  In order to approach the pion--multinucleon problem, we have found it
convenient to reformulate the general N--body theory starting from the fully
unclusterized (i.e., N <- N) amplitude. If we rewrite such an amplitude in
terms of new unknowns which can be later identified as the amplitudes for all
the (N-1) <- (N-1) cluster processes, and repeat recursively the procedure up
to the treatment of the 2 <- 2 cluster processes, we obtain very naturally the
hierarchy of equations which ranges from the N--body fully--disconnected
Lippmann--Schwinger equation to the N--body connected--kernel
Yakubovskii--Grassberger--Sandhas one. This revisitation turns out to be very
useful when considering the modifications required in case one of the bodies is
a pion and the remaining are nucleons, with the pion being allowed to disappear
and reappear through the action of a pion--nucleon vertex. In fact, we obtain a
new set of coupled pion-- multinucleon equations which allow a consistent and
simultaneous treatment of pion scattering and absorption. For the piNNN system,
the kernel of these coupled equations is shown to be connected after three
iterations.
