algebraic collective nuclear model and SO(5).
Contributors: Rowe, David J. (supervisor)
Published: 2005
Language: eng
Number of pages: 118
Subjects: Physics Theses.
Description: A new Bohr-Mottelson collective model is presented for the investigation of nuclear structure. It is based upon two ingredients: (i) that there exists a conceptually and computationally simple method for constructing bases of SO(5) wavefunctions that is analogous to the construction of the well known spherical harmonics on   R3 , which also provides a means for computing SO(5) coupling coefficients in a SO(3) basis, and (ii) that there exist generalised SU(1,1) wavefunctions, analogous to the radial functions of   R3 , appropriate for deformed nuclei that provide bases in which matrix elements of typical collective model operators can be computed in a completely algebraic manner. Together they make up what will be called the algebraic collective model. It is shown that the new basis of radial wavefunctions outperforms the standard spherical basis by an order of magnitude in the size of the basis when computing the spectrum and E2 quadrupole transition rates of a prototypical beta-deformed nucleus. The algebraic collective model is used to analyse a spherical to deformed collective shape phase transition of a Bohr model nucleus, and the results are compared to the analogous transition in the interacting boson model which has attracted much attention in the community over the past several years. Also presented is a method for the construction of all, completely generic representations of the   so (5) Lie algebra in the   so (3) basis of the collective model. It is likely the most ambitious application of vector coherent state theory to date.
Notes: Thesis (Ph.D.)--University of Toronto, 2005.

Electronic version licensed for access by U. of T. users.

Source: Dissertation Abstracts International, Volume: 66-06, Section: B, page: 3202.