$$\label{a4}
 V_{KN}( \bf{x-x_i}, \bf{x'-x_i}) =
\lambda ~\upsilon(\bf{x-x_i})~\upsilon(\bf{x'-x_i}),$$ where $\upsilon$ is a form-factor and $\lambda$ is a strength parameter. The eigenvalue equation is now reduced to $$\label{a5}
 \chi_K(\textbf{x},\textbf{x}_1,\textbf{x}_2) + \Sigma_i ~ \lambda ~\int \bf{dy}~ \frac {\exp[ip(\textbf{x}_1,\textbf{x}_2)\mid \bf{x-y}\mid ]}
 {4\pi \mid \bf{x-y}\mid } ~\upsilon(\bf{y-x_i})~ \int  \bf{dy'}~ \upsilon(\bf{y'-x_i})~\chi_K( \bf{y'},\textbf{x}_1,\textbf{x}_2) =0.$$ Equation (\[a5\]) becomes a matrix equation for wave amplitudes $\psi_i$ defined at each scatterer $i$ by $$\label{a6}
 \psi_i =  \lambda~ \int \bf{dx}~ \upsilon( \bf{x-x}_i) ~\chi_K( \bf{x},\textbf{x}_1,\textbf{x}_2).$$ To find the equations for $\psi_i $ one introduces the off-shell KN scattering matrices $f$ and matrix elements of the propagator $$\label{a7}
 G_{i,j}(\bf{x_i,x_j}) =  \int\bf{dy }\bf{dx } ~ \upsilon( \bf{x-x}_i)~
 \frac {\exp(ik\mid \bf{x-y}\mid )}{4\pi \mid \bf{x-y}\mid
 } ~\upsilon(\bf{y-x}_j).$$ The diagonal value, $G_{i,i}\equiv G$, determines the meson nucleon scattering matrix $t$ by the well known (see e.g. Ref. [@FOL69]) relation $$\label{a7t}
 t(E) = (1+\lambda ~ G )^{-1}~ \lambda$$ and this yields the full off-shell scattering amplitude $ f $ $$\label{a7f}
 f(k,E,k') =\upsilon(k)~t(E)~\upsilon(k').$$ Here, $k,k'$ are the initial and final momenta while the form-factor $v(k)$ is given by the Fourier transform of $\upsilon(r)$. The Yamaguchi form $\upsilon(k)=
1/(1+k^2/\kappa^2)$ with a free parameter $\kappa$ will be used in this paper. At zero momenta and at the threshold this choice normalizes 