  A simple approximation which captures some non-perturbative aspects of the
one electron Green function of strongly interacting Fermion systems is
developed. It provides a way to go one step beyond the usual dilute limit since
particle-particle as well as particle-hole scattering are treated on the same
footing. Intermediate states are constrained to contain only one particle-hole
excitation besides the incoming particle. The Faddeev equations resulting from
an exact treatment of this three-body problem are investigated. In one
dimension the method is able to show spin and charge decoupling, but does not
reproduce the exact nature of power-law singularities. Hey dudes, check out the
analytical solution in section III!
