Title page for ETD etd-1111103-171256

Type of Document Dissertation
Author Launey, Kristina D.
Author's Email Address ksvirac@lsu.edu
URN etd-1111103-171256
Title Group Theoretical Approach to Pairing and Non-Linear 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. El-Amawy Dean's Representative
  • significance of q-deformation
  • isobaric analog 0+ states
  • isospin symmetry
  • binding energy
  • non-linear many-body interactions
  • symplectic algebra
  • pairing correlations
  • pairing gaps
  • staggering
  • beta decay
  • isospin mixing
Date of Defense 2003-11-07
Availability unrestricted
The symplectic sp(4) algebra provides a natural framework for studying proton-neutron (pn) and like-nucleon pairing correlations as well as higher-J 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 q-deformed 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 identical-particle and pn pairing.

We suggest a non-deformed as well as a q-deformed algebraic descriptions of pairing for even-A 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 non-deformed 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 higher-J nuclear interactions. In a classification scheme that is inherent to the sp(4) algebraic approach, a finite energy difference technique is used to investigate two-particle separation energies, irregularities found around the N = Z region, and like-particle and pn isovector pairing gaps. The analysis identifies a prominent staggering behavior between groups of even-even and odd-odd 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 q-deformation can be used to gain a better understanding of higher-order effects in the interaction within each individual nucleus.

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