Insights into nuclear saturation density from parity-violating electron scattering

The saturation density of nuclear matter ${\rho }_0$ 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 ${\rho }_0=0.150\pm 0.010{\mathrm{fm}}^{-3}$. 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 $a$.

Figure 1

The experimental charge density of ${}^{208}\mathrm{Pb}$ [15] (red circles) and the corresponding SFermi function fit (solid red line). Also shown is the weak charge density as predicted by the FSUGold interaction [46] (blue circles) along with a SFermi function fit (solid black line).

Figure 2

The extrapolation factor $f_{\mathrm{ex}}$ defined in Eq. (6) as a function of the the neutron skin thickness of ${}^{208}\mathrm{Pb}$ for a number of nonrelativistic and relativistic EDFs. Shown with triangles is the extrapolation factor ${\tilde{f}}_{\mathrm{ex}}$ to asymmetric nuclear matter with the same ratio of neutrons to protons as ${}^{208}\mathrm{Pb}$.

Figure 3

Theoretical prediction for the baryon density of ${}^{208}\mathrm{Pb}$. The error band assumes that $R_{\mathrm{wk}}$ is measured to 1% and the surface thickness is constrained to 10%, see text for details. The corresponding curve for the weak charge density is also shown. Finally, the experimental charge density [15] is displayed along with a SFermi fit.