Kaon condensation and multi-strange matter

We report on dynamical calculations of multi- hypernuclei, which were performed by adding mesons to particle-stable configurations of nucleons, Λ and Ξ hyperons. The separation energy as well as the baryonic densities saturate with the number of antikaons. We demonstrate that the saturation is a robust feature of multi- hypernuclei. Because the separation energy does not exceed 200 MeV, we conclude that kaon condensation is unlikely to occur in finite strong-interaction self-bound {N,Λ,Ξ} strange hadronic systems.