Precision Determination of the Neutron Spin Structure Functiong1n

We report on a precision measurement of the neutron spin structure function $g_1^n$ using deep inelastic scattering of polarized electrons by polarized ${}^3\mathrm{He}$. For the kinematic range $0.014<x<\mathrm{}0.7\mathrm{}$ and $1<\mathrm{}{Q}^2<17\mathrm{}(\mathrm{GeV}/c{)}^2$, we obtain $\int {0.014}^{0.7}{g}_1^n\left(x\right)dx=-0.036\mathrm{}\pm 0.004\left(\mathrm{stat}\right)\pm 0.005\left(\mathrm{syst}\right)$ at an average $Q^2=5\mathrm{}(\mathrm{GeV}/c{)}^2$. We find relatively large negative values for $g_1^n$ at low $x$. The results call into question the usual Regge theory method for extrapolating to $x=0\mathrm{}$ to find the full neutron integral $\int 1^{}{g}_1^n\left(x\right)\mathrm{dx}$, needed for testing the quark-parton model and QCD sum rules.