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Analyses of strong-interaction data consisting of level shifts, widths and yields in strange atoms of K− mesons and Σ− hyperons are reviewed. Recent results obtained by fitting to comprehensive sets of data across the periodic table in terms of density-dependent optical potentials are discussed. The introduction of density dependence generally improves significantly the fit to the data, leading to novel results on the in-medium hadron-nucleon t matrix t(ρ) over a wide range of densities up to central nuclear densities. A strongly attractive K−-nuclear potential of order 150–200 MeV in nuclear matter is suggested by fits to K−-atom data, with interesting possible repercussions on condensation and on the evolution of strangeness in high-density stars. The case for relatively narrow deeply bound K− atomic states is made, essentially independent of the K− potential depth. In view of the recently reported inconclusive experimental signals of deeply bound states, dynamical models for calculating binding energies and widths of -nuclear states are discussed. Lower bounds on the width, MeV, are established. For Σ− atoms, the fitted potential becomes repulsive inside the nucleus, in agreement with recently reported (π−,K+) spectra from KEK, implying that Σ hyperons generally do not bind in nuclei. This repulsion significantly affects calculated compositions and masses of neutron stars.
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