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Gradient Terms in the Microscopic Description of K-Atoms

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.