  We use the Gribov-Zwanziger Lagrangian in QCD to evaluate the one loop
correction to the gluon propagator as a function of the Gribov volume and
verify that the propagator vanishes in the infrared limit. Using the
corresponding correction to the Faddeev-Popov ghost propagator we construct the
renormalization group invariant coupling constant, alpha^eff_S(p^2), from the
gluon and ghost form factors and verify, using the Gribov mass gap condition,
that it freezes out at zero momentum to a non-zero value. This is qualitatively
consistent with other approaches. We also show that there is an enhancement of
the propagator of one of the Zwanziger ghosts at two loops similar to that
which occurs for the Faddeev-Popov ghosts. From the exact evaluation of the
form factors we examine power corrections for the gluon propagator and the
effective coupling. We find that both have the same qualitative behaviour in
that the leading power correction is O(1/p^2) and not O(1/(p^2)^2).
