Weak charge form factor and radius of 208Pb through parity violation in electron scattering

TL;DR

This paper extracts the weak charge form factor, radius, and neutron skin thickness of 208Pb using parity-violating electron scattering data, revealing a weak charge skin and providing precise nuclear structure measurements.

Contribution

It introduces a method to determine the weak charge form factor and radius of 208Pb from PREX data, including uncertainties from models and strange quark contributions.

Findings

Weak charge radius R_W=5.826 ± 0.181 fm

Neutron radius R_n=5.751 ± 0.175 fm

Neutron skin thickness R_n - R_p=0.302 ± 0.175 fm

Abstract

We use distorted wave electron scattering calculations to extract the weak charge form factor F_W(q), the weak charge radius R_W, and the point neutron radius R_n, of 208Pb from the PREX parity violating asymmetry measurement. The form factor is the Fourier transform of the weak charge density at the average momentum transfer q=0.475 fm$^{-1}$. We find F_W(q) =0.204 \pm 0.028 (exp) \pm 0.001 (model). We use the Helm model to infer the weak radius from F_W(q). We find R_W= 5.826 \pm 0.181 (exp) \pm 0.027 (model) fm. Here the exp error includes PREX statistical and systematic errors, while the model error describes the uncertainty in R_W from uncertainties in the surface thickness \sigma of the weak charge density. The weak radius is larger than the charge radius, implying a "weak charge skin" where the surface region is relatively enriched in weak charges compared to (electromagnetic) charges. We extract the point neutron radius R_n=5.751 \pm 0.175 (exp) \pm 0.026 (model) \pm 0.005 (strange) fm$, from R_W. Here there is only a very small error (strange) from possible strange quark contributions. We find R_n to be slightly smaller than R_W because of the nucleon's size. Finally, we find a neutron skin thickness of R_n-R_p=0.302\pm 0.175 (exp) \pm 0.026 (model) \pm 0.005 (strange) fm, where R_p is the point proton radius.