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 ²⁰⁸Pb. Parity-violating electron scattering can determine the average interior weak charge and baryon densities in ²⁰⁸Pb. This requires not only measuring the weak radius R_wk 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 ±0.010 fm^-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 .