Density-dependent K^- nuclear optical potentials from kaonic atoms

The density depedence of the K^- optical potential V_opt(r) at zero kinetic energy is studied by fitting it to a comprehensive set of atomic data across the periodic table. Two families of solutions offering improved fits over that for a t_effρ{variant}(r) parameterization are identified, one containing solutions for V_opt with r.m.s. radii larger than those of the matter density ρ{variant}, as expected from finite-range folding corrections. The other gives rise to Re V_opt of a size smaller than that of ρ{variant}. The latter family offers substantially improved fits to the data, with particularly strong attraction inside the nucleus (200 ± 20 MeV). For a subfamily of solutions, V_opt becomes repulsive at large distances, and solutions satisfying the low-density limit V_opt → t_KNρ{variant} can be found. Comments are made on the relevance of Λ(1405) nuclear dynamics to these findings.