  In the framework of pionless nucleon-nucleon effective field theory we study
different approximation schemes for the nuclear many body problem. We consider,
in particular, ladder diagrams constructed from particle-particle, hole-hole,
and particle-hole pairs. We focus on the problem of finding a suitable starting
point for perturbative calculations near the unitary limit (k_Fa)->infinity and
(k_Fr)-> 0, where k_F is the Fermi momentum, a is the scattering length and r
is the effective range. We try to clarify the relationship between different
classes of diagrams and the large g and large D approximations, where g is the
fermion degeneracy and D is the number of space time dimensions. In the large D
limit we find that the energy per particle in the strongly interacting system
is 1/2 the result for free fermions.
