Insights into nuclear saturation density from parity-violating electron scattering

The saturation density of nuclear matter ρ0 is a fundamental nuclear physics property that is difficult to predict from fundamental principles. The saturation density is closely related to the interior density of a heavy nucleus, such as Pb208. Parity-violating electron scattering can determine the average interior weak charge and baryon densities in Pb208. This requires not only measuring the weak radius Rwk but also determining the surface thickness of the weak charge density a. We use the PREX experimental result for the weak radius of Pb and assume a 10% theoretical uncertainty in the presently unmeasured surface thickness to obtain ρ0=0.150±0.010fm-3. Here the 7% error also has contributions from the extrapolation to infinite nuclear matter. These errors can be improved with the upcoming PREX II results and with a new parity-violating electron scattering experiment, at a somewhat higher momentum transfer, to determine a.