Accurate Quantum Mechanical Decoupling Approximations for Molecular Scattering Theory
Mclenithan, Kelly Daniel
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https://hdl.handle.net/2142/70200
Description
Title
Accurate Quantum Mechanical Decoupling Approximations for Molecular Scattering Theory
Author(s)
Mclenithan, Kelly Daniel
Issue Date
1982
Department of Study
Chemistry
Discipline
Chemistry
Degree Granting Institution
University of Illinois at Urbana-Champaign
Degree Name
Ph.D.
Degree Level
Dissertation
Keyword(s)
Chemistry, Physical
Abstract
Recent work is reviewed on the theory of angular momentum decoupling approximations in inelastic molecular scattering theory. It is shown that the failure of these approximations is more extensive than previously believed, particularly for completely state-selected m-transitions. A new method is presented for systematically improving these approximations, which recouples the approximate solutions to first-order using the generalized distorted wave Born approximation. As an illustration of the generality of this new recoupling technique, formulae are derived for the corrections to the centrifugal decoupling, the energy sudden and the infinite-order sudden approximations. Completely state-selected differential and integral cross sections are computed under the centrifugal decoupling approximation and its first-order distorted wave correction for Ne + HD scattering at a total energy of 31.5 meV. Five choices of the partial wave decoupling parameter (including the three known ones) are studied. The numerical results show that with the partial wave parameter chosen to be the arithmetic mean of the initial and final l-quantum numbers, the corrected centrifugal decoupling approximation gives significantly more accurate inelastic differential and integral state-selected cross sections than its uncorrected counterpart.
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