UBC Theses and Dissertations
Some aspects of nuclear spin relaxation for dilute polyatomic gases Sanctuary, Bryan Clifford
The density dependence of nuclear spin relaxation in polyatomic gases is studied theoretically. In particular, the experimentally observed non-linear dependence of T₁ on density at high density is explained. A quantum mechanical Boltzmann equation is used to formulate the theory. The particular Boltzmann equation used describes the time evolution of a one particle density operator and this affords an adequate description of a dilute gas. No restriction on the internal states of the polyatomic molecules is required. An expression for T₁⁻¹ is obtained in terms of a relaxation matrix, the elements of which are collision Integrals between the various intramolecular transition processes which contribute to the relaxation rate. The diagonal terms of this matrix describe the relaxation rate and frequency shifts for each internal state transition frequency while the off-diagonal terms account for the collisional overlapping between the various internal state frequencies. The collision integrals are partially evaluated by a distorted wave Born approximation and are reduced to traces over internal states and integrals over the relative velocity of the colliding pair. The internal state traces are evaluated exactly while the relative velocity integrals are left as scaling parameters. The theoretical expression is applied to the symmetric top molecules CH₃F and CF₃H to account for the experimentally observed "step effect". On the basis of experimental evidence an intramolecular dipolar mechanism is used and it is shown that this gives adequate agreement with the experimental data. The steps arise as a result of the phase randomization of the low lying rotational K levels.
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