Annihilation of antiprotons on nuclear targets at low energies: a simple analysis

We set up a plane wave impulse approximation (PWIA) formalism for the analysis of the annihilation cross sections of antinucleons on nuclear targets at very low momenta (below 100 MeV/c), where semiclassical approximations can't be applied. Since, as we test here, PWIA fails in reproducing the unexpected ``inversion'' behavior of the $\bar{p}p$ and $\bar{p}-$nucleus annihilation cross sections found in a recent experiment\cite{obe1,obe2} we discuss some further possibilities, with a special attention to the optical potential model.