Variational method For Helium Atom

[Bishop556]

When using the variational method for the Helium atom, we determine that the lowest possible energy occurs when 1<z<2 where z is the atomic number. My professor elaborated that the number is within this range because there is a probability that the electron may be so close to one of the protons that it appears as if there are only two protons. My question is why can't 0<z<1? Why can't both electrons be located inside the nucleus of the atom? Would it still be possible to distinguish them if they were?

 

[DrDu]

I suppose z is the effective nuclear charge seen by an electron, ie the nuclear charge scrreened by the other electron. This can t be smaller than 1.