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Rotational Excitation II: Approximation Methods

  • Chapter
Atom - Molecule Collision Theory

Abstract

In this chapter, we shall describe several of the most useful quantal approximations for use in treating rotational excitation in atom-molecule collisions. In order to keep this discussion within manageable proportions, we shall not attempt to describe all the approximations developed in the past few years but rather focus on those which, in our admittedly prejudiced view, are the most useful, general, and computationally viable. As a result, there are a number of approximations which we will not discuss in any detail.

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References

  1. P. McGuire and D.J. Kouri, Quantum mechanical close coupling approach to molecular collisions: j z-conserving coupled states approximation, J. Chem. Phys. 60, 2488–2499 (1974).

    CAS  Google Scholar 

  2. R.T Pack, Space-fixed vs. body-fixed axes in atom-diatomic molecule scattering: Sudden approximations, J. Chem. Phys. 60, 633–639 (1974).

    CAS  Google Scholar 

  3. M. Tamir and M. Shapiro, The approximate conservation of P-helicity in rotational excitation: A new decoupling scheme, Chem. Phys. Lett. 31, 166–171 (1975).

    CAS  Google Scholar 

  4. R.B. Walker and J.C. Light, Body-fixed equations for atom-molecule scattering: Exact and centrifugal decoupling methods, Chem. Phys. 7, 84–93 (1975).

    CAS  Google Scholar 

  5. D. Secrest, Theory of angular momentum decoupling approximations for rotational transitions in scattering, J. Chem. Phys. 62, 710–719 (1975).

    CAS  Google Scholar 

  6. Y. Shimoni and D.J. Kouri, Accurate opacity functions for atom-diatom scattering: Average definite parity j z-conserving approximation, J. Chem. Phys. 65, 3372–3373 (1976).

    CAS  Google Scholar 

  7. Y. Shimoni and D.J. Kouri, On representative orbital angular momentum quantum numbers in the definite parity jzCCS approximation, J. Chem. Phys. 65, 3958–3967 (1976).

    CAS  Google Scholar 

  8. Y. Shimoni and D.J. Kouri, Quantum mechanical close coupling approach to molecular collisions: Averaged definite parity j z-conserving coupled states approximation, J. Chem. Phys. 66, 675–688 (1977).

    CAS  Google Scholar 

  9. Y. Shimoni and D.J. Kouri, Quantum mechanical close coupling approach to molecular collisions: Averaged definite parity j z approximation with Clebsch-Gordan weights, J. Chem. Phys. 66, 2841–2849 (1977).

    CAS  Google Scholar 

  10. G.A. Parker and R.T Pack, Identification of the partial wave parameter and simplification of the differential cross section in the jzCCS approximation in molecular scattering, J. Chem. Phys. 66, 2850–2853 (1977).

    CAS  Google Scholar 

  11. D.J. Kouri and Y. Shimoni, A new method for accurately approximating individual T-matrix elements in atom-diatom collisions, J. Chem. Phys. 65, 5021 - 5023 (1976).

    CAS  Google Scholar 

  12. D.J. Kouri and Y. Shimoni, On the j z-conserving coupled states approximation: Magnetic transitions and angular distributions in rotating and fixed frames, J. Chem. Phys. 67, 86–98 (1977).

    Google Scholar 

  13. R. Goldflam and D.J. Kouri, On accurate quantum mechanical approximations for molecular relaxation phenomena: Averaged j z-conserving coupled states approximation, J. Chem. Phys. 66, 542–547 (1977).

    CAS  Google Scholar 

  14. V. Khare, On the equivalence between the space fixed and the body fixed formulations of the j z-conserving approximation, J. Chem. Phys. 67, 3897–3900 (1977).

    CAS  Google Scholar 

  15. D.J. Kouri, R. Goldflam, and Y. Shimoni, On the coupled states and infinite order sudden approximations to the body frame wavefunction, J. Chem. Phys. 67, 4534–4544 (1977).

    CAS  Google Scholar 

  16. V. Khare, D.J. Kouri, and R.T Pack, On magnetic transitions and the interpretation of the partial wave parameter in the CS and IOS approximations in molecular scattering theory, J. Chem. Phys. 69, 4419–4430 (1978).

