Oganesson versus Uranium Hydrogen-like Ions and Beyond (from the Viewpoint of Old Quantum Mechanics)
Abstract
We compare, within the framework of the old Bohr-Sommerfeld atomic model, Uranium (Z=92) versus hypothetical Oganesson (Z=118) relativistic hydrogen-like ions and beyond. Existence of a self-intersecting orbit in the super strong static Coulomb field is demonstrated with the aid of Mathematica computer algebra system. A possibility of a similar 'Oganesson-type' effect in a strong gravitational field is also mentioned. Appearance of a multi self-intersecting trajectory is demonstrated in a hypothetical Unbibium, an element with Z = 122, and beyond with Z< 136. A topological classification of the strength for Coulomb fields in the superheavy transuranium elements may be given in terms of the 'winding' numbers.
Keywords
Cite
@article{arxiv.2509.06249,
title = {Oganesson versus Uranium Hydrogen-like Ions and Beyond (from the Viewpoint of Old Quantum Mechanics)},
author = {Kamal Barley and Andreas Ruffing and Sergei K. Suslov},
journal= {arXiv preprint arXiv:2509.06249},
year = {2025}
}
Comments
12 pages, 7 figures, 2 tables, 34 references