Multi-$\bar{K}$ hypernuclei

Relativistic mean field calculations of multi-$\bar{K}$ hypernuclei are performed by adding $K^-$ mesons to particle-stable configurations of nucleons, $\Lambda$ and $\Xi$ hyperons. For a given hypernuclear core, the calculated $\bar{K}$ separation energy $B_{\bar{K}}$ saturates with the number of $\bar{K}$ mesons for more than roughly 10 mesons, with $B_{\bar{K}}$ bounded from above by 200 MeV. The associated baryonic densities saturate at values 2-3 times nuclear-matter density within a small region where the $\bar{K}$-meson densities peak, similarly to what was found for multi-$\bar{K}$ nuclei. The calculations demonstrate that particle-stable multistrange $\{N,\Lambda,\Xi \}$ configurations are stable against strong-interaction conversions $\Lambda \to N \bar{K}$ and $\Xi \to N \bar{K} \bar{K}$, confirming and strengthening the conclusion that kaon condensation is unlikely to occur in strong-interaction self-bound strange hadronic matter.