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The s- and p-wave contributions to the $\bar K N$ interaction in densenuclear matter are obtained using a chiral unitary approach. We perform aself-consistent calculation of the $\bar K$ self-energy including Pauliblocking effects, meson self-energies modified by short-range correlations andbaryon binding potentials. We find that the on-shell factorization cannot beapplied to evaluate the in-medium corrections to p-wave amplitudes.Furthermore, the $\Lambda$ and $\Sigma$ develop a mass shift of -30 MeV atsaturation density while the $\Sigma^*$ width increases to 80 MeV. We concludethat no deep and narrow $\bar K$ bound states could be observed.Comment: 4 pages, 4 figures, to appear in the proceedings of the Yukawa  International Seminar (YKIS2006) on "New Frontiers on QCD", Kyoto, Japan,  November 20-December 8, 200

The In-Medium \barK NInteraction within a Chiral Unitary Approach