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I keep stumbling upon this approximation while reading papers on atomic physics, but I couldn't find a proper description of what it is in any textbook or pedagogical paper. The closest I could find was this paper, which is about cooking up a single active electron (SAE) potential. The methods used looked similar to stuff I've read on density functional theory (DFT), although as far as I can guess the methods achieve dimensional reduction by:

  • (DFT) exactly accounting for all electrons in an atom or molecule by dealing with a 3-dimensional functional (which would be miraculous if not by the fact that the exchange-correlation functional in the theory has to be computed essentially by trial and error and is by far not ab initio).
  • (SAE) endows a single super electron with the difficult task of behaving as if the responses of all the other electrons were encapsulated in it.

I don't understand how the SAE potential to which the super electron is exposed is calculated, but even if it works, double ionization should be impossible to be accounted for within the SAE approximation. I understand how it can work if the last atomic orbital contains either one or a bunch of electrons, but when it contains e.g. two, like the case of helium, I don't understand how either DFT or the SAE approximation can describe things like non-sequential double ionization.

After having expressed my troubles, perhaps it's worth it being a bit more specific: Where can I find a reference that, best case scenario, addresses what I wrote above; and in the worst case scenario, explains me what the heck the SAE approximation is?

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