Title: First Measurements of the Parity-Violating and Beam-Normal Single-Spin Asymmetries in Elastic Electron-Aluminum Scattering

The Q_weak collaboration has made the first measurements of the elastic parity-violating and beam-normal single-spin asymmetries from the ²⁷Al nucleus. Both are the result of ancillary measurements conducted during the Q_weak experiment at Jefferson Lab. The goal of the experimental was to determine the proton's weak charge, Q^p_W, via a measurement of the elastic parity-violating electron-proton scattering asymmetry. During the experiment, ancillary measurements were made with different beam configurations on a separate aluminum alloy target, in an effort to directly measure the aluminum background coming from the experiment's liquid hydrogen target cell. This dissertation discusses three primary results: the parity-violating ²⁷Al asymmetry analysis used to correct for the aluminum target background in the final Q_weak analysis, its extended analysis leading to the extraction of the pure elastic parity-violating ²⁷Al asymmetry, and the determination of the elastic beam-normal single-spin ²⁷Al asymmetry. The parity-violating result was also used to make a semi model-independent determination of ²⁷Al neutron distribution radius, an important test for models used to describe neutron-rich matter. The beam-normal single-spin asymmetry stands to possibly shed light on an observed disagreement between theory and a previous measurement performed on ²⁰⁸Pb, as ²⁷Al is the next highest atomic mass nucleus to have this observable measured. The elastic parity-violating ²⁷Al asymmetry was found to be 1.927 +/- 0.173 ppm at (Q²) = 0.0236 +/- 0.0001 GeV². This measured parity-violating asymmetry implies a ²⁷Al neutron distribution radius of 3.024 +/- 0.104 fm. Calculating the difference between this radius and the ²⁷Al proton distribution radius yields the neutron skin, which was found to be 0.092 +/- 0.104 fm. This skin value is consistent with zero, within its uncertainty, and it confirms the naive expectation for a light nucleus like ²⁷Al. The beam-normal single-spin ²⁷Al asymmetry was found to be -16.322 +/- 2.679 ppm at ⟨Q⟩ = 0.154 GeV. This value agrees with the previous observed trend of beam-normal single-spin asymmetries measured from light nuclei, which motivates the need for future measurements of higher atomic mass nuclei.