$f$ (and $t$) to the scattering length. Unfortunately for historical reasons the standard convention in the K-N system is to define the scattering length by $$\label{a7g}
 a+ib  = - f(k=0,E=0,k'=0)\equiv F(0,0,0)$$ and the capital $F$ will be used in several places to comply with the standard KN parameters.

In order to cast Eq. (\[a5\]) into a standard multiple scattering equation for $\psi_i$ one carries out the following three steps: 1) Integrates Eq. (\[a5\]) over the i-th form-factor $\upsilon(\bf{x-x_i})$. 2) Selects the i-th term from the R.H. side. 3) Multiplies Eq. (\[a5\]) by $ (1+\lambda
G)^{-1}$. In this way the kernel of the multiple scattering equation can be expressed in terms of scattering amplitudes $t_i$ at each nucleon $i$ and propagators describing the passage from the nucleon $i$ to the other nucleon $j$. One now arrives at a set of linear equations $$\label{a8}
 \psi_i +
 \Sigma_{j\neq i} ~ t_j~G_{i,j}~  \psi_j  =0,$$ which may be solved numerically. For the Yamaguchi form-factors, propagators $G_{i,j}$ allow analytic expressions $$\label{a9}
 G_{1,2}(r,k) =
\frac{1}{ r}~ \upsilon(k)^2 ~[ \exp(ikr)-\exp(-\kappa r)- r
\frac{\kappa^2 +k^2}{2\kappa} \exp(-\kappa r)] ~\equiv~G (r,k),$$ where $ \textbf{r }= \textbf{x}_2- \textbf{x}_1 $. For the sake of illustration, the KNN case is presented in some detail. 