Simple condensation of composite bosons in a number conserving approach to many fermion systems

We recently derived the Hamiltonian of fermionic composites by an exact procedure of bosonization. In the present paper expand this Hamiltonian in the inverse of the number of fermionic states in the composite wave function and give the necessary and sufficient conditions for the validity of such an expansion. We compare the results to the Random phase Approximation and the BCS theory and perform an illustrative application of the method.