{"id":{"repo_id":"lsu-thes","oai_identifier":"oai:repository.lsu.edu:gradschool_dissertations-1441"},"canonical_url":"https://search.dev.ndltd.org/etd/lsu-thes/oai:repository.lsu.edu:gradschool_dissertations-1441","repository":{"repo_id":"lsu-thes","name":"Lousiana State University","base_url":"https://repository.lsu.edu/do/oai/"},"display":{"title":"Group theoretical approach to pairing and non-linear phenomena in atomic nuclei","abstract":"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.","abstract_html":"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 &lt; A &lt; 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.","abstract_has_math":false,"creators":["Launey, Kristina D."],"institution":"Physics and Astronomy","degree_name":"Doctor of Philosophy (PhD)","degree_level":"Dissertation","degree_discipline":"Physical Sciences and Mathematics","degree_department":null,"school":null,"contributors":[],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2003,"date_issued":"2003-01-01T08:00:00Z","date_published":"2003-01-01T08:00:00Z","updated_at":"2026-07-24T02:57:39Z","subjects":["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"],"languages":[],"rights":["unrestricted","Release the entire work immediately for access worldwide."],"rights_urls":[],"identifier_entries":[{"key":"dc:identifier","label":"Identifier","values":["etd-1111103-171256","https://repository.lsu.edu/gradschool_dissertations/442"],"render_values":[{"text":"etd-1111103-171256","href":null,"code":true},{"text":"https://repository.lsu.edu/gradschool_dissertations/442","href":"https://repository.lsu.edu/gradschool_dissertations/442","code":true}]}]},"links":{"outbound_url":"https://doi.org/10.31390/gradschool_dissertations.442","outbound_label":"DOI","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:creator","label":"Author","values":["Launey, Kristina D."]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["2003-11-07"]},{"key":"dc:date.available","label":"Dc Date Available","values":["2022-05-12T23:08:50Z"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["Physical Sciences and Mathematics"]},{"key":"thesis:degree_level","label":"Degree Level","values":["Dissertation"]},{"key":"thesis:degree_name","label":"Degree Name","values":["Doctor of Philosophy (PhD)"]},{"key":"thesis:institution_name","label":"Thesis Institution Name","values":["Physics and Astronomy"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["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"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:rights","label":"Dc Rights","values":["unrestricted","Release the entire work immediately for access worldwide."]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["etd-1111103-171256","10.31390/gradschool_dissertations.442","https://repository.lsu.edu/gradschool_dissertations/442"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["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."]},{"key":"dc:title","label":"Title","values":["Group theoretical approach to pairing and non-linear phenomena in atomic nuclei"]}]}],"canonical_facts":{"dc:creator":["Launey, Kristina D."],"dc:date":["2003-11-07"],"dc:date.available":["2022-05-12T23:08:50Z"],"dc:description.abstract":["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."],"dc:identifier":["etd-1111103-171256","10.31390/gradschool_dissertations.442","https://repository.lsu.edu/gradschool_dissertations/442"],"dc:rights":["unrestricted","Release the entire work immediately for access worldwide."],"dc:subject":["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"],"dc:title":["Group theoretical approach to pairing and non-linear phenomena in atomic nuclei"],"thesis:degree_discipline":["Physical Sciences and Mathematics"],"thesis:degree_level":["Dissertation"],"thesis:degree_name":["Doctor of Philosophy (PhD)"],"thesis:institution_name":["Physics and Astronomy"]},"updated_at":"2026-07-24T02:57:39Z"}