Density dependence in kaonic atoms

We study phenomenologically the density dependence of the K^- optical potential V_opt(r) at zero kinetic energy by fitting it to a comprehensive set of atomic data across the periodic table. Two families of solutions offer improved fits over that for the standard t_effρ{variant}(r) paraameterization of V_opt. One family contains solutions for V_opt with RMS radii larger than those of the matter density ρ{variant}, as expected from finite-range folding corrections. The other family offers substantially improved fits to the data and gives rise to Re V_opt of a size smaller than that of ρ{variant}. The new family contains solutions for which V_opt is attractive inside the nucleus and on its surface, becoming repulsive at large distances. The repulsion can be made to approximately agree with the low-density limit V_opt→tρ{variant} where t is the free-space KN t matrix. It is argued that this sign flip might be expected from the underlying nuclear propagation of the Λ(1405).