KN form-factor.

If the scattering amplitude is dominated by a quasi-bound state, such as $\Lambda(1405)$, the related pole dominates and in some energy region $ f\simeq \gamma^2/(E-E^*)$, where $\gamma$ is a coupling constant and $E^*=E_r-i\Gamma_r/2$ is a complex $\Lambda(1405)$ binding energy. The full KNN binding energy, $V_K$, is given by the equation $ 1+ tG= 0 $ which becomes $$\label{a13} V_K(r) \simeq  E^* - \gamma^2 G(r,p).$$ Since Re $ G(r,p)$ close to the resonance is positive this solution offers binding stronger than the $\approx$ 28 MeV binding in the $\Lambda(1405)$. Asymptotically, for $r\rightarrow\infty$ one obtains $ V_K \rightarrow  E^* $, that is a kaon bound to a nucleon to form a $\Lambda(1405)$. This type of asymptotic behavior occurs in all of the K-few-nucleon systems of practical interest. Hence, the separation energy is understood here as the separation of the K-N-N system into the N-$\Lambda(1405)$ system.

The limits $ r \rightarrow0$ in Eqs. (\[a12\],\[a13\]) are regular. However, a joint limit of zero range KN interactions, $\kappa \rightarrow \infty$, and $ r\rightarrow0$ is singular and the KNN system collapses. Therefore, some care is necessary when this limit is taken. Here, we stay within a phenomenological approach and the standard expectation that the 