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

Abstract

The strongly absorptive optical potentials $V_{\rm opt}$ 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 $V_{\rm opt}$. 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 $Γ_{K^-} \sim 1.7$ MeV and %$Γ_{\bar p} \sim 1.9$ MeV for the $1s$ state in Pb, and should be reasonably well resolved. These predictions are insensitive to $V_{\rm opt}$, provided it was fitted to the observed X-ray spectra. In contrast, the {\it nuclear} states bound by $V_{\rm opt}$ are very broad and their spectrum depends sensitively on details of $V_{\rm opt}$. We discuss production reactions for $K^-$ atomic states using slow $K^-$ mesons from the decay of the $ϕ$(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