The usual calculations of vibrational energy exchange in a diatomic gas make use of first-order perturbation theory and are therefore limited to low transition probabilities. In actual practice, the thermally averaged transition probabilities in most gases are indeed small. However, this is partly because it is the relatively few molecules in the high-velocity ``tail'' of the velocity distribution which account for most of the energy exchange. The actual microscopic transition probabilities in these collisions may be too great to justify the perturbation method for many gases at high temperatures. We have therefore solved the time-dependent Schrödinger equation based on a semiclassical collision, subject to an assumed form of potential, to get exact transition probabilities in a molecular collision. At low velocities, our result reduces to the perturbation result. A thermal average of our transition probabilities should eliminate errors due to use of the perturbation solution in previous calculations. For N2, these errors only become important above 5000°K. For gases with lower vibrational frequencies such as O2, or strong attractive forces such as NO, these effects become important at much lower temperatures.
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1 June 1963
Research Article|
July 20 2004
Vibrational Energy Transfer in Molecular Collisions Involving Large Transition Probabilities
D. Rapp;
D. Rapp
Physical Sciences Laboratory, Research and Engineering, Lockheed Missiles & Space Company, Sunnyvale, California
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T. E. Sharp
T. E. Sharp
Physical Sciences Laboratory, Research and Engineering, Lockheed Missiles & Space Company, Sunnyvale, California
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J. Chem. Phys. 38, 2641–2648 (1963)
Article history
Received:
January 28 1963
Citation
D. Rapp, T. E. Sharp; Vibrational Energy Transfer in Molecular Collisions Involving Large Transition Probabilities. J. Chem. Phys. 1 June 1963; 38 (11): 2641–2648. https://doi.org/10.1063/1.1733565
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