  The finite-size correction to $\beta$-decay plays an important role in
determining the expected antineutrino spectra from reactors at a level that is
important for the reactor-neutrino anomaly. Here we express the leading-order
finite-size correction to allowed $\beta$-decay in terms of Zemach moments. We
calculate the Zemach moments within a Hartree-Fock model using a Skyrme-like
energy density functional. We find that the Zemach moments are increased
relative to predictions based on the simple assumption of identical uniform
nuclear-charge and weak-transition densities. However, for allowed ground-state
to ground-state transitions in medium and heavy nuclei, the detailed nuclear
structure calculations do not change the finite-size corrections significantly
from the simple model predictions, and are only 10-15% larger than the latter
even though the densities differ significantly.
