  We analyze the spectra of kaonic atoms using optical potentials withnon-local
(gradient) terms. The magnitude of the non-local termsfollows from a self
consistent many-body calculation of the kaon selfenergy in nuclear matter,
which is based on s-wave kaon nucleoninteractions. The optical potentials
exhibit strong non-linearitiesin the nucleon density and sizeable non-local
terms. We find that thenon-local terms are quantitatively important in the
analysis of thespectra and that a phenomenologically successful description can
be obtained for p-wave like optical potentials. It is suggested that
themicroscopic form of the non-local interaction terms is
obtainedsystematically by means of a semi-classical expansion of the
nucleusstructure. The resulting optical potential leads to less pronounced
non-local effects.
