Experiments with $\Xi^-$ atoms

Experiments with $\Xi^-$ atoms are proposed in order to study the nuclear interaction of $\Xi$ hyperons. The production of $\Xi^-$ in the ($K^{-}$, $K^{+}$) reaction, the $\Xi^-$ stopping in matter, and its atomic cascade are incorporated within a realistic evaluation of the results expected for $\Xi^-$ X-ray spectra across the periodic table, using an assumed $\Xi$-nucleus optical potential $V_{opt}$. Several optimal targets for measuring the strong-interaction shift and width of the X-ray transition to the `last' atomic level observed are singled out: F, Cl, I, Pb. The sensitivity of these observables to the parameters of $V_{opt}$ is considered. The relevance of such experiments is discussed in the context of strangeness -2 nuclear physics and multistrange nuclear matter. Finally, with particular reference to searches for the $H$ dibaryon, the properties of $\Xi^-d$ atoms are also discussed. The role of Stark mixing, its effect on $S$ and $P$ state capture of $\Xi^-$ by the deuteron, together with estimates of the resulting probability for producing the $H$ dibaryon are considered in detail.