Exploring Nuclear Structure In Varied Regimes: Beta Decay of Exotic Fluorines and Study of the Stellar Triple Alpha Process

In this dissertation, I present work that examines nuclear structure in two disparate cases that add to our fundamental understanding of the nuclear landscape. In the first portion of this dissertation, an investigation of several isotopes near or around the N=20 island of inversion, focusing on beta-delayed spectroscopy of $^{27,29}$F will be presented. Analyses include an extensive examination of isomeric transitions in all isotopes present in the dataset, a plethora of beta halflife measurements, beta-delayed gamma spectroscopy, beta-delayed neutron spectroscopy, $\beta n \gamma$ spectroscopy, and $\beta \gamma\gamma$ spectroscopy. This work represents the first beta delayed spectroscopy of $\elem{F}{27,29}{}$ and discusses the implications for the microscopic structure in the daughters. The second portion of the present dissertation discusses a measurement and analysis pertinent to the Hoyle state. The Hoyle state, also known as the triple-alpha resonance in $\elem{C}{12}{}$, is critical for the formation of $\elem{C}{12}{}$ in helium burning stars, and responsible for nearly all of the carbon necessary for life on earth. For $\elem{C}{12}{}$ to form, the Hoyle state must have a probability of de-exciting to the ground state, the E2 radiative (a two gamma ray cascade) and pair emission branches respectively. The two most recent direct measurements of the radiative branching ratio differ by a factor of 1.5. It is imperative to resolve the discrepancy in measured radiative branching ratios, as the inconsistency impacts stellar thermonuclear models of $\elem{C}{12}{}$ and $\elem{O}{16}{}$ formation, with substantial knock-on effects in r, p and i processes. In this work we utilize GODDESS to measure the radiative branching ratio of the Hoyle state by directly measuring its gamma ray cascade. The GODDESS particle-gamma spectrometer consists of state-of-the-art arrays ORRUBA, for charged particles, and GRETINA, for gamma rays. The unique combination of high energy resolution particle and gamma detectors with near 4$\pi$ solid angle coverage allows the unique capability of individually measuring the two gamma rays in the Hoyle state cascade.