G^{pp}_T$. Indices numbering the nucleons have been suppressed. The propagator $G^{ss}$ is given in Eq. (\[a9\]) and explicit formulas for $
G^{sp},G^{pp}_O , G^{pp}_T $ may be found in the appendix. All these functions are regular in the $ r\rightarrow 0$ limit. The determinant $D$ of this system factorizes into two terms $$\label{sp5}
 D = D_S~D_P,$$ where $$\label{sp6}
 D_S = ( 1 ~+~ G^{ss}~ f ^s)( 1~-~  G^{pp}~ f ^p )~ - ~ G^{sp}~r^2 ~f^s~ f ^p,$$ $$\label{sp7}
 D_P = ( 1~ -~ G^{ss}~ f ^s)( 1~ + ~ G^{pp}~f ^p )~-~G^{sp}~r^2~ f^s~ f^p.$$ Let us consider the solution of $D_S=0$ close to the $\Lambda(1405)$ resonance. It is given by an equation analogous to (\[a13\]) $$\label{sp8} E =  E^* - b^2~ G^{ss}(r,p(E)~ [ 1 ~-~ \frac{r^2(G^{sp})^2
f^p}{1 - G^{pp} f^p}~].$$ The second term in parentheses describes the effect of $P$ wave interactions. At energies below $\Sigma(1385)$ the amplitude $f^p$ is negative and generates an additional attraction.

Isospin symmetry simplifies the algebraic structure of the scattering equations which are (see next sections) expressed by appropriate isospin combinations of the isospin KN scattering amplitudes $f$. Equations (\[sp1\]-\[sp4\]) allow for a simple symmetry of the total KNN wave function. Thus, under the eigenvalue 