Insights into nuclear saturation density from parity violating electron scattering

TL;DR

This paper uses parity violating electron scattering to measure the interior densities of lead-208, providing a new estimate of nuclear saturation density with quantified uncertainties, and discusses future improvements.

Contribution

It introduces a novel method to determine nuclear saturation density using parity violating electron scattering measurements of weak charge densities.

Findings

Estimated nuclear saturation density as 0.150±0.010 fm$^{-3}$.

Identified key sources of error and potential for future precision improvements.

Proposed new experiments to refine measurements of weak charge density surface thickness.

Abstract

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 $^{208}$Pb. We use parity violating electron scattering to determine the average interior weak charge and baryon densities in $^{208}$Pb. This requires not only measuring the weak radius $R_{\rm wk}$ but also determining the surface thickness of the weak charge density $a$. We obtain $\rho_0=0.150\pm0.010$ fm$^{-3}$, where the 7\% error has contributions form the PREX error on the weak radius, an assumed 10\% uncertainty in the surface thickness $a$, and 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 $a$.