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This thesis reports on two experiments conducted by the HAPPEx (Hall A Proton Parity Experiment) collaboration at the Thomas Jefferson National Accelerator Facility. For both, the weak neutral current interaction (WNC, mediated by the Z0 boson) is used to probe novel properties of hadronic targets. The WNC interaction amplitude is extracted by measuring the parity-violating asymmetry in the elastic scattering of longitudinally polarized electrons off unpolarized target hadrons. HAPPEx-III, conducted in the Fall of 2009, used a liquid hydrogen target at a momentum transfer of Q2 = 0.62 GeV2. The measured asymmetry was used to set new constraints on the contribution of strange quark form factors ([special characters omitted]) to the nucleon electromagnetic form factors. A value of APV = −23.803 ± 0.778 (stat) ± 0.359 (syst) ppm resulted in [special characters omitted] = 0.003 ± 0.010 (stat) ± 0.004 (syst) ± 0.009 (FF). PREx, conducted in the Spring of 2010, used a polarized electron beam on a 208Pb target at a momentum transfer of Q 2 = 0.009 GeV2. This parity-violating asymmetry can be used to obtain a clean measurement of the root-mean-square radius of the neutrons in the 208Pb nucleus. The Z 0 boson couples mainly to neutrons; the neutron weak charge is much larger than that of the proton. The value of this asymmetry is at the sub-ppm level and has a projected experimental fractional precision of 3%. We will describe the accelerator setup used to set controls on helicity-correlated beam asymmetries and the analysis methods for finding the raw asymmetry for HAPPEx-III. We will also discuss in some detail the preparations to meet the experimental challenges associated with measuring such a small asymmetry with the degree of precision required for PREx.

The longitudinal relaxation time T$\sb1$ is calculated for a dilute Fermi gas. We include the possibility of arbitrary degrees of polarization P, and uniform external magnetic fields. At low temperatures T$\sb1$ is proportional to T$\sp{-2}$ for the unpolarized gas in agreement with earlier calculations. For a polarized system in zero applied field the separation between up and down Fermi spheres provides an open channel in phase space for spin flipping processes. As temperature is reduced to zero T$\sb1$ levels off and approaches a constant value which depends sensitively on P, leading to much smaller values of T$\sb1$ than in the unpolarized case. For relaxation in a uniform external field H, Zeeman energy conservation during spin flipping interactions essentially shifts the location of the T$\sp{-2}$ behavior from zero polarization to the polarization P(H) which would be produced in equilibrium with the external field H. When the initial polarization of the system is different from P(H), T$\sb1$ again approaches a constant value which is equally sensitive to the initial polarization as temperature is reduced to zero. We apply our calculations to the case of dilute $\sp3$He-HeII solutions. We also consider the calculation of density dependent corrections to T$\sb1$ for unpolarized, or weakly polarized $\sp3$He-HeII using the long wavelength limit of the Bardeen-Baym-Pines interaction as a form for the spin independent part of the $\sp3$He-$\sp3$He interaction. Owing to the positive sign of the antisymmetric Landau parameter $\rm F\sbsp{o}{a}$ in dilute $\sp3$He-HeII Fermi Liquid interactions act to screen the magnetic dipole interactions which cause relaxation. To lowest order in density we find that the relaxation rate 1/T$\sb1$ is reduced by factor $\rm (1 - 3F\sbsp{o}{a})$ which compares favorably with recent calculations of T$\sb1$ for pure $\sp3$He.

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.

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