Optical model potential analysis of $\bar nA$ and $nA$ interactions

We use a momentum-dependent optical model potential to analyze the annihilation cross sections of antineutron $\bar n$ on C, Al, Fe, Cu, Ag, Sn, and Pb nuclei for projectile momenta $p_{\rm lab}$ $\lesssim$ 500 MeV/$c$. We obtain good description of annihilation cross sections data of Barbina {\it et al.} [Nucl.~Phys.~A {\bf 612}, ~346~(1997)] and of Astrua {\it et al.} [Nucl.~Phys.~A {\bf 697},~209~(2002)] which exhibit an interesting dependence of the cross sections on the $p_{\rm lab}$ as well as on the target atomic mass number $A$. We also obtain the neutron ($n$) non-elastic reaction cross sections for the same targets. Contrasting the $nA$ reaction cross sections $\sigma^{nA}_{\rm rec}$ to the $\bar nA$ annihilation cross sections $\sigma^{\bar nA}_{\rm ann}$, we find the $\sigma^{\bar nA}_{\rm ann}$ is significantly larger than the $\sigma^{nA}_{\rm rec}$, that is, the $\sigma^{\bar nA}_{\rm ann}$/$\sigma^{nA}_{\rm rec}$ cross section ratio lies between the values of order 1.8 and 3.8 in the momentum region where comparison is possible. The dependence of the annihilation cross section on the projectile charge is also examined in comparison with antiproton $\bar p$. Here we predict the $\bar pA$ annihilation cross section on the simplest assumption that both $\bar pA$ and $\bar nA$ interactions have the same nuclear part of the optical model potential but differs only on the electrostatic Coulomb interaction. Deviation from such simple model extrapolation in measurements will provide new information on the difference between $\bar nA$ and $\bar pA$ potentials.