Helium ground state questions

[spaghetti3451]

I have having difficulty understanding why the ground state configuration of helium has a wavefunction that is the product of two hydrogenic 1s wavefunctions and the spin eigenstate of a singlet state.

Firstly, why is the space wavefcn hydrogenic,
and secondly, why is the spin wavefcn a singlet state?

 

[mfb]

If you neglect electron-electron interaction, you have the same potential as in the hydrogen atom - just scaled to account for the second proton in the nucleus. And if you evaluate the system numerically, it turns out that the approximation is not so bad.

As electrons are fermions, the wave-function has to be antisymmetric under the exchange of the two electrons. This is not possible with the space-like part of their wave functions - they both have the same state! Therefore, the spins have to be antisymmetric, which requires a singlet state.