A Measurement of the Electric Form Factor of the Neutron through $\vec{d}(\vec{e},e^{\mathrm{\prime }}n)p$ at $Q^2=0.5$ (GeV/c)${}^2$

We report the first measurement of the neutron electric form factor $G_E^n$ via $\vec{d}(\vec{e},e^{\mathrm{\prime }}n)p$ using a solid polarized target. $G_E^n$ was determined from the beam-target asymmetry in the scattering of longitudinally polarized electrons from polarized deuterated ammonia, ${}^{15}$ND${}_3$. The measurement was performed in Hall C at Thomas Jefferson National Accelerator Facility (TJNAF) in quasi free kinematics with the target polarization perpendicular to the momentum transfer. The electrons were detected in a magnetic spectrometer in coincidence with neutrons in a large solid angle segmented detector. We find $G_E^n = 0.04632\pm0.00616 (stat.) \pm0.00341 (syst.)$at$Q^2 = 0.495$(GeV\mathrm{/}c)$^2$.