Structure and Formation of the Deeply Bound $\bar{p}$ atoms

We study theoretically the structure and formation of the deeply bound $\bar{p}$ atoms. We find that the widths of the atomic states are narrower than the level spacing even for deeply bound states so that the well-isolated deeply bound $\bar{p}$ atoms are expected to exist. We also find the $\bar{p}$-nuclear states with huge widths. For the observation of the deep ${\bar p}$-atomic states, we investigate theoretically the $(\bar{p}, p)$ reactions for $^{12}$C, $^{16}$O, and $^{31}$P target nuclei. We find that the momentum transfer of the $( {\bar p},p)$ reaction is small and the formation of the ${\bar p}$-atomic states can be observed as the discrete peak structures in the $( {\bar p},p)$ spectrum. We conclude that the $(\bar{p}, p)$ reactions are very much suited for the $\bar{p}$ atom formation and the spectra of the reaction are expected to provide new valuable information on the ${\bar p}$ atoms and ${\bar p}$-nucleus interaction.