K^--nucleus relativistic mean field potentials consistent with kaonic atoms

K^- atomic data are used to test several models of the K^- nucleus interaction. The t(ρ)ρ optical potential, due to coupled channel models incorporating the Λ(1405) dynamics, fails to reproduce these data. A standard relativistic mean field (RMF) potential, disregarding the Λ(1405) dynamics at low densities, also fails. The only successful model is a hybrid of a theoretically motivated RMF approach in the nuclear interior and a completely phenomenological density dependent potential, which respects the low density theorem in the nuclear surface region. This best-fit K^- optical potential is found to be strongly attractive, with a depth of 180±20 MeV at the nuclear interior, in agreement with previous phenomenological analyses.