  It is found that the coupled piNNN-NNN system breaks into fragments in a
nontrivial way. Assuming the particles as distinguishable, there are indeed
four modes of fragmentation into two clusters, while in the standard three-body
problem there are three possible two-cluster partitions and conversely the
four-body problem has seven different possibilities. It is shown how to
formulate the pion-three-nucleon collision problem through the
integral-equation approach by taking into account the proper fragmentation of
the system. The final result does not depend on the assumption of separability
of the two-body t-matrices. Then, the quasiparticle method a' la
Grassberger-Sandhas is applied and effective two-cluster connected-kernel
equations are obtained. The corresponding bound-state problem is also
formulated, and the resulting homogeneous equation provides a new approach
which generalizes the commonly used techniques to describe the three-nucleon
bound-state problem, where the meson degrees of freedom are usually suppressed.