    CAS  Google Scholar 

  17. K.P. Lawley and J. Ross, Semiclassical theory of rotational excitation of a diatomic molecule by an atom, J. Chem. Phys. 43, 2930–2942 (1965).

    CAS  Google Scholar 

  18. H. Klar, Theory of collision induced rotational energy transfer in the ∏-state of diatomic molecules, J. Phys. B 6, 2139 - 2149 (1973).

    CAS  Google Scholar 

  19. A.E. De Pristo and M. Alexander, Relationships among the coupled states, P-helicity decoupling and effective potential methods, Chem. Phys. 19, 181–192 (1977).

    Google Scholar 

  20. D.J. Kouri, On the decoupling of angular momenta in molecular collisions, Chem. Phys. Lett. 31, 599–601 (1975).

    CAS  Google Scholar 

  21. H. Rabitz, Effective Hamiltonians in molecular collisions, in Modern Theoretical Chemistry, W.H. Miller, editor, Vol. 2, Plenum Press, New York (1976), pp. 33–80, and references therein.

    Google Scholar 

  22. B.H. Choi and K.T. Tang, On j z-conserving coupled-states approximation for molecular collisions, J. Chem. Phys. 62, 4568–4569 (1975).

    CAS  Google Scholar 

  23. P. McGuire, Elastic and inelastic angular distributions in thej z-conserving coupled states approximation for molecular collisions, Chem. Phys. Lett. 23, 575–578 (1973).

    CAS  Google Scholar 

  24. D.J. Kouri and P. McGuire, A coupled states approximation study of Li+ -H2 collisions, Chem. Phys. Lett. 29, 414–417 (1974).

    CAS  Google Scholar 

  25. S.I. Chu and A. Dalgarno, The rotational excitation of carbon monoxide by hydrogen atom impact, Proc. R. Soc. London A 342, 191–207 (1975).

    CAS  Google Scholar 

  26. P. McGuire and J.P. Toennies, A priori low temperature vibrational relaxation rates for He-H2, J. Chem. Phys. 62, 4623–4627 (1975).

    CAS  Google Scholar 

  27. P. McGuire and H. Kruger, Elastic and rotationally inelastic H-H2 and H-D2 collisions, J. Chem. Phys. 63, 1090–1094 (1975).

    CAS  Google Scholar 

  28. S.-I. Chu and A. Dalgarno, Approximations for the rotational excitation of molecules by atoms, J. Chem. Phys. 63, 2115–2118 (1975).

    CAS  Google Scholar 

  29. Erratum: Approximations for the rotational excitation of molecules by atoms [J. Chem. Phys. 63, 2115 (1975)], J. Chem. Phys. 64, 3085 (1976).

    Google Scholar 

  30. M. Tamir and M. Shapiro, Application of the PHD approximation to the high rotational transitions in the Ar + N2 system, Chem. Phys. Lett. 39, 79–81 (1976).

    CAS  Google Scholar 

  31. M. Alexander and P. McGuire, Cross sections and rate constants for low temperature 4He-H2 vibrational relaxation, J. Chem. Phys. 64, 452–459 (1976).

    CAS  Google Scholar 

  32. M. Shapiro and M. Tamir, Rotational excitation in the Ar + N2 system, Chem. Phys. 13, 215–225 (1976).

    CAS  Google Scholar 

  33. M. Alexander and P. McGuire, Inelastic collisions between 4He and H2: Study of dynamical approximations, Chem. Phys. Lett. 12, 31–36 (1976).

    CAS  Google Scholar 

  34. J.M. Launay, Body-fixed formulation of rotational excitation: Exact and centrifugal decoupling results for CO-He, J. Phys. B 9, 1823–1838 (1976).

    CAS  Google Scholar 

  35. L. Monchick and S. Green, Validity of approximate methods in molecular scattering. III. Effective potential and coupled states approximations for differential and gas kinetic cross sections, J. Chem. Phys. 66, 3085–3093 (1976).

    Google Scholar 

  36. S. Green and L. Monchick, Validity of approximate methods in molecular scattering: Thermal HC1-He collisions, J. Chem. Phys. 63, 4198–4205 (1975).

