Measurement of the Neutron Electric to Magnetic Form Factor Ratio atQ2=1.58 GeV2Using the ReactionHe→3(e→,e′n)pp

A measurement of beam helicity asymmetries in the reaction $^{3}\stackrel{\ensuremath{\rightarrow}}{\mathrm{He}}(\stackrel{\ensuremath{\rightarrow}}{e},{e}^{\ensuremath{'}}n)pp$ is performed at the Mainz Microtron in quasielastic kinematics to determine the electric to magnetic form factor ratio of the neutron ${G}_{E}^{n}/{G}_{M}^{n}$ at a four-momentum transfer ${Q}^{2}=1.58\text{ }\text{ }{\mathrm{GeV}}^{2}$. Longitudinally polarized electrons are scattered on a highly polarized $^{3}\mathrm{He}$ gas target. The scattered electrons are detected with a high-resolution magnetic spectrometer, and the ejected neutrons are detected with a dedicated neutron detector composed of scintillator bars. To reduce systematic errors, data are taken for four different target polarization orientations allowing the determination of ${G}_{E}^{n}/{G}_{M}^{n}$ from a double ratio. We find ${\ensuremath{\mu}}_{n}{G}_{E}^{n}/{G}_{M}^{n}=0.250\ifmmode\pm\else\textpm\fi{}0.058(\mathrm{stat})\ifmmode\pm\else\textpm\fi{}0.017(\mathrm{syst})$.