$[Background]$ Measurements of the neutron charge form factor, $G^n_E$, are
challenging due to the fact that 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 $G^n_E$ 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 $1~(\rm{GeV/c})^2$. 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 quasi-elastic reaction
$^3\overrightarrow{\rm{He}}(\overrightarrow{e},e')$ was measured at Jefferson
Lab. The neutron electric form factor, $G_E^n$, was extracted at $Q^2 =
0.98~(\rm{GeV/c})^2$ 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 $0.0414\pm0.0077\;{(stat)}\pm0.0022\;{(syst)}$; providing the
first high precision inclusive extraction of the neutron's charge form factor.
$[Conclusions]$ The use of the inclusive quasi-elastic
$^3\overrightarrow{\rm{He}}(\overrightarrow{e},e')$ with a four-momentum
transfer near $1~(\rm{GeV/c})^2$ has been used to provide a unique measurement
of $G^n_E$. This new result provides a systematically independent validation of
the exclusive extraction technique results.
