Theory of coupled pi--trinucleon systems

We derive the dynamical equations which couple the four-body (πNNN) system to the underlying three-nucleon system. Our treatment can be considered the proper generalization of the Afnan-Blankleider equations for the coupled NN-πNN system. The resulting connected-kernel equations resemble in structure the Yakubovskiǐ-Grassberger-Sandhas equations for the standard four-body problem, but involve 24 chain-labeled components (rather than the usual 18 ones) and, within the scheme where the Hilbert space is truncated to states with at most one pion, allow for a consistent evaluation of reaction amplitudes involving π absorption/production.