The condition for a bound state with two amplitudes $\psi_i$ leads to a pair of equations $$\label{a10}
 \psi_1 + t~G ~\psi_2 = 0, ~~~~  \psi_2+t~G~\psi_1 = 0.$$ When the determinant $$\label{a11a} D=  1-( t~G)^2$$ is put to zero, the binding “momenta” $p(r)$ may be obtained numerically. Two different solutions corresponding to $ 1+ tG = 0 $ or $ 1-tG = 0$ may exist. The first solution is symmetric $\psi_2= \psi_1$ and describes the meson in the $S$ wave state with respect to the NN center of mass. The second solution is antisymmetric $\psi_2= -
\psi_1$ and describes a $P$ wave solution. With the rank one separable interaction this latter solution does not exist in the full range of $r$. However, it arises with the more complicated rank two interactions discussed later.

Eigenvalues corresponding to unstable quasi-bound states are obtained in the second quadrant of complex $ p(r)\equiv p = p_R +i p_I$ plane. In this quadrant the kernel $$\label{a12}
 tG =f(p) ~[ \exp(-p_Ir) \exp(ip_Rr)-\exp(-\kappa r)~( 1+  r \frac{\kappa^2 - p^2}{2\kappa})]/r$$ is exponentially damped at large distances as required by the asymptotic form of the bound state wave function $\chi_K$. At short distances $ G $ is regularized by the 