sergei K. Suslov. 2025-10-15. Classification of Transuranium Elements in Terms of `Winding' Numbers in the Bohr-Sommerfeld Model. https://arxiv.org/abs/2510.14289

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