  We discuss a working approximation scheme to a recently developed formulation
of the coupled piNNN-NNN problem. The approximation scheme is based on the
physical assumption that, at low energies, the 2N-subsystem dynamics in the
elastic channel is conveniently described by the usual 2N-potential approach,
while the explicit pion dynamics describes small, correction-type effects.
Using the standard separable-expansion method, we obtain a dynamical equation
of the Alt-Grassberger-Sandhas (AGS) type. This is an important result, because
the computational techniques used for solving the normal AGS equation can also
be used to describe the pion dynamics in the 3N system once the matrix
dimension is increased by one component. We have also shown that this
approximation scheme treats the conventional 3N problem once the pion degrees
of freedom are projected out. Then the 3N system is described with an extended
AGS-type equation where the spin-off of the pion dynamics (beyond the 2N
potential) is taken into account in additional contributions to the driving
term. These new terms are shown to reproduce the diagrams leading to modern
3N-force models. We also recover two sets of irreducible diagrams that are
commonly neglected in 3N-force discussions, and conclude that these sets should
be further investigated, because a claimed cancellation is questionable.
