with fixed positions of the nucleons. An equation of similar structure with a zero range meson-nucleon pseudo-potential $U$ was used by Brueckner [@BRU] to calculate the scattering length of a meson on two nucleons. For a high energy scattering it was extensively discussed by Foldy and Walecka, who used finite range separable interactions $U$ [@FOL69]. With such interactions equation (\[a3\]) allows for semi-analytic solutions in the NN, and also in few nucleon cases. Here, the method is extended to the bound state problem. One looks for solutions of Eq. (\[a3\]) with no incident wave $
\chi_K(\textbf{x})^o$. The momentum $p$ becomes a complex eigenvalue $p(x_i)$ which determines the energy and width of the system for given nucleon positions $x_i$.

Equation (\[a3\]) is written in terms of the Klein-Gordon or Schrödinger propagator. The difference arises when the relation of energy and momentum is established. Reasons of simplicity, which will become clear later, favor the non-relativistic relation in the KN center of mass system. Thus, the interaction is presented as $U_{KN} =2\mu_{KN} V_{KN}$ where $\mu_{KN}$ is the reduced mass. Corrections for relativity may be introduced at a later stage. The potential $V_{KN}$ for an $S$ wave interaction is chosen in a separable form 