One of the key questions in nuclear astrophysics is understanding how elements heavier than iron are forged in the stars. Heavy element nucleosynthesis is primarily governed by the slow and rapid neutron capture processes. However, a relatively small group of naturally occurring, neutron-deficient isotopes, known as p nuclei, cannot be formed by either of those processes. These ~30 nuclei are believed to be synthesized in the γ process, where preexisting r- and s-process seeds are "burned" through a sequence of photodisintegration reactions. The astrophysical sites where such conditions occur have been a subject of controversy for more than 60 years, and is currently believed that the γ process can take place in the O/Ne layers of core collapse supernovae, and in thermonuclear supernovae. Reproducing solar p-nuclei abundances through nuclear reaction networks requires input on a large number of mostly radioactive isotopes. However, as experimental cross sections of γ-process reactions are very limited, and almost entirely unknown for radioactive nuclei, the related reaction rates are based on Hauser-Feshbach (HF) theoretical calculations and therefore carry large uncertainties. Therefore, it is crucial to develop techniques to accurately measure these reactions within the astrophysically relevant Gamow window with radioactive beams. The SuN group at the Facility for Rare Isotope Beams (FRIB) has been developing such a program for the past decade. This thesis focuses on implementing a technique to measure reaction cross sections in inverse kinematics with a radioactive beam. Specifically, this work presents data analysis from the proof-of-principle stable beam experiment for the 82Kr(p,γ)83Rb reaction, along with the measurement of the 73As(p,γ)74Se reaction in our first radioactive beam experiment. The latter reaction is particularly significant for the final abundance of the lightest p nucleus, 74Se, since the inverse reaction 74Se(γ,p)73As is one of the primary destruction mechanisms of 74Se. The experiments were conducted at FRIB at Michigan State University using the ReA facility. The 82Kr and 73As beams were directed onto a hydrogen gas cell located in the center of the Summing NaI(Tl) (SuN) detector and the obtained spectra were analyzed using the γ-summing technique. In addition to the total cross section measurements, this thesis also presents the development of an analysis technique to extract statistical properties of the compound nucleus (nuclear level density and $\gamma$-ray strength function) through a series of simulations. This approach enables the extraction of an experimentally constrained cross section across the entire Gamow window of the γ process. Finally, the experimentally constrained reaction rate for the 73As(p,γ)74Se reaction is used in Monte Carlo one-zone network simulations of the γ process to explore its impact on the production of the 74Se.
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