The quantum mechanical theory of rotational and vibrational transitions in atom-diatom systems is investigated and summarized. The time independent scattering formalism of Arthurs and Dalgarno is used, and the degeneracy-averaged cross section is expressed in terms of the scattering S matrix. The major emphasis is on the solution of the rotationally strongly coupled differential equations. Various methods of solving the scattering equations are examined and some of the inadequacies of these methods are discussed. A strong coupling (SC) approximation, valid for small energy exchange, is introduced and tested numerically on some model problems. A first-order iteration to the SC approximation is presented to improve the SC approximation and to extend the range of validity to cases of larger energy exchange. The SC results are compared with the accurate numerical solution and other approximate methods for some model problems. The comparison clearly demonstrates that the SC approximation is the computationally fastest, reasonably reliable method known for computing rotationally inelastic cross sections.
| Identifer | oai:union.ndltd.org:BGMYU2/oai:scholarsarchive.byu.edu:etd-9371 |
| Date | 01 May 1971 |
| Creators | Tsien, Thomas P. |
| Publisher | BYU ScholarsArchive |
| Source Sets | Brigham Young University |
| Detected Language | English |
| Type | text |
| Source | Theses and Dissertations |
| Rights | http://lib.byu.edu/about/copyright/ |
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