  We have found an expression for the full many-body Green's function of N
pairwise finite-range interacting atoms, in a form of a chain fraction
involving two-body T-matrices only, with no explicit presence of the
interaction potentials themselves. We show that in the limit of infinitely
small potential range, this expression reduces to the Green's function for N
atoms interacting via a generalized pseudo-potential, function of a free
parameter \Lambda. Using this \Lambda-freedom we resolve all inconsistensies of
the Hartree-Fock-Bogoliubov formalism known so far, with no ad hoc
modifications of the theory.
