Atmospheric and Oceanic Optics

, Volume 30, Issue 4, pp 316–323 | Cite as

Resonance functions in the theory of collisional broadening of molecule spectral lines at low temperatures

  • V. I. StarikovEmail author
Spectroscopy of Ambient Medium


Eleven resonance functions are calculated in the exact trajectory model, which can be used for calculation of broadening coefficients γ of molecular lines during interactions with atoms of inert gases at very low temperatures. These functions correspond to the atom-atom potential and the potential V(R, θ) written in terms of Legendre polynomials. The functions are represented in analytical form. The broadening coefficients γ are calculated for absorption lines of CO perturbed by He and Ar at temperatures T from 300 to 2 K using the potential V(R, θ). It is shown that the dependence γ(T) for low temperatures T is determined by the potential well depth. For the CO–He system, a comparison with the experimental data is performed.


collisional broadening resonance functions low temperatures 


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  1. 1.
    D. R. Willey, D. N. Bittner, and F. C. De Lucia, “Pressure broadening cross sections for H2S–He system in the temperature region between 4.3 and 1.8 K,” J. Mol Spectrosc. 134, 240–242 (1989).ADSCrossRefGoogle Scholar
  2. 2.
    D. C. Flatin, T. M. Goyette, M. M. Beaky, C. D. Ball, and F. C. De Lucia, “Rotational state dependence of collision induced line broadening and shift at low temperature,” J. Chem. Phys. 110, 2087–2098 (1999).ADSCrossRefGoogle Scholar
  3. 3.
    M. J. Dick, B. J. Drouin, and J. C. Pearson, “A collisional cooling investigation of the pressure broadening of the 110 ← 101 transition of water from 17 to 200 K,” J. Quant. Spectrosc. Radiat. Transfer 110, 619–627 (2009).ADSCrossRefGoogle Scholar
  4. 4.
    M. J. Dick, B. J. Drouin, and J. C. Pearson, “Collision cooling investigation of THz rotational of water,” Phys. Rev., A 81, Art. N 022706 (2010).Google Scholar
  5. 5.
    D. R. Willey, R. L. Crownover, D. N. Bittner, and F. C. De Lucia, “Very low temperature spectroscopy. The pressure broadening coefficients for CO–He between 4.3 and 1.7 K,” J. Chem. Phys. 89, 1923–1928 (1988).ADSCrossRefGoogle Scholar
  6. 6.
    D. R. Willey, T. M. Goyette, W. L. Ebenstein, D. N. Bittner, and F. C. De Lucia, “Collision cooling spectroscopy. Pressure broadening below 5 K,” J. Chem. Phys. 91, 122–125 (1989).ADSCrossRefGoogle Scholar
  7. 7.
    M. M. Beaky, T. M. Goyette, and F. C. De Lucia, “Pressure broadening and line shift measurements of carbon monoxide in collision with helium from 1 to 600 kelvin,” J. Chem. Phys. 105, 3994–4004 (1996).ADSCrossRefGoogle Scholar
  8. 8.
    C. D. Ball, M. Mengel, F. C. De Lucia, and D. E. Woon, “Quantum scattering calculations for H2S–He between 1–600 K in comparison with pressure broadening, shift, and time resolved double resonance experiments,” J. Chem. Phys. 111, 8893–8903 (1999).ADSCrossRefGoogle Scholar
  9. 9.
    M. Thachuk, C. E. Chuaqui, and R. J. Le Roy, “Linewidths and shifts of very low temperature CO in He: A challenge for theory or experiment,” J. Chem. Phys. 105, 4005–4014 (1996).ADSCrossRefGoogle Scholar
  10. 10.
    T. M. Petrova, A. M. Solodov, A. A. Solodov, and V. I. Starikov, “Vibrational dependence of an intermolecular potential for H2O–He system,” J. Quant. Spectrosc. Radiat. Transfer 129, 241–253 (2013).ADSCrossRefGoogle Scholar
  11. 11.
    V. I. Starikov, “Broadening of vibrational-rotational lines of the H2S molecule by pressure of monatomic gases,” Opt. Spectrosc. 115, 18–27 (2013).ADSCrossRefGoogle Scholar
  12. 12.
    C. J. Tsao and B. Curnutte, “Line-widths of pressurebroadening spectral lines,” J. Quant. Spectrosc. Radiat. Transfer 2, 41–91 (1962).ADSCrossRefGoogle Scholar
  13. 13.
    D. Robert and J. Bonamy, “Short range effects in semiclassical molecular line broadening calculations,” J. Phys. (Paris) 40, 923–943 (1979).CrossRefGoogle Scholar
  14. 14.
    A. D. Bykov, N. N. Lavrent’eva, and L. N. Sinitsa, “Resonance functions of the theory of broadening and shift of lines for actual trajectories,” Atmos. Ocean. Opt. 5 (11), 728–730 (1992).Google Scholar
  15. 15.
    V. I. Starikov and N. N. Lavrent’eva, Collisional Broadening of Spectral Lines of Absorption by Atmospheric Gas Molecules (Publishing House of IAO SB RAS, Tomsk, 2006) [in Russian].Google Scholar
  16. 16.
    J. Buldyreva, N. N. Lavrent’eva, and V. I. Starikov, Collisional Line Broadening and Shifting of Atmospheric Gases. A Practical Guide for Line Shape Modeling by Current Semi-Classical Approaches (Imperial College Press, London, 2010).CrossRefGoogle Scholar
  17. 17.
    E. W. Smith, M. Giraud, and J. Cooper, “A semiclassical theory for spectral line broadening in molecules,” J. Chem. Phys. 65, 1256–1267 (1976).ADSCrossRefGoogle Scholar
  18. 18.
    B. Labani, J. Bonamy, D. Robert, J.-M. Hartmann, and J. Taine, “Collisional broadening of rotationvibration lines for asymmetric top molecules. I. Theoretical model for both distant and close collisions,” J. Chem. Phys. 84, 4256–4267 (1986).ADSCrossRefGoogle Scholar
  19. 19.
    V. I. Starikov, “Bi-resonance functions in the theory of collisional broadening of the spectral lines of molecules,” Opt. Spectrosc. 112, 27–34 (2012).ADSCrossRefGoogle Scholar
  20. 20.
    L. Bidenkharn and Dzh. Lauk, Angular Momentum in Quantum Physics (Mir, Moscow, 1984) [in Russian].CrossRefGoogle Scholar
  21. 21.
    L. D. Landau and E. M. Lifshits, The Theory of Elasticity (Nauka, Moscow, 1965) [in Russian].Google Scholar
  22. 22.
    S. Green, “Calculation of pressure broadening parameters for the CO–He system at low temperatures,” J. Chem. Phys. 82, 4548–4550 (1985).ADSCrossRefGoogle Scholar
  23. 23.
    P. M. Sinclair, P. Duggan, R. Berman, J. R. Drummond, and A. D. May, “Line broadening in the fundamental band of CO in CO–He and CO–Ar mixtures,” J. Mol. Spectrosc. 191, 258–264 (1988).ADSCrossRefGoogle Scholar

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© Pleiades Publishing, Ltd. 2017

Authors and Affiliations

  1. 1.Tomsk State University of Control Systems and RadioelectronicsTomskRussia
  2. 2.National Research Tomsk Polytechnic UniversityTomskRussia

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