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Pressure broadening and coherence transients effects: a kinetic theory approach Coombe, Dennis Allan
Abstract
The response of a polyatomic gas to microwave radiation including both steady state (pressure broadening) and time dependent (coherence transients) effects  is described theoretically. The treatment is based on solutions of a quantum mechanical Boltzmahn equation and employs kinetic theory methods which have previously been used in the explanation of the field dependence of transport phenomena (SenftlebenBeenakker effects). Much of the recent theoretical work of pressure broadening and coherence transient phenomena is based on a two (energy) state model for the gas molecules. This model, when developed from a density operator point of view, results in a coupled set of three equations which are mathematically equivalent to the Bloch equations of NMR. The present work reexamines this description, and replaces it with a two level model for the gas system. Here, the term "level" implies explicit consideration of the rotational (magnetic) degeneracy associated with each energy state. This model gives a more appropriate representation of the interaction of microwave radiation with a real molecular system. In particular, a more complete set of coupled equations result from this description and involve quantities in addition to the three moments used in a two state approach. The most important of these latter effects are represented by spherical harmonics Ƴ(q) (J) in he angular momentum J of the relevant energy levels. An analogous treatment of rotational effects has previously been used in SenftlebenBeenakker studies. Specific molecular types of interest in microwave spectroscopy diamagnetic diatonics and linear polyatomics, symmetric tops, and inverting symmetric tops  are treated separately by this two level approach. The vector (and tensor) nature of the motions are emphasized throughout. The number of rotational polarizations that arise in the general two level case is often quite large. The simplest example of a two level system is the j=0 to j=l transition of a diamagnetic diatomic. This is studied in some detail. Here, the scalar component Ƴ⁽²⁾⁰(J) is the only rotational polarization affected by linearly polarized radiation in the usual experiments. The effect of this quantity on both steady state and transient phenomena is described, and a new "combination" experiment is suggested as the best way to detect the presence of this additional polarization. The Doppler effect is treated by appropriately including the effects of translational motion in the quantum Boltzmann equation. A more general set of coupled moment equations then results, and the manner in which the macroscopic velocity polarizations arise is thereby established. A model method solution of the quantum Boltzmann equation, emphasizing the parity invariance of the collision superoperator, is given for a steady state absorption experiment in the absence of saturation but including Doppler effects. Throughout this thesis, the relaxation rates, are related to kinetic theory collision cross sections by solving the quantum Boltzmann equation. Extensive use is made of rotational invariance to reduce the number of independent collision integrals, and their approximate evaluation is accomplished within the context of the distorted wave Born approximation. All collision integrals for the pure internal state polarizations are found tobe expressible in terms of one translational factor, which is itself further approximated by a modified Born approximation. Correspondingly, the translational factor which arises in the relaxation of macroscopic velocity polarizations is completely specified by relating it to the Ω(ℓ,s) integrals of traditional kinetic theory.
Item Metadata
Title  Pressure broadening and coherence transients effects: a kinetic theory approach 
Creator  Coombe, Dennis Allan 
Publisher  University of British Columbia 
Date Issued  1976 
Description 
The response of a polyatomic gas to microwave radiation including both steady state (pressure broadening) and time dependent (coherence transients) effects  is described theoretically. The treatment is based on solutions of a quantum mechanical Boltzmahn equation and employs kinetic theory methods which have previously been used in the explanation of the field dependence of transport phenomena (SenftlebenBeenakker effects).
Much of the recent theoretical work of pressure broadening and coherence transient phenomena is based on a two (energy) state model for the gas molecules. This model, when developed from a density operator point of view, results in a coupled set of three equations which are mathematically equivalent to the Bloch equations of NMR. The present work reexamines this description, and replaces it with a two level model for the gas system. Here, the term "level" implies explicit consideration of the rotational (magnetic) degeneracy associated with each energy state. This model gives a more appropriate representation of the interaction of microwave radiation with a real molecular system. In particular, a more complete set of coupled equations result from this description and involve quantities in addition to the three moments used in a two state approach. The most important of these latter effects are represented by spherical harmonics Ƴ(q) (J) in he angular momentum J of the relevant energy levels. An analogous treatment of rotational effects has previously been used in SenftlebenBeenakker studies. Specific molecular types of interest in microwave spectroscopy diamagnetic diatonics and linear polyatomics, symmetric tops, and inverting symmetric tops  are treated separately by this two level approach. The vector (and tensor) nature of the motions are emphasized throughout. The number of rotational polarizations that arise in the general two level case is often quite large. The simplest example of a two level system is the j=0 to j=l transition of a diamagnetic diatomic. This is studied in some detail. Here, the scalar component Ƴ⁽²⁾⁰(J) is the only rotational polarization affected by linearly polarized radiation in the usual experiments. The effect of this quantity on both steady state and transient phenomena is described, and a new "combination" experiment is suggested as the best way to detect the presence of this additional polarization.
The Doppler effect is treated by appropriately including the effects of translational motion in the quantum Boltzmann equation. A more general set of coupled moment equations then results, and the manner in which the macroscopic velocity polarizations arise is thereby established. A model method solution of the quantum Boltzmann equation, emphasizing the parity invariance of the collision superoperator, is given for a steady state absorption experiment in the absence of saturation but including Doppler effects.
Throughout this thesis, the relaxation rates, are related to kinetic theory collision cross sections by solving the quantum Boltzmann equation. Extensive use is made of rotational invariance to reduce the number of independent collision integrals, and their approximate evaluation is accomplished within the context of the distorted wave Born approximation. All collision integrals for the pure internal state polarizations are found tobe expressible in terms of one translational factor, which is itself further approximated by a modified Born approximation. Correspondingly, the translational factor which arises in the relaxation of
macroscopic velocity polarizations is completely specified by relating it to the Ω(ℓ,s) integrals of traditional kinetic theory.

Subject  Transport theory; Pressure broadening 
Genre  Thesis/Dissertation 
Type  Text 
Language  eng 
Date Available  20100212 
Provider  Vancouver : University of British Columbia Library 
Rights  For noncommercial purposes only, such as research, private study and education. Additional conditions apply, see Terms of Use https://open.library.ubc.ca/terms_of_use. 
DOI  10.14288/1.0059482 
URI  
Degree  Doctor of Philosophy  PhD 
Program  Chemistry 
Affiliation  Science, Faculty of; Chemistry, Department of 
Degree Grantor  University of British Columbia 
Campus  UBCV 
Scholarly Level  Graduate 
Aggregated Source Repository  DSpace 
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For noncommercial purposes only, such as research, private study and education. Additional conditions apply, see Terms of Use https://open.library.ubc.ca/terms_of_use.