  The ground and excited 0$^+$ states of $^{12}$C are investigated in a
3$\alpha$ macroscopic model using the deep potential of Buck, Friedrich and
Wheatley. The elimination of forbidden states is performed either by
constructing the allowed state space explicitly or by using the orthogonalizing
pseudopotential. The well-known enigmatic behavior of the latter approach is
resolved. It is safe to define the forbidden states referring to the underlying
microscopic model.
