Atoms as perfect oscillators?

TL;DR

This paper models atomic excitation spectra using a harmonic oscillator approach, revealing shell effects and collective electron oscillations across atoms with atomic numbers 2 to 36.

Contribution

It introduces a simple harmonic oscillator model fitted to experimental atomic spectra, highlighting shell filling effects and collective electron behavior.

Findings

Effective frequency .03 atomic units across atoms

Shell filling effects influence the degrees of freedom

Noble gases show high degrees of collective oscillations

Abstract

By using Supersymmetric Quantum Mechanics and Semiclassical Quantization, one may argue that the low-lying excited states of any quantum system can be modeled by a set of harmonic oscillators. In the present paper, we fit the experimental excitation spectra of atoms with atomic number 2< Z< 36 to a simple harmonic oscillator model with two parameters: the number of degrees of freedom, d, and the effective frequency, \omega. The obtained \hbar\omega takes values around 0.03 (in atomic units), whereas d shows clear shell filling effects, that is, takes high values for the noble gases, suggesting collective oscillations of the electrons occupying the last shell.