The applicability of asymptotic series expansions of the type introduced by Gailitis (1976) in heavy particle scattering calculations is examined. The convergence of the solutions, with respect to the value of the scattering coordinate is found to be greatly improved in a model problem of the rovibrational excitation of H(_2) by H(^+). The results of infinite order sudden (IOS) and breathing sphere (BS) calculations of cross sections for the rovibrational excitation of (^12)C(^16)O by para- H(_2) (J(_1) = 0 only) are presented. Comparisons are made with existing theoretical and experimental results. Allowing for remaining uncertainties in the interaction potential of Poulsen (1982), our results are in reasonable accord with the experimental results of Andrews and Simpson (1976) for the vibrational relaxation of CO (v(_2) = 1) by ortho-H(_2). IOS calculations of the vibrational deactivation of (^12)c(^16)o (v(_2) = 1) by H(_2) (J(_1) = 0 or 2) which simultaneously undergoes the rotational transitions ΔJ(_1) = 0,2, or 4 are presented. Of major interest is the near-resonance process CO(Vb = 1) + H(-2) (J(_1) = 2) → CO (V(_2) = 0) + H(_2) (J(_1) = 6) + 87.03 cm(^-1) Comparison is made with both recent quantum mechanical and semi-classical calculations of this process, and with experiment. The near-resonance process is insufficient to account for the experimentally determined difference

Far-infrared spectroscopy has been applied to the study of liquid phase molecular dynamics and interactions. The absorption and dispersion spectra of solutions of acetonitrile in carbon tetrachloride, across a range of temperatures and concentrations, have been obtained. These spectra have bean interpreted with the parameters obtained from a model developed from a generalised Langsvin equation of motion which includes intermolecular torque terms. The results obtained from the model analysis have been applied in an investigation of the non-reorientational contributions to the Raman and infrared bands arising from the and v(^1) and v(_3) modes. This study has shown that contrary to the assumptions commonly made, these contributions are not equal and some possible explanations for the discrepancies are given. A number of internal field theories are discussed and have been applied to the acetonitrile systems. The interpretation of the results of this analysis in terms of a simple model suggest that there is a preferred i.e. non-random orientation of the acetonitrile molecules in solution. A study of some tertiary alkyl ammonium halide solutions has revealed that there is a series of systems which separate into two liquid phases. Further investigation has highlighted the role of small amounts of water in these systems.

The straight line semi-classical Impact Parameter method has been modified for use with classical trajectories. Ion-atom collisions have been modelled using wavefunctions expanded in terms of atomic basis states which were centred on either the target or projectile ions. Total and differential charge exchange cross-sections are presented for (^4)He(^++) and (^4)He(^+) collisions within the centre of mass energy range 0.21 kev < E(_em) < 2.5 keV. Results using curved and straight line paths are compared with data from other authors. Significant trajectory effects were found at the lower energies in the range. The curved trajectory results were lower than those from the straight line model and also lower than previous calculations carried out. At higher energies in the range there was good agreement between straight line and curved trajectory models and previous work. Differential cross-sections were found to be sensitive to the trajectories employed, and comparisons have been made with previous work. Total, state specific and differential cross- sections for charge exchange are presented for Be(^++) and H collisions using a five state basis, within the centre of mass energy range 0.111 keV < E(_em) < 0.4444 keV. There was reasonable agreement between the straight line results and previous work. There were significant trajectory effects for all the final charge transfer states. Results are presented for low-energy collisions between positively charged muons and atomic hydrogen. An eight state basis has been used. Direct excitation cross sections for n = 2 atomic states and charge transfer cross sections to Is and n = 2 have been calculated. The effect on the cross sections of using different internuclear potentials has been examined. Trajectory effects were small for charge transfer to Is but were more pronounced in the direct excitation and charge exchange cross- sections to n = 2. These results have been compared to those obtained for curved trajectory H(^+) and H collisions at the same relative velocity, to assess the validity of velocity scaling. It was found that velocity scaling was reliable for charge transfer to Is and for total electron capture cross-sections. However, it was progressively inaccurate for direct excitation and for electron capture into excited states for µ(^+) impact energies of less than 300 eV. These results are discussed and suggestions for further work are made.

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In this thesis I review the definition of topological quantum field theories through state sums on triangulated manifolds. I describe the construction of state sum invariants of 3-manifolds from a graphical calculus and show how to evaluate the invariants as boundary amplitudes. I review how to define such a graphical calculus through SU(2) representation theory. I then review various geometricity results for the representation theory of SU(2), Spin(4) and SL(2,C), and define coherent boundary manifolds for state sums based on these representations. I derive the asymptotic geometry of the SU(2) based Ponzano-Regge invariant in three dimensions, and the SU(2) based Ooguri models amplitude in four dimensions. As a corollary to the latter results I derive the asymptotic behaviour of various recently proposed spin foam models motivated from the Plebanski formulation of general relativity. Finally the asymptotic geometry of the SL(2,C) based model is derived.