Precision Measurement of the Proton Spin Structure Function $g_1^p$

We have measured the ratio $\frac{g_1^p}{F_1^p}$ over the range $0.029<x<\mathrm{}0.8\mathrm{}$ and $1.3<\mathrm{}{Q}^2<10\mathrm{}$ ${(\mathrm{G}\mathrm{e}\mathrm{V}/\mathit{c})}^2$ using deep-inelastic scattering of polarized electrons from polarized ammonia. An evaluation of the integral $\int 0^1{g}_1^p(x, Q^2)\mathrm{dx}$ at fixed $Q^2=3\mathrm{}$ ${(\mathrm{G}\mathrm{e}\mathrm{V}/\mathit{c})}^2$ yields 0.127±0.004(stat)±0.010(syst), in agreement with previous experiments, but well below the Ellis-Jaffe sum rule prediction of 0.160±0.006. In the quark-parton model, this implies $\Delta q=0.27\mathrm{}\pm 0.10$.