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Globular clusters are dense aggregates of stars that evolve in relativeisolation. For the better part of $40$ years these clusters have been known topossess unique chemical signatures called abundance anomalies. Recentobservations have found these abundance anomalies to be the result of distinctstellar populations with the youngest population undergoing an unknownenrichment process. Understanding these chemical signatures requires a preciseunderstanding of the thermonuclear reaction rates at relatively lowtemperatures. At these low temperatures reaction rates suffer from largeuncertainties arising from poorly understood resonances in several keyreactions. Transfer reactions provide key constrains on nuclear inputs forthese resonances. This thesis presents an updated understanding of the sodiumand potassium destroying reactions $^{23}$Na$(p, \gamma)$ and $^{39}$K$(p,\gamma)$, respectively. A reevaluated rate for $^{39}$K$(p, \gamma)$ indicatesthat it is less precisely known than previously thought, and futureexperimental study is needed to reduce its impact on globular clusternucleosynthesis. Novel Bayesian techniques assess the uncertainties arisingfrom transfer measurements. These techniques are applied to the transferreaction $^{23}$Na$(^3\text{He}, d)$, which was carried out at TriangleUniversities Nuclear Laboratory. Results of this experiment indicate that theenergy of an important resonance in $^{23}$Na$(p, \gamma)$ is much lower thanpreviously thought at $E_r =132(3)$ keV. The transfer measurement alsoindicates tension between previous direct studies of the resonance strength andthe current transfer measurement. The impact of these uncertainties on the$^{23}$Na$(p, \gamma)$ reaction rate is investigated, and it is shown that thisrate requires more intensive study to provide the precision needed to constrainnucleosynthesis in globular clusters.

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