Single-and multi-nucleon K^- interactions with nuclei near threshold

Six recent SU(3) chiral-model EFT approaches to the K- -nucleon interaction near threshold, constrained by K^- p low-energy scattering and reaction data and by the kaonic hydrogen SIDDHARTA experiment, are used as input in kaonic atom calculations. Good agreement with the world-data on kaonic atoms is achieved with optical potentials built on the above models only when K- N amplitudes are supplemented by a phenomenological multi-nucleon term. Comparing predictions with experimental single-nucleon absorption-at-rest fractions on nuclei, only two of the models together with their associated phenomenological term are acceptable. The information content of K^--nucleus data near threshold is discussed and the topic of deeply-bound kaonic atoms is re-visited.