  We present a new dispersive formulation of the gamma-Z box radiative
corrections to weak charges of bound protons and neutrons in atomic parity
violation (APV) measurements on heavy nuclei such as 133-Cs and 213-Ra. We
evaluate for the first time a small but important additional correction arising
from Pauli blocking of nucleons in a heavy nucleus. Overall, we find a
significant shift in the gamma-Z correction to the weak charge of 133-Cs,
approximately 4 times larger than the current uncertainty on the value of
sin^2(theta_W), but with a reduced error compared to earlier estimates.
