Helium atom independent particle approximation

For many-electron atoms, the Schrodinger equation can be solved approximately, but very accurately nowadays, by transforming the difficult electron-electron repulsion terms into a spherically averaged form. Then, each electron can be considered to exhibit independent motion in the potential field due to the nucleus and the averaged repulsive interaction with the other electrons in the atom. This simplification leads to the Independent Particle Approximation preserving the orbital concept and first proposed by Hartree (1) for the simplest many-electron atom, helium, as the product... 

The question addressed in this paper is, in its most general terms To what extent is it appropriate to describe a few-body system in terms of one quantization scheme or another Slightly more precisely, we ask Which simple model, among the choices we can invent, is the best starting approximation for any designated state of a given system As our vehicle to study this problem, we use the system of the two valence electrons in the helium and alkaline earth atoms. The models we consider and compare are the Hartree-Fock, independent-particle model and the collective model like that for a linear triatomic molecule. 

---