Type of Document Dissertation Author Gueorguiev, Vesselin Gueorguiev Author's Email Address vesselin@mailaps.org URN etd-1028102-183920 Title Mixed-Symmetry Shell-Model Calculations in Nuclear Physics Degree Doctor of Philosophy (Ph.D.) Department Physics and Astronomy Advisory Committee

Advisor Name Title J. Draayer Committee Chair A. Rau Committee Member E. Zganjar Committee Member R. Haymaker Committee Member A. Raman Dean's Representative Keywords

- confinement
- coherent (adiabatic) mixing
- elliott su(3) model
- spherical and cylindrical symmetry
- spectrum
- b(e2) transition strengths
- quadrupole-quadrupole interaction
- generalized eigenvalue problem
- quasi-symmetry
- harmonic oscillator in a box
- cholesky
- spin-orbit interaction
- numerical methods
- oblique
- nuclear shell models
- lanczos
- nuclear structure
- ground state energy
- nuclear physics
Date of Defense 2002-10-18 Availability unrestricted AbstractAdvances in computer technologies allow calculations in ever larger model spaces. To keep our understanding growing along with this growth in computational power, we consider a novel approach to the nuclear shell model. The one-dimensional harmonic oscillator in a box is used to introduce the concept of an oblique-basis shell-model theory. By implementing the Lanczos method for diagonalization of large matrices, and the Cholesky algorithm for solving generalized eigenvalue problems, the method is applied to nuclei. The mixed-symmetry basis combines traditional spherical shell-model states with SU(3) collective configurations. We test the validity of this mixed-symmetry scheme on^{24}Mg and^{44}Ti. Results for^{24}Mg, obtained using the Wilthental USD intersection in a space that spans less than 10% of the full-space, reproduce the binding energy within 2% as well as an accurate reproduction of the low-energy spectrum and the structure of the states -- 90% overlap with the exact eigenstates. In contrast, for an m-scheme calculation, one needs about 60% of the full space to obtain compatible results. Calculations for^{44}Ti support the mixed-mode scheme although the pure SU(3) calculations with few irreps are not as good as the standard m-scheme calculations. The strong breaking of the SU(3) symmetry results in relatively small enhancements within the combined basis. However, an oblique-basis calculation in 50% of the full pf-shell space is as good as a usual m-scheme calculation in 80% of the space. Results for the lower pf-shell nuclei^{44-48}Ti and^{48}Cr, using the Kuo-Brown-3 interaction, show that SU(3) symmetry breaking in this region is driven by the single-particle spin-orbit splitting. In our study we observe some interesting coherent structures, such as coherent mixing of basis states, quasi-perturbative behavior in the toy model, and enhanced B(E2) strengths close to the SU(3) limit even though SU(3) appears to be rather badly broken. The results suggest that a mixed-mode shell-model theory may be useful in situations where competing degrees of freedom dominate the dynamics, and full-space calculations are not feasible.Files

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