This thesis describes longitudinal nuclear relaxation measurements of solid 129Xe near 77 K with previously unattainable reproducibility, and demonstrates differences in relaxation, dependent upon the way in which the solid is condensed. These results are directly applicable to the generation and storage of large quantities of hyperpolarized 129Xe for various applications, such as lung magnetic resonance imaging (MRI). The thesis features a sophisticated theoretical approach to these data sets, including modifications to a well-established Raman-phonon scattering theory that may explain the larger scatter in and discrepancies with previous work.