  Upon investigating whether the variation of the antineutron-nucleus
annihilation cross-sections at very low energies satisfy Bethe-Landau's power
law of $\sigma_{\rm ann} (p) \propto 1/p^{\alpha}$ behavior as a function of
the antineutron momentum $p$, we uncover unexpected regular oscillatory
structures in the low antineutron energy region from 0.001 to 10 MeV, with
small amplitudes and narrow periodicity in the logarithm of the antineutron
energies, for large-$A$ nuclei such as Pb and Ag. Subsequent semiclassical
analyses of the $S$ matrices reveal that these oscillations are pocket
resonances that arise from quasi-bound states inside the pocket and the
interference between the waves reflecting inside the optical potential pockets
with those from beyond the potential barriers, implicit in the nuclear Ramsauer
effect. They are the continuation of bound states in the continuum.
Experimental observations of these pocket resonances will provide vital
information on the properties of the optical model potentials and the nature of
the antineutron annihilation process.
