Kaonic nuclei

Limits on the possible existence of narrow K^- nuclear states and on their widths are explored. Deeply bound K^- nuclear states are generated dynamically. Substantial polarization of the core nucleus is found for light K^- nuclei. The widths of the states are mostly determined by the phase-space suppression on top of the increase provided by the density of the compressed nuclei. The behaviour of the calculated widths as function of the K^- binding energy provides useful guidance for the interpretation of recent experimental results.