The work reported in Part I of this thesis concerns ionisation and spin exchange. The familiar time-dependent perturbation equations are derived from the time-dependent Schrodinger wave equation. Coriolis coupling is explicitly taken account of, the relevant coupled equations are set up for several M + X systems and are solved numerically. The results are presented in §1.10 and §I.11 where the solutions arc compared with the Landau-Zenar approximation and with the numerical solution of a simple two-state problem. In Part II elastic and inelastic differential cross sections for two crossing monotonic repulsive potentials are calculated. Two model potentials are used and the scattered amplitudes are evaluated as a partial wave summation. The S-matrix elements are calculated using the Landau-Zener-Stuer-Kelberg approximation and phase shifts are evaluated analytically by using a straight line approximation to the trajectory. The results, which are interpreted in an analysis due to Ford and ?heeler, are presented in §11.6. In Part III the quadrupole-quadrupole mechanism for fine structure transitions in heavy atoms induced by collision with H2 IID and D2 is considered. Transition probabilities were evaluated using first order time-dependent perturbation theory. The quadrupole-quadrupole term of the nailtipolar expansion of the electrostatic interaction potential is evaluated in two co-ordinate systems. An analytic expression for the transition probabilities is obtained in terms of atomic and molecular matrix elements, atomic and molecular quantum numbers and an integral ever the collision trajectory. The matrix elements were evaluated using best available wave functions. Transition probabilities as functions of impact parameter and velocity were obtained by numerically integrating the trajectory integrals. The probability functions were numerically integrated first over impact parameter and finally over the Boltzmann velocity distribution to obtain rate constants as functions of temperature. The rate constants so calculated were compared with experimental values and the results are presented in §111.5.
| Identifer | oai:union.ndltd.org:bl.uk/oai:ethos.bl.uk:651138 |
| Date | January 1975 |
| Creators | French, Neil Peter Donaldson |
| Publisher | University of Edinburgh |
| Source Sets | Ethos UK |
| Detected Language | English |
| Type | Electronic Thesis or Dissertation |
| Source | http://hdl.handle.net/1842/13857 |
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