We analyze the spectra of kaonic atoms using optical potentials with non-local (gradient) terms. The magnitude of the non-local terms follows from a self consistent many-body calculation of the kaon self energy in nuclear matter, which is based on s-wave kaon nucleon interactions. The optical potentials exhibit strong non-linearities in the nucleon density and sizeable non-local terms. We find that the non-local terms are quantitatively important in the analysis of the spectra and that a phenomenologically successful description can be obtained for p-wave like optical potentials. It is suggested that the microscopic form of the non-local interaction terms is obtained systematically by means of a semi-classical expansion of the nucleus structure. The resulting optical potential leads to less pronounced non-local effects.

PACS numbers: 13.75.Jz, 36.10.--k