Den=338 MeV to ensure the correct binding energy of the deuteron.

The precision of variational estimates for E ( used in the next sections) may be checked against numerical solutions of the Schrödinger equation. It is about 0.3 MeV, compared with the overall binding of $\sim 50$ MeV. The width of the state is calculated as $$\Gamma/2 =  < \chi_{NN}\mid Im~ V_K \mid \chi_{NN} > .
\label{gamma}$$

Interactions in the decay channels
----------------------------------

The decay channel $ \Sigma\pi$ coupled to the basic KN channel is now introduced explicitly. The wave function at each scattering center has two components one in the KN the other in the $
\Sigma\pi$ channel. The scattering amplitudes are two dimensional vectors $ \psi_i \rightarrow  [\psi_i^K,~ \psi_i^\pi
$\] at each nucleon. Multiple scattering equations given in the previous section are now changed accordingly. One has $$\label{t1}
 \psi_1^K + t^{K,K}~G^{K,K}~ \psi_2^K +  t^{K,\pi}~G^{\pi,\pi}~ \psi_2^\pi  = 0$$ $$\label{t2}
 \psi_1^\pi  +G^{\pi,\pi}~t^{\pi,\pi}~ \psi_2^\pi + t^{\pi,K}~G^{K,K}~ \psi_2^K  = 0$$ and an analogous pair with $1\leftrightarrow 2$. The notation has been changed to describe channel indices and the $2\times 2
$ scattering matrix $\hat{f}$. The determinant related to these equations gives the complex eigenvalue $p(x_i)$ in the KN channel. The eigen-equation is 