Study of chirally motivated low-energy $K^-$ optical potentials

The $K^-$ optical potential in the nuclear medium is evaluated self consistently from a free-space $K^-N$ $t$ matrix constructed within a coupled-channel chiral approach to the low-energy $bar K N$ data. The chiral-model parameters are fitted to a select subset of the low-energy data {it plus} the $K^-$ atomic data throughout the periodic table. The resulting attractive $K^-$ optical potentials are relatively `shallow, with central depth of the real part about 55 MeV, for a fairly reasonable reproduction of the atomic data with $chi^2 / N approx 2.2$. Relatively `deep attractive potentials of depth about 180 MeV, which result in other phenomenological approaches with $chi^2 / N approx 1.5$, are ruled out within chirally motivated models. Different physical data input is required to distinguish between shallow and deep $K^-$ optical potentials. The ($K^{-}_{rm stop},pi$) reaction could provide such a test, with exclusive rates differing by over a factor of three for the two classes of potentials. Finally, forward ($K^-,p$) differential cross sections for the production of relatively narrow deeply bound $K^-$ {it nuclear} states are evaluated for deep $K^-$ optical potentials, yielding values considerably lower than those estimated before.