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Thesis--University of California, Berkeley, 1961. / "UC-34 Physics" -t.p. "TID-4500 (16th Ed.)" -t.p. Includes bibliographical references (p. 158-159).

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In the Skyrme model, nuclei are described as topological solitons known as Skyrmions. To make contact with nuclear data one must quantise these Skyrmions; most calculations to date have used rigid body quantisation, where the Skyrmions are allowed to rotate but remain rigid. The method reproduces some experimental results for light nuclei but there are some contradictions with data. In this thesis we study a more sophisticated quantisation scheme where the Skyrmions may deform, called vibrational quantisation, in the hope of fixing some of these problems. Vibrational quantisation is applied to the dodecahedral $B=7$ Skyrmion, which models Lithium-$7$. Using rigid body quantisation, the Skyrme model predicts a spin $\frac{7}{2}$ ground state while in reality the Lithium-$7$ nucleus ground state has spin $\frac{3}{2}$. We show that a quantisation which includes a $5$-dimensional vibrational manifold of deformed Skyrme configurations remedies this problem, giving the correct ground state spin. Further, the model leads to a robust prediction that the ground state of the nucleus has a larger root mean square matter radius than the second quantum state, in contrast with standard nuclear models. We consider the vibrational modes of the tetrahedral $B=16$ Skyrmion, to describe Oxygen-$16$. Motivated by Skyrme dynamics, a special $2$-dimensional submanifold of configurations is constructed. We study the manifold in detail by modelling it as a $6$-punctured sphere with constant negative curvature. The Schr\"odinger equation is solved on the sphere and the results give an excellent fit to the experimental energy spectrum. The model describes an energy splitting between certain states with equal spins but opposite parities, which is hard to explain in other models. We also find the first ever isospin $0$, spin-parity $0^-$ state in the Skyrme model. A method to calculate electromagnetic transition rates between states is formulated and then applied to our system. By considering a special type of Skyrme configuration, where a single Skyrmion orbits a large core, we show that the Skyrme model can reproduce a classical spin-orbit force due to the structure of the Skyrme fields. We quantise this model to try and find out if the classical picture holds quantum mechanically.

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The alpha-particle reduced widths for the ground state in Po²¹² are calculated on the basis of the nuclear shell model, employing the technique of Harada, but treating the nuclear surface in a more direct manner. It is contended that the calculations of previous authors, who have generally used a square-edge nucleus and a Coulomb barrier rounded-off by the nuclear potential of Igo, have, essentially, used the equivalent square-edge nucleus model of Vogt. Their J.W.K.B. estimate of the barrier penetrabilities is checked by an analytic calculation in Chapter 3 and is found to be reasonable. It is shown in Chapter 4 that, in the scattering of an alpha-particle from the ground state of Pb²⁰⁸, the diffuse nuclear edge considerably enhances the one-body reduced widths and, in a direct manner, that it similarly enhances the one-body differential elastic scattering cross-section. In this manner, it is demonstrated that the radius involved in the equivalent square-edge nucleus model must be considerably larger than that of the diffuse-edge nucleus to which it corresponds. This is shown directly in Chapter 5, where the validity of the equivalent square-edge nucleus model in heavy nuclei is examined. It is contended that this explains the large radii found in previous calculations. This is demonstrated directly by repeating the calculation of Harada with the diffuse nuclear edge being introduced in a direct manner. Although the effects of configuration mixing have not been directly examined, it has been concluded that shell model calculations can explain the major part of rates provided that the nuclear surface is manner. / Science, Faculty of / Physics and Astronomy, Department of / Graduate