Deep inelastic scattering of polarized electrons by polarized ${}_{}{}^3{}_{}{}^{}\mathrm{He}$ 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 $0.03<x<\mathrm{}0.6\mathrm{}$ 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 $\int {0.03}^{0.6}{g}_1^n\mathrm{}\left(x\right)\mathrm{dx}=-0.028\mathrm{}\pm 0.006 \left(\mathrm{stat}\right)\pm 0.006 \left(\mathrm{syst}\right)$. Assuming Regge behavior at low $x$, we extract ${\Gamma }_1^n=\int 0^1{g}_1^n\mathrm{}\left(x\right)\mathrm{dx}=-0.031\mathrm{}\pm 0.006 \left(\mathrm{stat}\right)\pm 0.009 \left(\mathrm{syst}\right)$. Combined with previous proton integral results from SLAC experiment E143, we find ${\Gamma }_1^p-{\Gamma }_1^n=0.160\mathrm{}\pm 0.015$ in agreement with the Bjorken sum rule prediction ${\Gamma }_1^p-{\Gamma }_1^n=0.176\mathrm{}\pm 0.008$ at a $Q^2$ value of 3 ${(\mathrm{G}\mathrm{e}\mathrm{V}/\mathit{c})}^2$ evaluated using ${\alpha }_s=0.32\mathrm{}\pm 0.05$.