Date of Completion
ultracold scattering, Milne equation, phase-amplitude approach, Efimov system
Field of Study
Doctor of Philosophy
A fundamental aspect of scattering is the appearance of resonances, which appear in many systems. Although their effect is often lost due to averaging at room temperatures or higher, they can become dominant features at low or ultralow temperatures, where only a few partial waves contribute to the scattering process. Our ability to form and manipulate ultracold molecules provides the seed to study in a precise and controlled fashion the role of single partial waves, and state-to-state processes in chemical systems. We explore resonances occurring due to the existence of a quasi-bound state in the entrance channel of a scattering system and explain the energy scaling due to these near threshold resonances (NTR) based on the properties of the Jost functions. We also investigate the threshold resonance effects in the Efimov systems which have been studied in a variety of context, such as three-body Coulomb systems and nuclear three-body systems. Numerical schemes based on Milne's phase-amplitude approach are formulated to analyze NTR effects. We present a simple and practical approach to solve the long-standing problem of finding the non-oscillatory solution to Milne's equation. Our numerical approach also gives an integral representation of scattering phase shift and allows us to compute ultra-narrow shape resonances.
Shu, Di, "Threshold Resonance Effects and the Phase-Amplitude Approach" (2018). Doctoral Dissertations. 1957.