TITLE:
A Vortex-Based Geometric Interpretation of Atomic Shells and Periodicity
AUTHORS:
Nader Butto
KEYWORDS:
Atomic Shell Structure, Quantum Numbers, Vortex Geometry, Orbital Topology, Electron Configuration, Pauli Exclusion Principle, Subshell Overlap and Contraction, Periodic System Unification
JOURNAL NAME:
Journal of High Energy Physics, Gravitation and Cosmology,
Vol.12 No.2,
April
8,
2026
ABSTRACT: The structure of atoms and the ordering of electronic states are traditionally described within quantum mechanics through abstract wavefunctions and empirical filling rules. While this formalism successfully predicts atomic spectra and chemical behavior, it provides limited physical intuition regarding the spatial organization of shells, subshells, and orbitals, as well as the origin of well-known filling anomalies observed in transition elements. In this work, we propose a geometric reinterpretation of atomic structure based on a vortex framework, in which electrons are described as localized vortex excitations embedded in a structured vacuum. Atomic shells are modeled as concentric vortex structures, subshells as internal vortex layers, and orbitals as stable localization regions arising from vortex topology. Within this framework, the principal, azimuthal, magnetic, and spin quantum numbers acquire a coherent geometric meaning without modifying their standard quantum-mechanical definitions. The model naturally reproduces fundamental results such as the shell capacity rule
N=2
n
2
and the subshell orbital multiplicity
2ℓ+1
, while providing a physical explanation for the Aufbau principle, the
n+ℓ
(Madelung) rule, and their apparent exceptions. In particular, the configurations of chromium and copper, as well as the distinction between orbital filling order and ionization order in transition metals, emerge as consequences of subshell overlap, radial scaling, and vortex stability. Recent high-resolution experiments demonstrating spatially extended atom-light interaction regions are consistent with the physical plausibility of structured atomic interaction zones. The analysis further shows that the same geometric counting laws governing electron capacity within atomic shells also determine the recurrence of elements across periods, indicating that atomic structure and chemical periodicity arise from a unified organizing principle. Taken together, these results suggest that atomic structure and periodicity may be understood as manifestations of a hierarchical vortex organization, offering a physically intuitive complement to the conventional quantum-mechanical description.