conditions reduce the total width. That is an effect of interference in the decay channel. Scattering in the decay channel turns out to be constructive in the KNN case but it is not necessarily so in some heavier systems.

 S and P wave interactions
--------------------------

With the KN interactions allowed in both $S$ and $P$ waves the scattering equation (\[a8\]) is a $4\otimes 4$ matrix equation relating four amplitudes $ \psi_i$. The amplitudes for $S$ waves are now denoted by $ \psi_1^s ,\psi_2^s$. For $P$ wave interactions the corresponding amplitudes are vectors. As there is only one vector in the $NN$ system, the relative separation, the $P$ amplitudes are chosen to be $ \textbf{r}\psi_1^p $ and $
\textbf{r}\psi_2^p $. The scattering is now described by three types of propagators $ G^{a,b}$ related to consecutive collisions in the $(S,S)$ $(S,P)$ and $(P,P)$ waves. The scattering equations are $$\label{sp1}
 \psi_1^s ~+ ~f^s ~G^{ss}~\psi_2^s   - ~f^s~G^{sp}~r^2 ~\psi_2^p  =0$$

$$\label{sp2}
 \psi_2^s ~+ ~f^s ~G^{ss}~\psi_1^s   + ~f^s~G^{sp}~r^2 ~\psi_1^p  =0$$

$$\label{sp3}
 \psi_1^p ~+ ~f^p ~G^{pp}~\psi_2^p   + ~f^p~G^{sp} ~\psi_2^s  =0$$

$$\label{sp4} \psi_2^p ~+ ~f^p ~G^{pp}~\psi_1^p   - ~f^p~G^{sp}
~\psi_1^s  =0,$$

where the propagation in between two $P$ wave interactions is described by $   G^{pp} = G^{pp}_O +  r^2 