Ah okay, I think I see that. So for 3 or more particles the spin wavefunction is always symmetric, meaning that (for fermions) the spatial wavefunction has to be anti-symmetric?
Assuming no spin-position-coupling, the total wavefunction is \psi(r_1,r_2,r_3) \chi(s_1,s_2,s_3). But if I use the...