  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.

Nuclear Theory