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 R_n can be measured in several nuclei, as long as the nuclear excited states are not too low in energy. We present error estimates for R_n 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 A_pv 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 A_pv. Measuring R_n in ⁴⁸Ca appears very promising because it has a higher figure of merit than ²⁰⁸Pb. In addition, R_n(⁴⁸Ca) may be more easily related to two-nucleon and three-nucleon interactions, including very interesting three-neutron forces, than R_n(²⁰⁸Pb). After measuring R_n, one can constrain the surface thickness of the neutron density a_n with a second measurement at somewhat higher momentum transfers. We present statistical error estimates for measuring a_n in ⁴⁸Ca, ¹²⁰Sn and ²⁰⁸Pb. Again, we find that a_n is easier to measure in smaller nuclei.