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Mixed-Symmetry Shell-Model Calculations In Nuclear Physics, Vesselin Gueorguiev Gueorguiev

LSU Doctoral Dissertations

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 …