Theory of Coupled Pion--Trinucleon Systems

We derive the dynamical equations which consistently couple the four--body ($\pi$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--$\pi$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 $\pi$ absorption/production.