Extraction of the neutron electric form factor from measurements of inclusive double spin asymmetries

Background: Measurements of the neutron charge form factor, ${G}_{E}^{n}$, are challenging because the neutron has no net charge. In addition, measurements of the neutron form factors must use nuclear targets which require accurately accounting for nuclear effects. Extracting ${G}_{E}^{n}$ with different targets and techniques provides an important test of our handling of these effects.Purpose: The goal of the measurement was to use an inclusive asymmetry measurement technique to extract the neutron charge form factor at a four-momentum transfer of $1\phantom{\rule{0.16em}{0ex}}{(\mathrm{GeV}/\mathrm{c})}^{2}$. This technique has very different systematic uncertainties than traditional exclusive measurements and thus serves as an independent check of whether nuclear effects have been taken into account correctly.Method: The inclusive quasielastic reaction ${}^{3}\stackrel{P\vec}{\mathrm{He}}(\stackrel{P\vec}{e},{e}^{\ensuremath{'}})$ was measured at Jefferson Laboratory. The neutron electric form factor, ${G}_{E}^{n}$, was extracted at ${Q}^{2}=0.98\phantom{\rule{0.16em}{0ex}}{(\mathrm{GeV}/\mathrm{c})}^{2}$ from ratios of electron-polarization asymmetries measured for two orthogonal target spin orientations. This ${Q}^{2}$ is high enough that the sensitivity to ${G}_{E}^{n}$ is not overwhelmed by the neutron magnetic contribution, and yet low enough that explicit neutron detection is not required to suppress pion production.Results: The neutron electric form factor, ${G}_{E}^{n}$, was determined to be $0.0414\ifmmode\pm\else\textpm\fi{}0.0077\phantom{\rule{0.28em}{0ex}}(\text{stat})\ifmmode\pm\else\textpm\fi{}0.0022\phantom{\rule{0.28em}{0ex}}(\text{syst})$, providing the first high-precision inclusive extraction of the neutron's charge form factor.Conclusions: The use of the inclusive quasielastic ${}^{3}\stackrel{P\vec}{\mathrm{He}}(\stackrel{P\vec}{e},{e}^{\ensuremath{'}})$ with a four-momentum transfer near $1\phantom{\rule{0.28em}{0ex}}{(\mathrm{GeV}/\mathrm{c})}^{2}$ has been used to provide a unique measurement of ${G}_{E}^{n}$. This new result provides a systematically independent validation of the exclusive extraction technique results and implies that the nuclear corrections are understood. This is contrary to the proton form factor where asymmetry and differential cross section measurements have been shown to have large systematic differences.