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

Abstract

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 ($K_{\mathrm{stop}}^{-},\pi$) 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.

Comments: 22 pages, 3 figures, minor revisions, Nucl. Phys. A in press