Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

SIGMA 13 (2017), 038, 15 pages      arXiv:1706.02535      https://doi.org/10.3842/SIGMA.2017.038

Mendeleev Table: a Proof of Madelung Rule and Atomic Tietz Potential

Eugene D. Belokolos
Department of Theoretical Physics, Institute of Magnetism, National Academy of Sciences of Ukraine, 36-b Vernadsky Blvd., Kyiv, 252142, Ukraine

Received February 27, 2017, in final form May 22, 2017; Published online June 07, 2017

Abstract
We prove that a neutral atom in mean-field approximation has ${\rm O}(4)$ symmetry and this fact explains the empirical $[n+l,n]$-rule or Madelung rule which describes effectively periods, structure and other properties of the Mendeleev table of chemical elements.

Key words: Madelung rule; Mendeleev periodic system of elements; Tietz potential.

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