Rovibrational Dynamics of Nuclei and Molecules

We study quantized rotation-vibration dynamics with applications to nuclear and molecular models. Firstly we consider small vibrations of Skyrmions (topological solitons which model atomic nuclei), developing new approximations to their quantum energy spectra which incor- porate both rotation-vibration and isorotation-vibration corrections. We find that the forms of these corrections are highly restricted as a consequence of the large symmetry groups of Skyrmions, and we determine them using representation theory. We explore the implications for the Helium-4 nucleus and the Lithium-7/Beryllium-7 isodoublet, comparing our findings with experimental data. We propose a model for the Carbon-12 nucleus based on point ↵-particles restricted to isosceles triangular configurations, inspired by linear chain and equilateral triangular Skyrmions. The configuration space is not a manifold but has a graph-like structure, and we make use of Quantum Graph Theory to study the quantized dynamics. The resulting energy spectrum reproduces the experimental data rather well. Nuclear physicists are interested in more than just the quantum energy spectrum: elec- tromagnetic transition rates, for instance, measure -decay between two nuclear states and can be measured in the laboratory. We develop a formalism to compute electromagnetic transition rates within rotation-vibration models and compare the results of our Carbon-12 model and a recent Oxygen-16 model to experimental data. We go on to propose some ways in which the Oxygen-16 model might be improved. Finally, we turn from nuclear physics to molecular physics and study the protonated methane molecular ion, introducing a quantum graph model for the complex rotation-vibration dynamics. We find good agreement with other numerical work where available and compute states up to angular momentum J = 4 for the first time