Nuclear $\overline{K}$ bound states in light nuclei

The possible existence of deeply bound nuclear $\overline{K}$ states is investigated theoretically for few-body systems. The nuclear ground states of a $K^{-}$ in ${}^3\mathrm{He},$ ${}^4\mathrm{He},$ and ${}^8\mathrm{Be}$ are predicted to be discrete states with binding energies of 108, 86, and 113 MeV and widths of 20, 34, and 38 MeV, respectively. The smallness of the widths arises from their energy-level locations below the $\Sigma \pi$ emission threshold. It is found that a substantial contraction of the surrounding nucleus is induced due to the strong attraction of the $I=0\mathrm{}$ $\overline{K}N$ pair, thus forming an unusually dense nuclear medium. Formation of the $T=0\mathrm{}{K}^{-}{\otimes }^3\mathrm{He}+K^0{\otimes }^3\mathrm{H}$ state in the ${}^4\mathrm{He}$ (stopped $K^{-},$ $n)$ reaction is proposed, with a calculated branching ratio of about 2%.