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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2510.14289 |
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| _version_ | 1866911267534405632 |
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| author | Suslov, Sergei K. |
| author_facet | Suslov, Sergei K. |
| contents | 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 Although superseded by the Dirac equation and modern quantum electrodynamics, the semiclassical approach offers a historically and pedagogically valuable perspective.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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_14289 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Classification of Transuranium Elements in Terms of `Winding' Numbers in the Bohr-Sommerfeld Model Suslov, Sergei K. Quantum Physics 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 Although superseded by the Dirac equation and modern quantum electrodynamics, the semiclassical approach offers a historically and pedagogically valuable perspective.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. |
| title | Classification of Transuranium Elements in Terms of `Winding' Numbers in the Bohr-Sommerfeld Model |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2510.14289 |