This dissertation includes the design and development of the Summing NaI (SuN) 4pi gamma-ray detector at the National Superconducting Cyclotron Laboratory to measure proton and alpha radiative capture reactions relevant in the astrophysical p process. Discussions of p-process nucleosynthesis, the relevant nuclear reaction theory, experimental details, and analysis procedures are included. All reaction measurements were performed at the Nuclear Science Laboratory of the University of Notre Dame. The commissioning experiments in both regular and inverse kinematics were done using known resonances in the 27Al(p,g)28Si and 58Ni(p,g)59Cu reactions, and the results agree well with previous literature values. The success of these proof-of-principle measurements marks the first time that the gamma-summing technique has been implemented in inverse kinematics. Furthermore, in an effort to investigate the synthesis of the light p-process nuclei, the 74Ge(p,g)75As, 74Ge(a,g)78Se, and 90,92Zr(a,g)94,96Mo reactions were measured and compared to theoretical calculations using the nuclear statistical model. It was found that the new 74Ge(p,g)75As measurements cause an enhancement in the overproduction of 74Se in p-process models, and that the updated 90Zr(a,g)94Mo reaction rate seems to confirms the p-process branching point at 94Mo. Finally, the 58Ni(a,g)62Zn reaction was measured for its role in nucleosynthesis in type Ia supernovae. The measurements here lower the reaction rate used in astrophysical models, which leads to a 5% reduction in the calculated abundances of several isotopes. All of the measurements in this dissertation greatly reduce the uncertainty in the reaction cross section.
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