  We have examined modifications to the nuclear weak charge due to small
differences between the spatial distributions of neutrons and protons in the Cs
nucleus. We derive approximate formulae to estimate the value and uncertainty
of this modification based only on nuclear rms neutron and proton radii.
Present uncertainties in neutron distributions in Cs are difficult to quantify,
but we conclude that they should not be neglected when using atomic parity
nonconservation experiments as a means to test the Standard Model.
