The quest for chaos in many-electron atoms

In view of the fact that the periodic table is so well accounted for using an independent electron model, there is not much room for quantum chaos to develop in the spectra of unperturbed many-electron atoms. 

The strongest pieces of evidence complex atoms provide in favour of independent electron modes and simple Bohr-Sommerfeld quantisation are (i) the existence of Rydberg series and (ii) the regularity of the periodic table of the elements. As a corollary, we should look for quantum chaos (if it occurs) in atoms for which there is some breakdown in the quality of the shell structure, combined with prolific and heavily perturbed overlapping series of interacting levels. These conditions are most readily met, as will be shown below, in the spectra of the alkaline-earth elements, as a result of d-orbital collapse. 

This problem is in a sense analogous to the classical problem of anhar-monically coupled oscillators, which is an example of a chaotic system. 

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