In experiment E154 at the Stanford Linear Accelerator Center the spin dependent structure function $g\sbsp{1}{n}(x,Q\sp2)$ of the neutron was measured by scattering longitudinally polarized 48.3 GeV electrons off a longitudinally polarized $\sp3$He target. The high beam energy allowed us to extend the kinematic coverage compared to the previous SLAC experiments to $0.014\leq x\leq0.7$ with an average $Q\sp2$ of 5 GeV$\sp2.$ We report the integral of the spin dependent structure function in the measured range to be $\int\sbsp{0.014}{0.7}dx\ g\sbsp{1}{n}(x,5\ {\rm GeV}\sp2)={-}0.036\pm0.004({\rm stat}.)\pm0.005({\rm syst}.).$ We observe relatively large values of $g\sbsp{1}{n}$ at low x that call into question the reliability of data extrapolation to $x\to0.$ Such divergent behavior disagrees with predictions of the conventional Regge theory, but is qualitatively explained by perturbative QCD. We perform a Next-to-Leading Order perturbative QCD analysis of the world data on the nucleon spin dependent structure functions $g\sbsp{1}{p}$ and $g\sbsp{1}{n}$ paying careful attention to the experimental and theoretical uncertainties. Using the parameterizations of the helicity-dependent parton distributions obtained in the analysis, we evolve the data to $Q\sp2$ = 5 GeV$\sp2,$ determine the first moments of the polarized structure functions of the proton and neutron, and find agreement with the Bjorken sum rule.

Experiment E690 at Fermilab recorded 5.5 billion $p + p \to p + X$ events using an 800 GeV/c proton beam and a liquid hydrogen target, during the 1991 fixed target run. We use a 0.5 billion subset of this sample, to study the reaction $p + p \to p\sb{s}(\pi\sp+\pi\sp-)p\sb{f}$ for dipion invariant mass between threshold and 2.3 GeV/c$\sp2.$ We perform a partial wave analysis for dipion invariant mass between threshold and 1.5 GeV/c$\sp2.$ The assumption of S-wave dominance near threshold is sufficient to determine a single, continuous solution throughout the considered mass spectrum. Precision measurement of the production amplitude aids the mapping the low lying meson spectrum. Other possible studies using this data sample and analysis technique are: (1) the extension of the amplitude analysis above the 1.5 GeV/c$\sp2$ mass region using a the full event sample, and (2) the study of the produced amplitudes as a function of the relative angle between the two proton planes.

Results are presented on a study of resonant structure in the $\omega\pi\sp0$ and $\omega\eta$ final states produced in $\pi\sp-p$ interactions at 18 GeV/c where $\omega\to \pi\sp+\pi\sp-\pi\sp0,\ \pi\sp0\to 2\gamma,$ and $\eta\to 2\gamma.$ Final states such as $\omega\pi\sp0$ and $\omega\eta,$ which contain a vector meson are allowed in the extended flux-tube model for the decay of hybrid mesons. For the $\omega\eta$ final state, the data exhibit the well-known $b\sb1$(1235) and $\rho\sb3$(1690) resonances. A one-pion exchange mechanism is clearly seen for the $\rho\sb3$(1690). The result of a partial wave analysis for the $\omega\eta$ final state finds a new $1\sp{+-}$ meson state $h\sb1$(1540) with a mass $M = 1542\pm 13$ MeV and a width $\Gamma = 285\pm 30$ MeV, which shows phase motion relative to the $\omega$(1600). The decay mode of $\omega(1600)\to \omega\eta$ has not been previously reported.

Two areas of nonleptonic weak interactions are examined: parity-violation in nucleon-nucleon interactions including $\Delta$ excitations, and strangeness-changing hypernuclear decay processes. In both cases we utilize SU(6)$\sb{w}$-based quark model pictures to describe the weak hadronic physics. In the first part of this dissertation we develop an effective parity-violating Hamiltonian for the weak interactions of $\Delta$'s with hadrons and mesons. We evaluate weak parity-violating $\Delta$-$\Delta$-meson and $\Delta$-nucleon-meson vertices for $\pi$, $\rho$, and $\omega$ mesons, thus extending previous work involving only nucleons and mesons. The second part of this dissertation presents the results of calculations for several observables involving the decay of hypernuclei. We examine the model dependence of these observables by considering several variations of the model and its parameters.