    CAS  Google Scholar 

  37. S. Green, Accuracy of decoupling approximations for rotational excitation: Low energy CO-He collisions, Chem. Phys. Lett. 38, 293–296 (1976).

    CAS  Google Scholar 

  38. T.G. Heil, Atom-molecule scattering: Close coupled and coupled states calculations for argon-methane scattering, Ph.D. Thesis, Department of Chemistry, University of Illinois, 1977.

    Google Scholar 

  39. T.G. Heil and D. Secrest, private communication.

    Google Scholar 

  40. P. McGuire, Validity of the coupled states approximation for molecular collisions, Chem. Phys. 13, 81–94 (1976).

    CAS  Google Scholar 

  41. A.B. Elkowitz and R.E. Wyatt, J z-conserving approximation for the hydrogen exchange reaction, Mol. Phys. 31, 189–201 (1976).

    CAS  Google Scholar 

  42. A. Kuppermann, G.C. Schatz, and J.P. Dwyer, Angular momentum decoupling approximations in the quantum dynamics of reactive systems, Chem. Phys. Lett. 45, 71–73 (1977).

    CAS  Google Scholar 

  43. L.A. Collins and N.F. Lane, Quantum mechanical calculations of rotational excitation cross sections for HC1, DC1, HF and DF in slow collisions with He, Phys. Rev. A 14, 1358–1367 (1976).

    CAS  Google Scholar 

  44. R. Goldflam and D.J. Kouri, Quantum scattering theory of relaxation phenomena: Coupled states calculations of rotational relaxation and spectral line shapes in He- H2 gas mixtures, J. Chem. Phys. 66, 2452–2456 (1977).

    CAS  Google Scholar 

  45. P. McGuire, Convergence of the elastic and the inelastic cross sections in the coupled- states and the close coupling methods, Chem. Phys. 8, 231–238 (1975).

    CAS  Google Scholar 

  46. T.G. Heil and D.J. Kouri, Diatom-diatom collisions: j z-conserving coupled states calculations for para-H2 + para-H2 scattering, Chem. Phys. Lett. 40, 375–389 (1976).

    CAS  Google Scholar 

  47. S. Green, L. Monchick, R. Goldflam, and D.J. Kouri, Computational tests of angular momentum decoupling approximations for pressure broadening cross sections, J. Chem. Phys. 66, 1409–1412 (1977).

    CAS  Google Scholar 

  48. D.E. Fitz and P. McGuire, Comparison of the coupled states, infinite order sudden, and exponential Born methods for Ar-CsF collisions, Chem. Phys. Lett. 44, 503–506 (1976).

    CAS  Google Scholar 

  49. S. Green, On the accuracy of the “decoupled l-dominant” approximation for atom- molecule scattering, J. Chem. Phys. 65, 68–70 (1976).

    CAS  Google Scholar 

  50. U. Buck and P. McGuire, Rotational excitation of HC1 by Ar impact, Chem. Phys. 16, 101–108 (1976).

    CAS  Google Scholar 

  51. R. Goldflam and D.J. Kouri, On predicting quantal cross sections by interpolation: Surprisal analysis of jzCCS and statistical results, J. Chem. Phys. 65, 4218–4227 (1976).

    CAS  Google Scholar 

  52. G.D. Billing, The semiclassical coupled states method, J. Chem. Phys. 65, 1–6 (1976).

    CAS  Google Scholar 

  53. P. McGuire, Coupled-states approach for elastic and for rotationally and vibrationally inelastic atom-molecule collisions, J. Chem. Phys. 62, 525–534 (1975).

    CAS  Google Scholar 

  54. P. McGuire, Coupled states approximation study of inelastic H+ -H2 collisions at 3.7 eV, J. Chem. Phys. 65, 3275–3279 (1976).

    CAS  Google Scholar 

  55. P. McGuire, K. Rudolph, and J.P. Toennies, Comparison of quantum and experimental rotational transition probabilities for H+ -H2 collisions at 3.7 eV. J. Chem. Phys. 65, 5522–5523 (1976).

