Pocket resonances in low-energy antineutrons reactions with nuclei

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.