$K^{-}$ and $\bar{p}$ deeply bound atomic states

Abstract

The strongly absorptive optical potentials $V_{\mathrm{opt}}$ which have been deduced from the strong-interaction level shifts and widths in X-ray spectra of $K^{-}$ and $\bar{p}$ atoms produce effective repulsion leading to substantial suppression of the {\it atomic} wave functions within the nucleus. The width of atomic levels then saturates as function of the strength of Im $V_{\mathrm{opt}}$. We find that `deeply bound' atomic states, which are inaccessible in the atomic cascade process, are generally narrow, due to this mechanism, over the entire periodic table %reaching values of ${\Gamma }_{K^{-}}\sim 1.7$ MeV and %${\Gamma }_{\bar{p}}\sim 1.9$ MeV for the $1s$ state in Pb, and should be reasonably well resolved. These predictions are insensitive to $V_{\mathrm{opt}}$, provided it was fitted to the observed X-ray spectra. In contrast, the {\it nuclear} states bound by $V_{\mathrm{opt}}$ are very broad and their spectrum depends sensitively on details of $V_{\mathrm{opt}}$. We discuss production reactions for $K^{-}$ atomic states using slow $K^{-}$ mesons from the decay of the $\varphi$(1020) vector meson, and the ($\bar{p},p$) reaction for $\bar{p}$ atomic states. Rough cross-section estimates are given.

22 pages, 9 figures, submitted to NPA

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