Weak charge form factor and radius of $^{208}\text{Pb}$ through parity violation in electron scattering

Abstract

We use distorted wave electron scattering calculations to extract the weak charge form factor $F_W(\bar{q})$, the weak charge radius $R_W$, and the point neutron radius $R_n$ of $^{208}\text{Pb}$ from the Lead Radius Experiment (PREX) parity-violating asymmetry measurement. The form factor is the Fourier transform of the weak charge density at the average momentum transfer $\bar{q}=0.475$ $\text{fm}^{-1}$. We find $F_W(\bar{q})=0.204±0.028$ $(\text{exp})±0.001$ $(\text{model})$. We use the Helm model to infer the weak radius from $F_W(\bar{q})$. We find $R_W=5.826±0.181$ $(\text{exp})±0.027$ $(\text{model})$ $\text{fm}$. Here the experimental 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 $R_n=5.751±0.175$ $(\text{exp})±0.026$ $(\text{model})±0.005$ $(\text{strange})$ $\text{fm}$ 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 $R_n-R_p=0.302±0.175$ $(\text{exp})±0.026$ $(\text{model})±0.005$ $(\text{strange})$ $\text{fm}$, where $R_p$ is the point proton radius.