The results of the measurements of the antiproton annihilation cross s
ections on the nuclei Be, C, Al, Fe, Cu, Cd, and Pb at the momentum ra
nge 0.70 - 2.50 GeV/c are presented. The A-dependence of the cross sec
tions is described by the formula sigma(0)A(alpha). The behavior of th
e parameters sigma(0) and alpha does not agree with optical model in t
he Glauber approach. It is suggested that such a behavior is a result
of the Coulomb influence on the annihilation processes at the low mome
nta. The description of cross sections using formula sigma = A(2/3)(a(
0) + a(1)Z + a(2)Z(2)) is made and the parameters a(0), a(1), and a(2)
are evaluated. In the framework of the high-energy approach, the form
ula for the absorption cross section is derived: sigma(abs) = -2/($) o
ver bar hv integral d(2) bdz Im V exp{(ik integral(-infinity)(z)[root
1+2/pv V-root 1+2/pv V]d xi)}. This formula takes into account the in
fluence of the Coulomb potential and the real part of the nuclear pote
ntial on the absorption cross section. A comparison with the experimen
tal results is made in the framework of the Glauber optical model. The
agreement is not good.