Title page for ETD etd-11022008-231524

Type of Document Dissertation
Author Dytrych, Tomas
Author's Email Address tdytrych@gmail.com
URN etd-11022008-231524
Title Evidence for Symplectic Symmetry in Ab Initio No-Core Shell Model Results
Degree Doctor of Philosophy (Ph.D.)
Department Physics & Astronomy
Advisory Committee
Advisor Name Title
Draayer, Jerry P Committee Chair
Blackmon, Jeffery C Jr Committee Member
Lehner, Luis R Committee Member
Rau, A Ravi P Committee Member
Karki, Bijaya B Dean's Representative
  • spin decomposition
  • collective model of nuclear structure
  • nuclear collective phenomena
  • symplectic shell model
  • nuclear physics
  • center of mass spurious excitations
  • structure of nuclear wave functions
Date of Defense 2008-10-15
Availability unrestricted
Advances in the construction of realistic internucleon interactions together

with the advent of massively parallel computers have resulted in a successful

utilization of the ab initio approaches to the investigation of

properties of light nuclei. The no-core shell model is a prominent ab initio method that yields a good description of the low-lying states in

few-nucleon systems as well as in more complex p-shell nuclei. Nevertheless,

its applicability is limited by the rapid growth of the many-body basis with

larger model spaces and increasing number of nucleons.

To extend the scope of the ab initio no-core shell model to heavier

nuclei and larger model spaces, we analyze the possibility of augmenting the

spherical harmonic oscillator basis with symplectic Sp(3,R) symmetry-adapted

configurations of the symplectic shell model which describe naturally the

monopole-quadrupole vibrational and rotational modes, and also partially

incorporate α-cluster correlations. In our study we project low-lying

states of 12C and 16O determined by the no-core shell model with the

JISP16 realistic interaction onto Sp(3,R)-symmetric model space that is free of

spurious center-of-mass excitations. The eigenstates under investigation are

found to project at the 85-90% level onto a few of the most deformed

symplectic basis states that span only a small fraction (≈0.001%) of

the full model space. The results are nearly independent of whether the bare

or renormalized effective interactions are used in the analysis.

The outcome of this study points to the relevance of the symplectic extension

of the ab initio no-core shell model. Further, it serves to reaffirm the

Elliott SU(3) model upon which the symplectic scheme is built. While

extensions of this work are clearly going to be required if the theory is to

become a model of choice for nuclear structure calculations, these early

results seem to suggest that there may be simplicity within the complexity of

nuclear structure that has heretofore not been fully appreciated. As follow-on

work to what is reported in this thesis, we expect to develop a stand alone

shell-model code that builds upon the underlying symmetries of the symplectic


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