Sp(6,R) Symmetry and the Giant Quadrupole Resonance in Magnesium-24.

Microscopic nuclear calculations are approached by partitioning the many-nucleon Hilbert space as a direct sum of symplectic b and s. Computational techniques and algorithms which utilize commutator methods, and which are more powerful than the more straight-forward purely shell-model approach, are developed for calculating the matrix elements of two-body operators within such an Sp(6,R) (R-HOOK) U(3) symmetry-adapted basis. These techniques may be generalized to n-body operators of any n. These computational tools are applied to the study of the Giant Quadrupole Resonance in ('24)Mg: the final calculation presented uses a microscopic Hamiltonian consisting of the kinetic energy plus the semi-realistic two-body Brink-Boeker B1 potential within a space consisting of three symplectic b and s up to 6(H/2PI)(omega) total excitation.PhDNuclear physicsUniversity of Michiganhttp://deepblue.lib.umich.edu/bitstream/2027.42/160022/1/8412233.pd