Investigating Globular Cluster Elemental Abundance Anomalies Using $(^3\text{He},d)$ Proton Transfer Reactions

Globular clusters are dense aggregates of stars that evolve in relative isolation. For the better part of $40$ years these clusters have been known to possess unique chemical signatures called abundance anomalies. Recent observations have found these abundance anomalies to be the result of distinct stellar populations with the youngest population undergoing an unknown enrichment process. Understanding these chemical signatures requires a precise understanding of the thermonuclear reaction rates at relatively low temperatures. At these low temperatures reaction rates suffer from large uncertainties arising from poorly understood resonances in several key reactions. Transfer reactions provide key constrains on nuclear inputs for these resonances. This thesis presents an updated understanding of the sodium and potassium destroying reactions $^{23}$Na$(p, \gamma)$ and $^{39}$K$(p, \gamma)$, respectively. A reevaluated rate for $^{39}$K$(p, \gamma)$ indicates that it is less precisely known than previously thought, and future experimental study is needed to reduce its impact on globular cluster nucleosynthesis. Novel Bayesian techniques assess the uncertainties arising from transfer measurements. These techniques are applied to the transfer reaction $^{23}$Na$(^3\text{He}, d)$, which was carried out at Triangle Universities Nuclear Laboratory. Results of this experiment indicate that the energy of an important resonance in $^{23}$Na$(p, \gamma)$ is much lower than previously thought at $E_r =132(3)$ keV. The transfer measurement also indicates tension between previous direct studies of the resonance strength and the current transfer measurement. The impact of these uncertainties on the $^{23}$Na$(p, \gamma)$ reaction rate is investigated, and it is shown that this rate requires more intensive study to provide the precision needed to constrain nucleosynthesis in globular clusters.