  Parity violating elastic electron-nucleus scattering provides an accurate and
model independent measurement of neutron densities, because the $Z^0$ couples
primarily to neutrons. Coulomb distortion corrections to the parity violating
asymmetry $A_l$ are calculated exactly using a relativistic optical model.
Distortions significantly reduce $A_l$ in a heavy nucleus. However even with
distortions, an experiment to measure the neutron radius is feasible. This will
aid the interpretation of future atomic parity violation measurements and
provide fundamental nuclear structure information. Coulomb distortions and
small differences between neutron and proton radii could be important for a
standard model test on $^4$He, $^{12}$C or $^{16}$O.
