Barrett, The Honors College Thesis/Creative Project Collection
Barrett, The Honors College at Arizona State University proudly showcases the work of undergraduate honors students by sharing this collection exclusively with the ASU community.
Barrett accepts high performing, academically engaged undergraduate students and works with them in collaboration with all of the other academic units at Arizona State University. All Barrett students complete a thesis or creative project which is an opportunity to explore an intellectual interest and produce an original piece of scholarly research. The thesis or creative project is supervised and defended in front of a faculty committee. Students are able to engage with professors who are nationally recognized in their fields and committed to working with honors students. Completing a Barrett thesis or creative project is an opportunity for undergraduate honors students to contribute to the ASU academic community in a meaningful way.
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- Creators: Department of Physics
Despite being bound by the strong force, bottomonium exhibits a rich spectrum of resonances corresponding to excited states extremely analogous to that of positronium or even familiar atomic systems. Transitions between these levels are possible via the absorption or emission of either a photon, gluon, or gluons manifesting as light hadrons. The goal of this thesis was to establish a theoretical value for the currently unmeasured partial decay width for one such transition—the electromagnetic decay channel hb -> etab gamma. To this end, two methods were utilized.
The first approach relied on the presumption of a nonrelativistic constituent quark model interacting via a simple static potential, allowing for radial wave functions and energy eigenvalues to be obtained for the states of interest via the Schrödinger equation. Upon an application of the standard electromagnetic multipole expansion followed by a utilization of the electric dipole E1 decay width formula, a value of 57.7 ± 0.4 keV was obtained.
The second approach stemmed from the effective Lagrangian describing the bottomonium P to S electromagnetic transitions and relied on the presumption that a single coupling constant could be approximated as describing all nP to mS transitions regardless of spin. A value for this coupling constant could then be extracted from the 1P to 1S spin triplet data and used to predict the width for the singlet 1P to 1S transition. The partial decay width value found in this manner was 47.8 ± 2.0 keV.
Various other methods and models have established a predicted range of 35 to 60 keV for this partial decay width. As the values determined in this thesis fall within the expected range, they agree well with our current understanding of this electromagnetic transition and place further confidence on the expected range.
We present the isotope yields of two post-explosion, three-dimensional 15 M_sol core-collapse supernova models, 15S and 15A, and compare them to the carbon, nitrogen, silicon, aluminum, sulfur, calcium, titanium, iron, and nickel isotopic compositions of presolar SiC stardust. We find that material from the interior of a core-collapse supernova can form a rare subset of SiC stardust, called SiC D grains, characterized by enrichments of the isotopes 13C and 15N. The innermost material of these core-collapse supernovae is operating in the neutrino-driven regime and undergoes rapid proton capture early in the explosion, providing these isotopes which are not present in such large abundances in other stardust grains of supernova origin.
This is a primer on the mathematic foundation of quantum mechanics. It seeks to introduce the topic in such a way that it is useful to both mathematicians and physicists by providing an extended example of abstract math concepts to work through and by going more in-depth in the math formalism than would normally be covered in a quantum mechanics class. The thesis begins by investigating functional analysis topics such as the Hilbert space and operators acting on them. Then it goes on to the postulates of quantum mechanics which extends the math formalism covered before to physics and works as the foundation for the rest of quantum mechanics.