Deep inelastic scattering of polarized electrons by polarized<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mmultiscripts><mml:mrow><mml:mi mathvariant="normal">He</mml:mi></mml:mrow><mml:mprescripts/><mml:mrow/><mml:mrow><mml:mn>3</mml:mn></mml:mrow><mml:mrow/><mml:mrow/></mml:mmultiscripts></mml:mrow></mml:math>and the study of the neutron spin structure

The neutron longitudinal and transverse asymmetries ${A}_{1}^{n}$ and ${A}_{2}^{n}$ have been extracted from deep inelastic scattering of polarized electrons by a polarized $^{3}\mathrm{He}$ target at incident energies of 19.42, 22.66, and 25.51 GeV. The measurement allows for the determination of the neutron spin structure functions ${g}_{1}^{n}(x, {Q}^{2})$ and ${g}_{2}^{n}(x, {Q}^{2})$ over the range $0.03&lt;x&lt;0.6$ at an average ${Q}^{2}$ of 2 ${(\mathrm{G}\mathrm{e}\mathrm{V}/\mathit{c})}^{2}$. The data are used for the evaluation of the Ellis-Jaffe and Bjorken sum rules. The neutron spin structure function ${g}_{1}^{n}(x, {Q}^{2})$ is small and negative within the range of our measurement, yielding an integral $\ensuremath{\int}{0.03}^{0.6}{g}_{1}^{n}(x)\mathrm{dx}=\ensuremath{-}0.028\ifmmode\pm\else\textpm\fi{}0.006 (\mathrm{stat})\ifmmode\pm\else\textpm\fi{}0.006 (\mathrm{syst})$. Assuming Regge behavior at low $x$, we extract ${\ensuremath{\Gamma}}_{1}^{n}=\ensuremath{\int}{0}^{1}{g}_{1}^{n}(x)\mathrm{dx}=\ensuremath{-}0.031\ifmmode\pm\else\textpm\fi{}0.006 (\mathrm{stat})\ifmmode\pm\else\textpm\fi{}0.009 (\mathrm{syst})$. Combined with previous proton integral results from SLAC experiment E143, we find ${\ensuremath{\Gamma}}_{1}^{p}\ensuremath{-}{\ensuremath{\Gamma}}_{1}^{n}=0.160\ifmmode\pm\else\textpm\fi{}0.015$ in agreement with the Bjorken sum rule prediction ${\ensuremath{\Gamma}}_{1}^{p}\ensuremath{-}{\ensuremath{\Gamma}}_{1}^{n}=0.176\ifmmode\pm\else\textpm\fi{}0.008$ at a ${Q}^{2}$ value of 3 ${(\mathrm{G}\mathrm{e}\mathrm{V}/\mathit{c})}^{2}$ evaluated using ${\ensuremath{\alpha}}_{s}=0.32\ifmmode\pm\else\textpm\fi{}0.05$.