Effects of spatial neutron distributions on low-energy parity-violating observables

We investigate the optimal kinematic conditions for extracting information about the spatial distribution of neutrons in heavy spin-0 nuclei from a hy pothetical parity-violating electron scattering (PVES) experiment. We furth er investigate the extent to which present uncertainties in the shape of th e neutron distribution affect the extraction of the rms neutron radius (the first moment of the distribution R,). We conclude that present theoretical uncertainties in the shape of the neutron distribution will not preclude a PVES measurement of R, at the 1% level in lead. We also calculate the addi tional constraints provided by measurements at two different values of the momentum transfer. Finally, we examine the connection to atomic parity non- conservation (PNC) observables and find that a single optimally designed PV ES experiment could eliminate nuclear structure uncertainties in future pre cision tests of the standard model at the sub-l% level.