Insights into nuclear saturation density from parity-violating electron scattering
C. J. Horowitz, J. Piekarewicz, Brendan T. Reed
Abstract
The saturation density of nuclear matter ${\ensuremath{\rho}}_{0}$ 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 $^{208}\mathrm{Pb}$. Parity-violating electron scattering can determine the average interior weak charge and baryon densities in $^{208}\mathrm{Pb}$. This requires not only measuring the weak radius ${R}_{\mathrm{wk}}$ 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 ${\ensuremath{\rho}}_{0}=0.150\ifmmode\pm\else\textpm\fi{}0.010\phantom{\rule{4pt}{0ex}}{\mathrm{fm}}^{\ensuremath{-}3}$. 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 $a$.