Classical novae occur in binary star systems involving a compact white dwarf and a low-mass stellar companion. In these events, material siphoned from the donor star forms an accretion disk around the white dwarf. This hydrogen-rich fuel is compressed, heated, and mixed with the outer layers of the underlying white dwarf until it eventually ignites in a thermonuclear runaway. These violent explosions eject freshly synthesized nuclear material into the interstellar medium, contributing to the chemical evolution of the galaxy.Nova sensitivity studies involving the most massive oxygen-neon (ONe) white dwarfs have identified the thermonuclear rate of the 30P(\uD835\uDC5D, \uD835\uDEFE) 31S reaction to be the largest remaining source of nuclear physics uncertainty associated with modeling nucleosynthesis for intermediate-mass elements in these highly energetic events. Over the past two decades, considerable experimental effort has been devoted to determining the rate of this proton-capture reaction, but until now, it has remained essentially unconstrained. A recent 31Cl \uD835\uDEFD-delayed \uD835\uDEFE experiment revealed the existence of a crucial low-energy, l = 0 resonance that could potentially dominate the total 30P(\uD835\uDC5D, \uD835\uDEFE) 31S rate. At the National Superconducting Cyclotron Laboratory (NSCL), on the campus of Michigan State University, we developed the Gaseous Detector with Germanium Tagging (GADGET) system in order to measure the weak, low-energy, \uD835\uDEFD-delayed proton decay of 31Cl through this astrophysically important resonance. In GADGET's first dedicated science experiment, we measured the weakest \uD835\uDEFD-delayed charged-particle decay ever reported for resonances below 400 keV. Combining our experimentally determined proton branching ratio with shell-model calculations of the state's lifetime and with past work on other resonances, we computed the total thermonuclear rate for the 30P(\uD835\uDC5D, \uD835\uDEFE) 31S reaction across peak classical nova temperatures. Our new, recommended rate was used in fully hydrodynamic nova model simulations to predict the elemental and isotopic abundances in ONe nova ejecta. In this dissertation, we will discuss the experimental methods and analysis employed to achieve our scientific results and investigate their astrophysical impact by comparing to observations from astronomy. Furthermore, we present the first-ever detailed look at the 31Cl(\uD835\uDEFD\uD835\uDC5D\uD835\uDEFE) 30P decay scheme, reporting preliminary energies and intensities for previously unobserved \uD835\uDEFD-delayed proton transitions to 30P excited states.
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