Exploring the Fusion of Alpha and Carbon-12

Two linked fusion processes, which occur inside the cores of massive stars, largely determine our universe's carbon-to-oxygen ratio. Three alpha particles first fuse to create Carbon-12, which then captures an additional alpha particle to fuse into Oxygen-16. However, this last nuclear process occurs at an energy level which is difficult to measure in a lab. Additionally, the relatively large number of particles in the Carbon-12 target and the alpha beam make the reaction difficult to simulate exactly. Thus, theorists model the target nucleus and the beam nucleus as point particles, while determining the effective interaction between the two from ab initio (or from first principles) large-scale simulations. This provides ab initio predictions about the relative motion of the fusion fragments, known as the cluster wavefunction, which is in turn used to calculate reaction rates. In this project, we will determine the effective Carbon-alpha potential energy by using a Markov-Chain Monte-Carlo (MCMC) sampling procedure and Bayesian analysis to fit the microscopic cluster wavefunctions for the composite nucleus of Oxygen-16's bound states. The ultimate goal is to use that effective potential energy to fit resonant states in Oxygen-16, which will allow us to estimate the reaction rate and better quantify the carbon-to-oxygen ratio in our universe.