Effects of neutron spatial distributions on atomic parity nonconservation in cesium

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.