  We examine the momentum dependence of $\bar p$$p$ and $\bar n$$p$
annihilation cross sections by considering the transmission through a nuclear
potential and the $\bar p p$ Coulomb interaction. Compared to the $\bar n p$
annihilation cross section, the $\bar p p$ annihilation cross section is
significantly enhanced by the Coulomb interaction for projectile momenta below
$p_{\rm lab} <$ 500 MeV/$c$, and the two annihilation cross sections approach
the Pomeranchuk's equality limit [JETP Lett. {\bb 30}, 423 (1956)] at $p_{\rm
lab}\sim 500$ MeV/$c$. Using these elementary cross sections as the basic input
data, the extended Glauber model is employed to evaluate the annihilation cross
sections for $\bar n$ and $\bar p$ interaction with nuclei and the results
compare well with experimental data.
