Saturation of low-energy antiproton annihilation on nuclei

Recent measurements of very low-energy ($p_{L}<100$ MeV/c) $\bar p$ annihilation on light nuclei reveal apparent suppression of annihilation upon increasing the atomic charge $Z$ and mass number $A$. Using $\bar p$-nucleus optical potentials $V_{{\rm opt}}$, fitted to $\bar p$-atom energy-shifts and -widths, we resolve this suppression as due to the strong effective repulsion produced by the very absorptive $V_{{\rm opt}}$. The low-energy $\bar p$-nucleus wavefunction is kept substantially outside the nuclear surface and the resulting reaction cross section saturates as function of the strength of Im $V_{{\rm opt}}$. This feature, for $E >0$, parallels the recent prediction, for $E < 0$, that the level widths of $\bar p$ atoms saturate and, hence, that $\bar p$ deeply bound atomic states are relatively narrow. Antiproton annihilation cross sections are calculated at $p_{L}=57$ MeV/c across the periodic table, and their dependence on $Z$ and $A$ is classified and discussed with respect to the Coulomb focussing effect at very low energies.