$\bar K$-Nuclear Deeply Bound States?
  Following the prediction by Akaishi and Yamazaki of relatively narrow $\bar K$-nuclear states, deeply bound by over 100 MeV where the main decay channel $\bar K N \to \pi \Sigma$ is closed, several experimental signals in stopped $K^-$ reactions on light nuclei have been interpreted recently as due to such states. In this talk I review (i) the evidence from $K^-$-atom data for a {\it deep} $\bar K$-nucleus potential, as attractive as $V_{\bar K}(\rho_0) \sim -(150 - 200)$ MeV at nuclear matter density, that could support such states; and (ii) the theoretical arguments for a {\it shallow} potential, $V_{\bar K}(\rho_0) \sim -(40 - 60)$ MeV. I then review a recent work by Mare\v{s}, Friedman and Gal in which $\bar K$-nuclear bound states are generated dynamically across the periodic table, using a RMF Lagrangian that couples the $\bar K$ to the scalar and vector meson fields mediating the nuclear interactions. Substantial polarization of the core nucleus is found for light nuclei, with central nuclear densities enhanced by almost a factor of two. The binding energies and widths calculated in this dynamical model differ appreciably from those calculated for a static nucleus. These calculations provide a lower limit of $\Gamma_{\bar K} \sim 50 \pm 10$ MeV on the width of nuclear bound states for $\bar K$ binding energy in the range $B_{\bar K} = 100 - 200$ MeV. 
Avraham Gal