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 cant 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 experimentcite{obe1,obe2} we discuss some further possibilities, with a special attention to the optical potential model.