| 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 |
Abstract
Advances 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 24Mg and 44Ti. Results for 24Mg, 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 44Ti 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 44-48Ti and 48Cr, 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.
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