The Interacting Boson Model (IBM) of Arima and Iachello and co-workers is one of the most successful theories for describing the properties of the low-lying energy levels of medium-to-heavy mass nuclei. A review of the principles and phenomenology of the IBM is presented. The basic IBM is then applied to the even tungsten isotopes and compared with experimental observables associated with the low-lying states. These observable include transition rates, branching ratios, ρ(EO) values, quadrupole moments of the first two excited 2⁺ states, two-neutron separation energies, and isomer and isotope shifts. The results are seen to agree very well with the experimental data. Following the study of the tungsten isotopes an extension of the IBM to describe configuration mixing is presented. This extension is seen to be necessary when there are only a few valence protons or neutrons. In such cases the low-lying energy levels can be built upon more than one configuration. For example, states involving a two-particle-two-hole excitation from the core may occur in the same energy region as states made from only the valence nucleons. The extension of the IBM presented to handle such situations is quite general. A specific example using the light mercury isotopes and the molybdenum isotopes is given. The IBM is then examined from a microscopic point of view, using the generalized seniority scheme. The structure of the bosons of the IBM is given in terms of correlated fermion pairs. Predictions for the IBM parameters are obtained by constructing the zeroth-order image of the corresponding fermion operator. The predictions of a single j-shell approximation are compared with empirical results. In this approximation the valence nucleons are assumed to occupy a single j-shell whose effective j value is chosen so as to reproduce the total occupancy of the valence shell. Next, the predictions of a two non-degenerate j-shell approximation are compared with empirical results. This appoximation appears to be valid in both the 50-82 and the 82-126 neutron shells whose single-particle levels seem naturally to form two sub-shells. The predictions for the IBM parameters dependent on neutron number are seen to be in better agreement with empirically determined values than the predictions for the single j-shell (the proton-number dependent parameters are not treated). Furthermore, the two j-shell calculations reproduce the observed SU(3) or rotational character of the low-lying states of many mid-shell nuclides in the medium-to-heavy mass region. Finally, a brief description of the Interacting Boson-Fermion Model is given. This model is seen to be very successful in describing nuclei with an odd number of protons or neutrons. A calculation of the energy spectrum of the odd tungsten isotopes is presented.

Quantization in generalized coordinate systems and in non-Euclidean spaces has attracted much recent attention. The aim of this thesis is to discuss the problem for spaces of constant curvature. Chapter I is a brief review of tensor analysis on manifolds and the Hamiltonian formulation of classical mechanics. Chapter II deals with the canonical quantization scheme. It is proved that this scheme is unsatisfactory since it often fails to produce an essentially self-adjoin operator corresponding to a generalized momentum. It is shown that the only case for which we can obtain a unique well-defined pair of canonical quantum observables is that when the range of the generalized coordinate is the entire real line. Chapter III is devoted for discussing the quantization in spaces of constant curvature. An approach by Mackey circumvents the difficulties facing the canonical quantization scheme and is adopted instead. It is shown that a more physical meaning is gained if we impose on Mackey's momenta the condition that they are metric- preserving. Such a condition makes the momenta constants of the free motion. §4 in essence demonstrates that the dynamics in a space of constant curvature are rooted in its geometry. Utilizing the metric-preserving momenta, the quantum Hamiltonian is built up from symmetry considerations, and is uniquely determined as the Laplacian up to a multiplicative constant and an additive constant. In §5-§8 the quantization in spaces of constant curvature is studied in detail. The quantum and classical momenta are found explicitly. Eigenvalues and Eigenfunctions of the momentum observables are evaluated. Also it is shown that spaces of different curvature are physically distinguishable. An interesting relation between the momenta, the curvature of the space and the Hamiltonian holds classically and quantum-mechanically. The well-known relation giving the Hamiltonian as proportional to the sum of squares of the momenta (in Euclidean spaces with Cartesian coordinates) is just a special case of a more general relation in which the momenta, the angular momenta and the curvature of the space take part in forming the Hamiltonian classically or quantum-mechanically. §9 of chapter III discusses the Lie algebraic treatment of quantization. It is shown that such a treatment cannot be taken as a general quantization scheme. The sets of all classical and quantal momenta (metric-preserving and non- metric-preserving) do not form Lie algebras. However when we confine ourselves to those momenta which are generated by motions of the space, then these sets form isomorphic Lie algebras. The striking parallelism between quantum and classical mechanics observed throughout §4-§8 is pushed further in §9. It is shown that the quantum and classical Hamiltonians are, respectively, related to the Casimir operators of the Lie algebras of quantum and classical momenta in the same way. Chapter IV envisages the problem of quantization from an intrinsic point of view. A space of constant curvature is looked on as a hypersurface in a flat space. In §4 we verify that Dirac's scheme for quantizing a constrained classical system works when the constraints are geometrical.

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Bibliography: p. 84-91. / ii, 91 p. ; 30 cm. / Title page, contents and abstract only. The complete thesis in print form is available from the University Library. / Thesis (Ph.D.)--University of Adelaide, Dept. of Physics and Mathematical Physics, 1994

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Thesis (Ph. D.)--University of Michigan, 1932. / Cover title. "Reprinted from the Physical review, vol. 43, 7, April 1, 1933."

Please read the abstract in the section 00front of this document / Dissertation (MSc (Mathematics))--University of Pretoria, 2006. / Mathematics and Applied Mathematics / unrestricted

Call number: LD2668 .T4 1957 S94 / Master of Science

Thesis (M. Phil.)--University of Hong Kong, 2001. / Includes bibliographical references (leaves [87]-89).