UC San Diego

Using a modified version of the Lanczos matrix diagonalization algorithm for spectral decompositions, properties beyond basic nuclear structure can be computed. In this dissertation, this method is applied to solutions of the nuclear Hamiltonian under symmetry group operators and weak nuclear force transition operators. In Chapter 2, I decompose state vectors for chromium isotopes decomposed into the basis of Casimir operators of symmetry groups relevant to nuclei. While these symmetries are broken under the nuclear interaction, the decompositions tend to hold their patterns for certain progressions of states identified to be crossing rotational bands in the energy spectrum, where the spectra are related to the phenomena of backbending. These patterns are known as quasi-dynamical symmetries. In Chapter 3, I compute weak nuclear force transition strength functions, specifically Gamow-Teller transitions for certain pf-shell isotopes relevant to massive stellar collapse and nucleosynthesis. I examine these transitions in terms of the Brink-Axel hypothesis, which states that transition strength distributions from excited states are identical to the transition strength distribution from the ground state. I develop a method for computing weak transition rates in stellar environments based on a localized Brink-Axel statement. This allows for the access of highly excited states, which have heretofore been prohibitive, and therefore improved thermal weak rates of heavy nuclei at temperatures occurring in stellar cores near collapse. As such, the methods developed in this dissertation are a contribution to progress on this topic.