now more complicated. Introducing a new notation in channel indices $ U^{a,b} =G^{a,a}t^{a,b}$ the determinant becomes $$\label{t3} D=
 [(1+ U^{K,K})(1+ U^{\pi,\pi})~
- U^{\pi,K}U^{K,\pi}][(1-U^{K,K})(1-U^{\pi,\pi})~
-U^{K,\pi}U^{\pi,K}].$$ The $D=0$ condition is more transparent close to the singularity in the case of a scattering amplitude given by $$\label{t4}
 f^{a,b} \approx \frac{\gamma_a \gamma_b} { E - E_o+ i \Gamma/2}.$$ Consistency requires the width to be $ \Gamma/2=
p_\pi(\gamma_{\pi})^2$, where $p_\pi $ is the momentum in the decay channel. The singular term (\[t4\]) permits one to find a solution of Eq. (\[t3\]) in a fairly simple form. It is presented below in the limit of zero range KN ( and $ \Sigma\pi$ ) force. The binding energy $$\label{t5} \emph{Re } E =  E_o  - (\gamma_K)^2\frac{cos(p_Rr)}{r}
\exp(-p_Ir) - (\gamma_{\pi})^2 \frac{cos(p_\pi r)}{r}$$ becomes larger than the binding of the resonance but the collisions in the decay channel indicates oscillations. This oscillatory behavior is also seen in the width of the system $$\label{t6}  \emph{Im}~E = - (\gamma_{\pi})^2 ~ p_\pi~[
 1+\frac{sin(p_{\pi}r)}{p_{\pi}r}] -  (\gamma_K)^2\frac{sin(p_Rr)}{r}\exp(-p_Ir).$$ The effect of KN scattering represented by the second term enlarges the width as $p_R$ is negative. The contribution from multiple scattering in the decay channel is sizable in general but it oscillates and may under some 