Doctor of Philosophy (PhD)
Physics and Astronomy
Most nuclei are deformed! This simple fact has been established since Bohr and Mot- telson, and successfully demonstrated from first principles by nuclear structure calculations carried out using the ab-initio Symmetry-Adapted No-Core Shell Model (SA-NCSM) us- ing realistic interactions. This simple fact has been the main driver towards understanding the underlying physics; namely, that symplectic symmetry describes deformation and is a dominant symmetry in all nuclei independent of A (nucleon number) and of the realistic interaction used. These two simple observations laid the foundation of this thesis work to explore the applications of symplectic symmetry towards defining a deformed symplectic model algebra. We show how a deformed no-core shell model could be constructed that al- lows one to carry out nuclear structure calculations in smaller model spaces without the need of huge computational resources. Furthermore, we develop the overlaps (transformation coef- ficients) between deformed and non-deformed spherical, cylindrical and Cartesian harmonic oscillator basis states that could also be utilized for reducing computational complexities within the scope of nuclear physics studies. Finally, the emergence of symplectic symmetry within a simple field theoretical framework that paved the way for the development of the Symplectic Effective Field Theory (SpEFT) is presented.
SpEFT is in principle applicable to any nucleus across the nuclear chart and can reproduce energy spectra, B(E2) strengths and radii, using only a laptop computer without the need of supercomputing resources, since it takes full advantage of the underlying symmetry. It accurately depicts how rotations and vibrations in nuclei occur, and how they affect nuclear observables. Results from the application of this theory on 12C, 20Ne and 166Er are presented, and are in remarkable agreement with experiment.
Kekejian, David, "Deformed No-Core Shell Model and Symplectic Effective Field Theory" (2022). LSU Doctoral Dissertations. 5748.