Reaction rates are critical in understanding the nuclear evolution of stellar environments suchas Classical Novae and Type I X-ray Bursts. Nuclear properties of the neutron-deficient nucleus 18Ne are needed to reduce uncertainties in the reaction rate calculations of the sequence 14O(α,p)17F(p,γ)18Ne, which leads to breakout from the HCNO cycle. This thesis presents the results of branching ratio measurements of resonance states in 18Ne through the SiO(3He,n) re- action at E3He = 15 MeV. The 28Si(3He,n)30S reaction at E3He = 15 MeV was also measured to subtract the 30S contribution. Excited states of 18Ne at Eex. = 5.17 MeV, Eex. = 6.15 MeV, Eex. = 6.31 MeV, Eex. = 6.93 MeV, Eex. = 7.32 MeV, and Eex. = 7.87 MeV were analyzed, and their decay branching ratios were extracted. Using these branching ratios, new reaction rate parameters were determined for calculations of the 14O(α,p)17F reaction for a temperature range of T = 0.1-5 GK, typical of Type I X-ray Bursts. These measurements were performed at the John D. Fox Laboratory at Florida State University using the CATRiNA neutron detector array in conjunction with the CHARON silicon detector array for coincidences between neutrons and charged particles. A method for extracting neutron energies without relying on time-of-flight information, called "spectrum unfolding", and a full characterization of the CATRiNA neutron detector array through reactions 9Be(d,n) and 27Al(d,n) are also presented. Furthermore, differential cross sections from low-lying excited states of 13N through the 12C(d,n)13N reaction were extracted using "spectrum unfolding" and time-of-flight information. The differences between the methods are discussed. The 9Be(d,n), 27Al(d,n), and 12C(d,n)13N were all measured at the Edwards Accelerator Laboratory at Ohio University.
