  We demonstrate how solutions to quantum few-fermion scattering problems can
be the point-of-departure of a new treatment of a generalized many-body wave
function. Our focus is on a particular ansatz for the ground state wave
function of a superfluid Fermi gas introduced earlier (cond-mat/0506293). Our
method is perturbative in the sense that the probability amplitudes for
few-fermion scattering processes are treated as small quantities; it is also
NONPERTURBATIVE in the sense that whenever such scattering events occur,
nonperturbative quantum few-fermion scattering physics dominates. This approach
can be viewed as a new diagrammatic methodology, based on a wave function as
distinct from a perturbation series in the interparticle interactions. Some
generic properties of the wave function are studied, and its parameters in the
Bose-Einstein condensed limit are computed beyond mean-field. These results
enable us to predict many observable properties of this Fermi gas with
well-controlled accuracy, such as the superfluid pairing function, the
four-fermion and six-fermion correlation functions, the momentum distribution,
and the two-body reduced density matrix, etc.
