The abstract of my master’s thesis, titled “An Algebraic Approach to First-Order Quantum Phase Transitions Between Two Deformed Nuclear Shapes” can be found below. If you’re still intersted after reading it, the full thesis can be downloaded here.

Abstract

With the advancement of experimental techniques over the last few years, many medium-heavy nuclei in and outside the region of stability were found to have a coexistence of axially-deformed shapes. The interacting boson model (IBM) has been used extensively for describing medium-heavy even-even nuclei. The vast majority of applications have employed an Hamiltonian with two-body interactions. In conjunction with quantum phase transitions, such an Hamiltonian can accommodate coexistence of one spherical and one axially-deformed shapes. The two-body IBM Hamiltonian, however, cannot describe first-order shape phase transitions between prolate and oblate shapes. To achieve these, a three-body Hamiltonian is needed. The three-body IBM has 17 independent terms, which requires selection criteria in order to find the relevant operators. In this work we address this problem by a novel method based on the resolution of the Hamiltonian into intrinsic and collective parts and coherent states. The intrinsic Hamiltonian is first analyzed by various approaches, and the affect of adding the collective parts is then examined.