Type of Document 
Dissertation 
Author 
Launey, Kristina D.

Author's Email Address 
ksvirac@lsu.edu 
URN 
etd1111103171256 
Title 
Group Theoretical Approach to Pairing and NonLinear Phenomena in Atomic Nuclei 
Degree 
Doctor of Philosophy (Ph.D.) 
Department 
Physics & Astronomy 
Advisory Committee 
Advisor Name 
Title 
Jerry P. Draayer 
Committee Chair 
A. I. Georgieva 
Committee Member 
A. R. P. Rau 
Committee Member 
E. F. Zganjar 
Committee Member 
P. N. Kirk 
Committee Member 
A. ElAmawy 
Dean's Representative 

Keywords 
 significance of qdeformation
 isobaric analog 0+ states
 isospin symmetry
 binding energy
 nonlinear manybody interactions
 symplectic algebra
 pairing correlations
 pairing gaps
 staggering
 beta decay
 isospin mixing

Date of Defense 
20031107 
Availability 
unrestricted 
Abstract
The symplectic sp(4) algebra provides a natural framework for studying protonneutron (pn) and likenucleon pairing correlations as well as higherJ pn interactions in nuclei when protons and neutrons occupy the same shell. While these correlations manifest themselves most clearly in the binding energies of 0+ ground states, they also have a large effect on the spectra of excited isobaric analog 0+ states. With a view towards nuclear structure applications, a fermion realization of sp(4) is explored and its qdeformed extension, sp(4)q, is constructed for single and multiple shells. The su(2)(q) substructures that enter are associated with isospin symmetry and with identicalparticle and pn pairing.
We suggest a nondeformed as well as a qdeformed algebraic descriptions of pairing for evenA nuclei of the mass 32 < A < 164 region. A Hamiltonian with a symplectic dynamical symmetry is constructed and its eigenvalues are fit to the relevant Coulomb corrected experimental 0+ state energies in both the “classical” and “deformed” cases. While the nondeformed microscopic theory yields results that are comparable to other models for light nuclei, the present approach succeeds in providing a reasonable estimate for interaction strength parameters as well as a detailed investigation of isovector pairing, symmetry energy and symmetry breaking effects. It also reproduces the relevant ground and excited 0+ state energies and predicts some that are not yet measured. The model successfully interprets fine features driven by pairing correlations and higherJ nuclear interactions. In a classification scheme that is inherent to the sp(4) algebraic approach, a finite energy difference technique is used to investigate twoparticle separation energies, irregularities found around the N = Z region, and likeparticle and pn isovector pairing gaps. The analysis identifies a prominent staggering behavior between groups of eveneven and oddodd nuclides that is due to discontinuities in the pairing and symmetry terms. While the “classical” limit of the theory provides good overall results, the analysis also shows that qdeformation can be used to gain a better understanding of higherorder effects in the interaction within each individual nucleus.

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