Atmospheric and Oceanic Optics

, Volume 32, Issue 3, pp 257–265 | Cite as

Comparison of Spectral Line Profiles in Hard and Soft Collision Models

  • V.P. KochanovEmail author


The qualitative and quantitative effects on the line profile of hard and soft velocity-changing large- and small-angle scattering collisions of absorbing molecules, respectively, are considered. It is shown that large-angle scattering significantly contributes to the diffusion profile model, known as the “soft” collision model, as compared to that in the hard collision model. The difference between these traditional models lies only in the mathematical representation of the collision integral, either in integral or differential form, and the following analytical expressions for the profiles. Simple approximate formulas for the profile are derived and tested, which simultaneously take into account hard and soft collisions.


line profile hard collisions soft collisions diffusion 



  1. 1.
    W. Voigt, Uber Das Gesetz Intensitätsverteilung Innerhalb Der Linien Eines Gasspektrams (Sitzber. Bayr Akad., Munchen, Berlin, 1912).zbMATHGoogle Scholar
  2. 2.
    L. Galatry, “Simultaneous effect of doppler and foreign gas broadening on spectral lines,” Phys. Rev. 122, 1218 (1961).CrossRefzbMATHGoogle Scholar
  3. 3.
    M. I. Podgoretskii and A. V. Stepanov, “The Doppler width of emission and absorption lines,” JETF 13 (2), 393–396 (1961).Google Scholar
  4. 4.
    M. Nelkin and A. Ghatak, “Simple binary collision model for Van Hove’S Gs(r, t),” Phys. Rev. 135, A4–A9 (1964).MathSciNetCrossRefGoogle Scholar
  5. 5.
    S. G. Rautian and I. I. Sobel’man, “The effect of collisions on Doppler broadening of spectral lines,” Phys.-Uspekhi 9 (5), 701–716 (1967).CrossRefGoogle Scholar
  6. 6.
    S. G. Rautian, “Certain questions of the theory of quantum gas generators,” Tr. FIAN 43, 3–115 (1968).Google Scholar
  7. 7.
    R. H. Dicke, “The effect of collisions upon the Doppler width of spectral lines,” Phys. Rev. 89, 472–473 (1953).CrossRefGoogle Scholar
  8. 8.
    J. P. Wittke and R. H. Dicke, “Redetermination of the hyperfine splitting in the ground state of atomic hydrogen,” Phys. Rev. 103, 620–631 (1956).CrossRefGoogle Scholar
  9. 9.
    P. Duggan, P. M. Sinclair, R. Berman, A. D. May, and J. R. Drummond, “Testing lineshape models: Measurements for v = 1–0 CO broadened by He and Ar,” J. Mol. Spectrosc. 186 (1), 90–98 (1997).CrossRefGoogle Scholar
  10. 10.
    R. Ciurylo, R. Jaworski, J. Jurkowski, A. S. Pine, and J. Szudy, “Spectral line shapes modeled by a quadratic speed-dependent Galatry PRofile,” Phys. Rev. A 63 (3), 032507 (2001).CrossRefGoogle Scholar
  11. 11.
    P. Duggan, P. M. Sinclair, A. D. May, and J. R. Drummond, “Line-shape analysis of speed-dependent collisional width inhomogeneities in CO broadened by Xe, N2, and He,” Phys. Rev. A 51 (1), 218–224 (1995).CrossRefGoogle Scholar
  12. 12.
    R. Ciurylo, “Shapes of pressure- and Doppler-broadened spectral lines in the core and near wings,” Phys. Rev. A 58 (2), 1029–1039 (1998).CrossRefGoogle Scholar
  13. 13.
    M. D. De Vizia, A. Castrillo, E. Fasci, L. Moretti, F. Rohart, and L. Gianfrani, “Speed dependence of collision parameters in the H2 18O near-IR spectrum: Experimental test of the quadratic approximation,” Phys. Rev. A 85 (6), 062512–7 (2012).CrossRefGoogle Scholar
  14. 14.
    H. Tran, J.-M. Hartmann, F. Chaussard, and M. Gupta, “An isolated line-shape model based on the Keilson–Storer function for velocity changes. II. Molecular dynamics simulations and the Q(1) lines for pure H2,” J. Chem. Phys. 131 (15), 154303 (2009).CrossRefGoogle Scholar
  15. 15.
    J. H. Ferziger and H. G. Kaper, Mathematical Theory of Transport Processes in Gases (North-Holland Publ. Comp., Amsterdam–London, 1972).Google Scholar
  16. 16.
    P. R. Berman, J. E. M. Haverkort, and J. P. Woerdman, “Collision kernels and transport coefficients,” Phys. Rev. A 34 (6), 4647–4656 (1986).CrossRefGoogle Scholar
  17. 17.
    S. G. Rautian, “The diffusion approximation in the problem of migration of particles in a gas,” iffuzionnoe priblizhenie v zadache o migratsii chastits v gaze,” Phys.-Uspekhi 34 (11), 1008–1017 (1991).CrossRefGoogle Scholar
  18. 18.
    V. P. Kochanov, “Manifestations of small-angle molecular scattering in spectral line profiles,” JETP 118 (3), 335–350. 2014CrossRefGoogle Scholar
