  Dispersive corrections to the total cross section for high-energy scattering
from a heavy nucleus are calculated using a matrix model, based on the
triple-Pomeron behavior of diffractive scattering from a single nucleon, for
the cross section operator connecting different states of the projectile
nucleon . Energy-dependent effects due to the decrease in longitudinal momentum
transfers and the opening of more channels with increasing energy are included.
The three leading terms in an expansion in the number of inelastic transitions
are evaluated and compared to exact results for the model in the uniform
nuclear density approximation for the the scattering of nucleons from Pb^{208}
for laboratory momenta ranging from 50 to 200 GeV/c.
