Atoms as perfect oscillators?

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.