Skyrmions -- beyond rigid body quantisation

Halcrow, Christopher James (2017-10-01)


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.