N-Body Theory Revisited and its Extension to the pinnn-NNN Problem^*
  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. 
G. Cattapan and L. Canton