Now imagine (trying to make) an 
molecule. Each He atom now
contributes two electrons for a total of four. By the Pauli
exclusion principle, only two electrons may settle into the lowest
energy state, and the remaining electrons must then go into the
next higher, odd state. Show that, to lowest order, the
energy of the He atoms does not decrease with their separation, that
in fact, in terms of the total energy, they don't really notice each
other at all.
Note: Chemists refer to the odd state here as an ``anti-bonding'' state.