  19. 19.
    V. P. Kochanov, “Combined effect of small- and large-angle scattering collisions on a spectral line shape,” J. Quant. Spectrosc. Radiat. Transfer 159, 32–38 (2015).CrossRefGoogle Scholar
  20. 20.
    V. P. Kochanov, “Speed-dependent spectral line profile including line narrowing and mixing,” J. Quant. Spectrosc. Radiat. Transfer 177, 261–268 (2016).CrossRefGoogle Scholar
  21. 21.
    V. P. Kochanov, “Algebraic approximation of the spectral line profile with allowance for hard and soft speed-related collisions,” Atmos. Ocean. Opt. 28 (5), 394–399 (2015).CrossRefGoogle Scholar
  22. 22.
    V. P. Kochanov and I. V. Ptashnik, “Approximation of the width of the line profile narrowed by collisions,” Opt. Spectrosc. 89 (5), 678–683 (2000).CrossRefGoogle Scholar
  23. 23.
    C. Claveau, A. Henry, D. Hurtmans, and A. Valentin, “Narrowing and broadening parameters of H2O lines perturbed by He, Ne, Ar, Kr, and nitrogen in the spectral range 1850-2140 cm–1,” J. Quant. Spectrosc. Radiat. Transfer 68 (3), 273–298 (2001).CrossRefGoogle Scholar
  24. 24.
    T. L. Andreeva, “Diffusion equation for the density matrix,” Zh. Exp. Teor. Fiz. 54 (2). 641–651 (1968).Google Scholar
  25. 25.
    V. A. Alekseev, T. L. Andreeva, and I. I. Sobel’man, “The quantum kinetic equation method for atoms and molecules and its application to the calculation of optical characteristics of gases,” JETP 32 (2), 325–330 (1972).Google Scholar
  26. 26.
    V. A. Alekseev, T. L. Andreeva, and I. I. Sobel’man, “Contributions to the theory of nonlinear power resonances in gas lasers,” JETP 37 (3), 413–419 (1973).Google Scholar
  27. 27.
    P. R. Berman, “Theory of collision effects on atomic and molecular line shapes,” Appl. Phys. 6, 283–296 (1975).CrossRefGoogle Scholar
  28. 28.
    E. G. Pestov and S. G. Rautian, “Field narrowing of spectral lines,” JETP 37 (6), 1025–1031 (1973).Google Scholar
  29. 29.
    S. G. Rautian, G. I. Smirnov, and A. M. Shalagin, Nonlinear Resonances in Atomic and Molecular Spectra (Nauka, Novosibirsk, 1979) [in Russian].Google Scholar
  30. 30.
    R. Blackmore, “A modified Boltzmann kinetic equation for line shape functions,” J. Chem. Phys. 87, 791 (1987).CrossRefGoogle Scholar
  31. 31.
    E. G. Pestov, “Theory of quantum system relaxations in a strong electromagnetic field,” Tr. FIAN 187, 60–116 (1988).Google Scholar
  32. 32.
    V. P. Kochanov, “The effect of molecule diffraction on collisional line narrowing,” Opt. Spektrosk. 89 (5), 743–748 (2000).Google Scholar
  33. 33.
    S. Chandrasekar, Stochastic Problems in Physics and Astronomy (Inostrannaya Literatura, Moscow, 1947) [in Russian].Google Scholar
  34. 34.
    Handbook on Special Functions, Ed. by M. Abramovits and I. Stigan (Nauka, Moscow, 1979) [in Russian].Google Scholar
  35. 35.
    V. P. Kochanov, “Efficient approximations of the Voigt and Rautian–Sobelman profiles,” Atmos. Ocean. Opt. 24 (5), 432–435 (2011).CrossRefGoogle Scholar
  36. 36.
    V. P. Kochanov, “On one-dimensional velocity approximation for speed-dependent spectral line profiles,” J. Quant. Spectrosc. Radiat. Transfer 121, 105–110 (2013).CrossRefGoogle Scholar
  37. 37.
    P. R. Berman, “Speed-dependent collisional width and shift parameters in spectral line profiles,” J. Quant. Spectrosc. Radiat. Transfer 12, 1331–1342 (1972).CrossRefGoogle Scholar
  38. 38.
    V. P. Kochanov, “On parameterization of spectral line profiles including the speed-dependence in the case of gas mixture,” J. Quant. Spectrosc. Radiat. Transfer 189, 18–23 (2017).CrossRefGoogle Scholar
  39. 39.
    V. P. Kochanov and I. Morino, “Methane line shapes and spectral line parameters in the 5647–6164 cm–1 region,” J. Quant. Spectrosc. Radiat. Transfer 206, 313–322 (2018).CrossRefGoogle Scholar
  40. 40.
    V. P. Kochanov, “Line profiles for the description of line mixing, narrowing, and dependence of relaxation constants on speed,” J. Quant. Spectrosc. Radiat. Transfer 112, 1931–1941 (2011).CrossRefGoogle Scholar
  41. 41.
    S. G. Rautian, “Universal asymptotic profile of a spectral line under a small Doppler broadening,” Opt. Spectrosc. 90 (1), 30–40 (2001).CrossRefGoogle Scholar

Copyright information

© Pleiades Publishing, Ltd. 2019

Authors and Affiliations

  1. 1.V.E. Zuev Institute of Atmospheric Optics, Siberian Branch, Russian Academy of SciencesTomskRussia

Personalised recommendations