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.