J. Morgenstern

The spin structure function of the neutron ${\mathit{g}}_{1}^{\mathit{n}}$ has been determined over the range 0.03x0.6 at an average ${\mathit{Q}}^{2}$ of 2 (GeV/c${)}^{2}$ by measuring the asymmetry in deep inelastic scattering of polarized electrons from a polarized $^{3}\mathrm{He}$ target at energies between 19 and 26 GeV. The integral of the neutron spin structure function is found to be ${\mathcal{F}}_{0}^{1}$${\mathit{g}}_{1}^{\mathit{n}}$(x)dx=-0.022\ifmmode\pm\else\textpm\fi{}0.011. Earlier reported proton results together with the Bjorken sum rule predict ${\mathcal{F}}_{0}^{1}$${\mathit{g}}_{1}^{\mathit{n}}$(x)dx=-0.059\ifmmode\pm\else\textpm\fi{}0.019.

Measurements are reported of the proton and deuteron spin structure functions ${g}_{1}^{p}$ and ${g}_{1}^{d}$ at beam energies of 29.1, 16.2, and 9.7 GeV, and ${g}_{2}^{p}$ and ${g}_{2}^{d}$ at a beam energy of 29.1 GeV. The integrals ${\ensuremath{\Gamma}}_{p}={\ensuremath{\int}}_{0}^{1}{g}_{1}^{p}{(x,Q}^{2})dx$ and ${\ensuremath{\Gamma}}_{d}={\ensuremath{\int}}_{0}^{1}{g}_{1}^{d}{(x,Q}^{2})dx$ were evaluated at fixed ${Q}^{2}=3(\mathrm{GeV}{/c)}^{2}$ using the full data set to yield ${\ensuremath{\Gamma}}_{p}=0.132\ifmmode\pm\else\textpm\fi{}0.003(\mathrm{stat})\ifmmode\pm\else\textpm\fi{}0.009(\mathrm{syst})$ and ${\ensuremath{\Gamma}}_{d}=0.047\ifmmode\pm\else\textpm\fi{}0.003\ifmmode\pm\else\textpm\fi{}0.006.$ The ${Q}^{2}$ dependence of the ratio ${g}_{1}{/F}_{1}$ was studied and found to be small for ${Q}^{2}>1(\mathrm{GeV}{/c)}^{2}.$ Within experimental precision the ${g}_{2}$ data are well described by the twist-2 contribution, ${g}_{2}^{\mathrm{WW}}.$ Twist-3 matrix elements were extracted and compared to theoretical predictions. The asymmetry ${A}_{2}$ was measured and found to be significantly smaller than the positivity limit $\sqrt{R}$ for both proton and deuteron targets. ${A}_{2}^{p}$ is found to be positive and inconsistent with zero. Measurements of ${g}_{1}$ in the resonance region show strong variations with $x$ and ${Q}^{2},$ consistent with resonant amplitudes extracted from unpolarized data. These data allow us to study the ${Q}^{2}$ dependence of the integrals ${\ensuremath{\Gamma}}_{p}$ and ${\ensuremath{\Gamma}}_{n}$ below the scaling region.

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

Deep-inelastic electron scattering from $^{40}\mathrm{Ca}$, $^{48}\mathrm{Ca}$, and $^{56}\mathrm{Fe}$ has been measured at 60\ifmmode^\circ\else\textdegree\fi{}, 90\ifmmode^\circ\else\textdegree\fi{}, and 140\ifmmode^\circ\else\textdegree\fi{} and at inelasticities up to and including the $\ensuremath{\Delta}(3,3)$ region. Longitudinal response functions in the momentum interval $300 \mathrm{MeV}/c<|\stackrel{\ensuremath{\rightarrow}}{\mathrm{q}}|<600 \mathrm{MeV}/c$ were extracted. The experimental Coulomb sum rule is observed between the two calcium isotopes.