Simple Analytic Collisional Rates for non-LTE Vibrational Populations in Astrophysical Environments: the Cases of Circumstellar SiO Masers and Shocked H2

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Rates for collisionally induced transitions between molecular vibrational levels are important in modeling a variety of non-LTE processes in astrophysical environments. Two examples are SiO masering in circumstellar envelopes in certain late-type stars [1] and the vibrational populations of molecular hydrogen in shocked interstellar medium [cf 2]. A simple exponential-potential model of molecular collisions leads to a two-parameter analytic expression for state-to-state and thermally averaged rates for collisionally induced vibrational-translational (VT) transitions in diatomic molecules [3,4]. The thermally averaged rates predicted by this formula have been shown to be in excellent numerical agreement with absolute experimental and quantum mechanical rates over large temperature ranges and initial vibrational excitation levels in a variety of species, e.g., OH, O2, N2 [3] and even for the rate of H2(v=1)+H2, which changes by five orders of magnitude in the temperature range 50-2000 K [4]. Analogous analytic rates will be reported for vibrational transitions in SiO due to collisions with H2 and compared to the numerical fit of quantum-mechanical rates calculated by Bieniek and Green [5].
[1] Palov, A.P., Gray, M.D., Field, D., & Balint-Kurti, G.G. 2006, ApJ, 639, 204.
[2] Flower, D. 2007, Molecular Collisions in the Interstellar Medium (Cambridge: Cambridge Univ. Press)
[3] Bieniek, R.J. & Lipson, S.J. 1996, Chem. Phys. Lett. 263, 276.
[4] Bieniek, R.J. 2006, Proc. NASA LAW (Lab. Astrophys. Workshop) 2006, 299; http://www.physics.unlv.edu/labastro/nasalaw2006proceedings.pdf.
[5] Bieniek, R.J., & Green, S. 1983, ApJ, 265, L29 and 1983, ApJ, 270, L101.

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