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It is found that the coupled piNNN-NNN system breaks into fragments in anontrivial way. Assuming the particles as distinguishable, there are indeedfour modes of fragmentation into two clusters, while in the standard three-bodyproblem there are three possible two-cluster partitions and conversely thefour-body problem has seven different possibilities. It is shown how toformulate the pion-three-nucleon collision problem through theintegral-equation approach by taking into account the proper fragmentation ofthe system. The final result does not depend on the assumption of separabilityof the two-body t-matrices. Then, the quasiparticle method a' laGrassberger-Sandhas is applied and effective two-cluster connected-kernelequations are obtained. The corresponding bound-state problem is alsoformulated, and the resulting homogeneous equation provides a new approachwhich generalizes the commonly used techniques to describe the three-nucleonbound-state problem, where the meson degrees of freedom are usually suppressed.Comment: 20 pages, REVTeX, with 3 COLOR figures (PostScript

Pion-three-nucleon problem with two-cluster connected-kernel equations