Multi-kaonic hypernuclei and kaon condensation

This contribution reports on dynamical, self-consistent calculations of multi-K̄ hypernuclei, which were performed by adding antikaons to particle-stable nuclear configurations of nucleons, Λ and Ξ hyperons. Our results show a robust pattern of saturation of the K̄ separation energy B_K̄ as a function of the number of K̄ mesons, with B _K̄ bounded from above by 200 MeV. The associated baryon densities saturate at values 2-3 times nuclear-matter density. The main reason for saturation is the repulsion induced by the vector meson fields between K̄ mesons, similarly to what was found for multi-K̄ nuclei. The calculations confirm that strangeness in finite strong-interaction self-bound systems is realized through hyperons, with no room for kaon condensation.