Louisiana State University
Launey, Kristina D.
Group theoretical approach to pairing and non-linear phenomena in atomic nuclei.
Degree: PhD, Physical Sciences and Mathematics, 2003, Louisiana State University
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.
Subjects/Keywords: 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
to Zotero / EndNote / Reference
APA (6th Edition):
Launey, K. D. (2003). Group theoretical approach to pairing and non-linear phenomena in atomic nuclei. (Doctoral Dissertation). Louisiana State University. Retrieved from etd-1111103-171256 ; https://digitalcommons.lsu.edu/gradschool_dissertations/442
Chicago Manual of Style (16th Edition):
Launey, Kristina D. “Group theoretical approach to pairing and non-linear phenomena in atomic nuclei.” 2003. Doctoral Dissertation, Louisiana State University. Accessed July 14, 2020.
etd-1111103-171256 ; https://digitalcommons.lsu.edu/gradschool_dissertations/442.
MLA Handbook (7th Edition):
Launey, Kristina D. “Group theoretical approach to pairing and non-linear phenomena in atomic nuclei.” 2003. Web. 14 Jul 2020.
Launey KD. Group theoretical approach to pairing and non-linear phenomena in atomic nuclei. [Internet] [Doctoral dissertation]. Louisiana State University; 2003. [cited 2020 Jul 14].
Available from: etd-1111103-171256 ; https://digitalcommons.lsu.edu/gradschool_dissertations/442.
Council of Science Editors:
Launey KD. Group theoretical approach to pairing and non-linear phenomena in atomic nuclei. [Doctoral Dissertation]. Louisiana State University; 2003. Available from: etd-1111103-171256 ; https://digitalcommons.lsu.edu/gradschool_dissertations/442