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Title: A study of the sp(6) [contains] u(3) algebra of the fermion dynamical symmetry model of nuclei

Abstract

The fermion dynamical symmetry model (FDSM) is a model of nuclear structure based on a fermion pair algebra and has been used to study nuclei throughout the periodic table. This thesis performs detailed calculations which raise questions regarding certain fundamental assumptions used in constructing the FDSM. Specifically, in the FDSM a truncation of the shell model space to a subspace of favored pair operators is effected by a Hamiltonian which for the actinides consists of generators of the sp(6) [contains] u(3) algebra. The Hamiltonian is diagnolized in the truncated basis which is expanded in terms of eigenstates of the generalized seniority u. It is claimed that the dominant contribution for the lowest eigenstate of the Hamiltonian arises from the lowest u state. The author addresses this issue by using a more realistic Hamiltonian which includes operators outside the sp(6) algebra, such as the quadrupole moment operator, Q[sup 2][sub [mu]] = r[sup 2]Y[sup 2][sub [mu]], which mixes states of different seniority u. Analytical expressions for the matrix elements of such operators, taken from earlier developments in vector coherent state theory, are applied to the case of actinide nuclei with two valence protons or neutrons. The author found strong generalized seniority mixingmore » for a Hamiltonian which includes pairing and reasonable Q [center dot] Q strengths. Moreover, it is shown that (i) the relative phases of the shell model radial functions affect the overlap of the realistic eigenstates with the FDSM basis states, and (ii) in all cases the overlap between the truncated FDSM subspace and the complete shell model space is very small. Taken as a whole, the results indicate that the FDSM truncation of the shell model is not a valid one.« less

Authors:
Publication Date:
Research Org.:
Michigan Univ., Ann Arbor, MI (United States)
OSTI Identifier:
7005780
Resource Type:
Miscellaneous
Resource Relation:
Other Information: Thesis (Ph.D.)
Country of Publication:
United States
Language:
English
Subject:
73 NUCLEAR PHYSICS AND RADIATION PHYSICS; NUCLEI; BOSON-FERMION SYMMETRY; SHELL MODELS; ALGEBRA; SP GROUPS; U-3 GROUPS; LIE GROUPS; MATHEMATICAL MODELS; MATHEMATICS; NUCLEAR MODELS; SYMMETRY; SYMMETRY GROUPS; U GROUPS; 663120* - Nuclear Structure Models & Methods- (1992-)

Citation Formats

Swaminathan, S R. A study of the sp(6) [contains] u(3) algebra of the fermion dynamical symmetry model of nuclei. United States: N. p., 1993. Web.
Swaminathan, S R. A study of the sp(6) [contains] u(3) algebra of the fermion dynamical symmetry model of nuclei. United States.
Swaminathan, S R. 1993. "A study of the sp(6) [contains] u(3) algebra of the fermion dynamical symmetry model of nuclei". United States.
@article{osti_7005780,
title = {A study of the sp(6) [contains] u(3) algebra of the fermion dynamical symmetry model of nuclei},
author = {Swaminathan, S R},
abstractNote = {The fermion dynamical symmetry model (FDSM) is a model of nuclear structure based on a fermion pair algebra and has been used to study nuclei throughout the periodic table. This thesis performs detailed calculations which raise questions regarding certain fundamental assumptions used in constructing the FDSM. Specifically, in the FDSM a truncation of the shell model space to a subspace of favored pair operators is effected by a Hamiltonian which for the actinides consists of generators of the sp(6) [contains] u(3) algebra. The Hamiltonian is diagnolized in the truncated basis which is expanded in terms of eigenstates of the generalized seniority u. It is claimed that the dominant contribution for the lowest eigenstate of the Hamiltonian arises from the lowest u state. The author addresses this issue by using a more realistic Hamiltonian which includes operators outside the sp(6) algebra, such as the quadrupole moment operator, Q[sup 2][sub [mu]] = r[sup 2]Y[sup 2][sub [mu]], which mixes states of different seniority u. Analytical expressions for the matrix elements of such operators, taken from earlier developments in vector coherent state theory, are applied to the case of actinide nuclei with two valence protons or neutrons. The author found strong generalized seniority mixing for a Hamiltonian which includes pairing and reasonable Q [center dot] Q strengths. Moreover, it is shown that (i) the relative phases of the shell model radial functions affect the overlap of the realistic eigenstates with the FDSM basis states, and (ii) in all cases the overlap between the truncated FDSM subspace and the complete shell model space is very small. Taken as a whole, the results indicate that the FDSM truncation of the shell model is not a valid one.},
doi = {},
url = {https://www.osti.gov/biblio/7005780}, journal = {},
number = ,
volume = ,
place = {United States},
year = {Fri Jan 01 00:00:00 EST 1993},
month = {Fri Jan 01 00:00:00 EST 1993}
}

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