Parity violating electron scattering measurements of neutron densities

Parity violating electron scattering allows model-independent measurements of neutron densities that are free from most strong interaction uncertainties. In this paper, we present statistical error estimates for a variety of experiments. The neutron radius Rn can be measured in several nuclei, as long as the nuclear excited states are not too low in energy. We present error estimates for Rn measurements in 40Ca, 48Ca, 112Sn, 120Sn, 124Sn and 208Pb. In general, we find that the smaller the nucleus, the easier the measurement. This is because smaller nuclei can be measured at higher momentum transfers where the parity violating asymmetry Apv is larger. Also in general, the more neutron rich the isotope, the easier the measurement, because neutron-rich isotopes have larger weak charges and larger Apv. Measuring Rn in 48Ca appears very promising because it has a higher figure of merit than 208Pb. In addition, Rn(48Ca) may be more easily related to two-nucleon and three-nucleon interactions, including very interesting three-neutron forces, than Rn(208Pb). After measuring Rn, one can constrain the surface thickness of the neutron density an with a second measurement at somewhat higher momentum transfers. We present statistical error estimates for measuring an in 48Ca, 120Sn and 208Pb. Again, we find that an is easier to measure in smaller nuclei.