2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/192302We derive the dynamical equations which consistently couple the four--body ($π$NNN) system to the underlying three--nucleon system. Our treatment can be considered the proper generalization of the Afnan--Blankleider equations for the coupled NN--$π$NN system. The resulting connected--kernel equation resembles in structure the Yakubovskii--Grassberger--Sandhas equation for the standard four--body problem, but involves 24 chain--labelled components (rather than the usual 18 ones) and allows for a consistent evaluation of reaction amplitudes involving $π$ absorption/production.REVTEX, 13 pages, Padova, DFPD 93/TH/77Nuclear Theorytext