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

## TL;DR

This paper demonstrates that a neutral atom's mean-field approximation exhibits O(4) symmetry, providing a theoretical proof for the empirical Madelung rule that governs the periodic table's structure.

## Contribution

It offers a theoretical proof linking atomic symmetry to the Madelung rule, enhancing understanding of periodic table organization.

## Key findings

- Neutral atoms in mean-field approximation have O(4) symmetry.
- The O(4) symmetry explains the Madelung rule.
- The proof clarifies the structure and properties of the periodic table.

## 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.