Calculating the state for Helium

[randomafk]

So, when dealing with the Hydrogen molecule (H2) we know each electron is antisymmetric since they're fermions
i.e. $\Psi_\_ = 1/\sqrt(2) * (\Psi_a(r1) * \Psi_b(r2) - \Psi_b(r1) * \Psi_a(r2))$

and then similarly for the spinor such that the total state, $\Psi\chi$ is antisymmetric

When you deal with atoms, like helim, we can approximate the state of the system as the product of hydrogen wave ($\Psi = \Psi_a *\Psi_b$). But in doing so, aren't we assuming the electrons are distinct? Why not with that formula for $\Psi_\_$

 

[andrien]

I think this is just the lowest order approximation in which ,interaction between the electrons is neglected.it is called 'independent particle approximation'.