    CAS  Google Scholar 

  56. B.J. Garrison and W.A. Lester, Jr., Coupled states cross sections for rotational ex. citation of H2CO by He impact at interstellar temperatures, J. Chem. Phys. 66, 531–536 (1977).

    CAS  Google Scholar 

  57. S. Green, Rotational excitation of symmetric top molecules by collisions with atoms: Close coupling, coupled states and effective potential calculations for NH3-He, J. Chem. Phys. 64, 3463–3473 (1976).

    CAS  Google Scholar 

  58. T.G. Heil, S. Green, and D.J. Kouri, The coupled states approximation for scattering of two diatoms, J. Chem. Phys. 68, 2562–2583 (1978).

    CAS  Google Scholar 

  59. P. McGuire, H. Schmidt, V. Hermann, and F. Linder, Quantum oscillations in the transition probability for rotational excitation of H2 by H+ impact at 4.67 eV, J. Chem. Phys. 66, 4243–4244 (1977).

    CAS  Google Scholar 

  60. S.M. Tarr, H. Rabitz, D.E. Fitz, and R.A. Marcus, Classical and quantum centrifugal decoupling approximations for HCl-Ar, J. Chem. Phys. 66, 2854–2859 (1977).

    CAS  Google Scholar 

  61. L. Monchick and D.J. Kouri, Magnetic transitions in the initial-labeled CS approximation: Computations for He + HC1, J. Chem. Phys. 69, 3262–3267 (1978).

    CAS  Google Scholar 

  62. D.J. Kouri, T.G. Heil, and Y. Shimoni, On the Lippmann-Schwinger equation for atom-diatom collisions: A rotating frame treatment, J. Chem. Phys. 65, 226–235 (1976).

    CAS  Google Scholar 

  63. D.J. Kouri, T.G. Heil, and Y. Shimoni, Sufficiency conditions for the validity of the j z-conserving coupled states approximation, J. Chem. Phys. 65, 1462–1473 (1976).

    CAS  Google Scholar 

  64. B.A. Lippmann and J. Schwinger, Variational principles for scattering processes. I, Phys. Rev. 79, 469–480 (1950).

    Google Scholar 

  65. R.D. Levine, Quantum Mechanics of Molecular Rate Processes, Clarendon Press, Oxford (1969).

    Google Scholar 

  66. R. Goldflam, Formal and computational studies of molecular collision dynamics, Ph.D. Thesis, Department of Physics, University of Houston, May 1977.

    Google Scholar 

  67. W.N. Sams and D.J. Kouri, Noniterative solutions of integral equations for scattering. I. Single channels, J. Chem. Phys. 51, 4809–4814 (1969).

    CAS  Google Scholar 

  68. W.N. Sams and D.J. Kouri, Noniterative solutions of integral equations for scattering. II. Coupled channels, J. Chem. Phys. 51, 4815–4819 (1969).

    CAS  Google Scholar 

  69. D. Secrest, Amplitude densities in molecular scattering, in Methods in Computational Physics, B. Alder, S. Fernbach, and M. Rotenberg, editors, Vol. 10, Academic Press, New York (1971), pp. 243–286.

    Google Scholar 

  70. R.A. White and E.F. Hayes, A model potential for vibrational excitation of diatomic molecules, Chem. Phys. Lett. 14, 98–102 (1972).

    CAS  Google Scholar 

  71. R.A. White and E.F. Hayes, Quantum mechanical studies of the vibrational excitation of H2 by Li+, J. Chem. Phys. 57, 2985–2993 (1972).

    CAS  Google Scholar 

  72. E.R. Smith and R.J.W. Henry, Noniterative integral-equation approach to scattering problems, Phys. Rev. A 7, 1585–1590 (1973).

    Google Scholar 

  73. A.M. Arthurs and A. Dalgarno, The theory of scattering by a rigid rotator, Proc. R. Soc. London A 256, 540–551 (1960).

    Google Scholar 

  74. M.H. Alexander, P.J. Dagdigian, and A.E. De Pristo, Quantum interpretation of fully state selected rotationally inelastic collision experiments, J. Chem. Phys. 66, 59–66 (1977).

    CAS  Google Scholar 

  75. A.R. Edmonds, Angular Momentum in Quantum Mechanics, Princeton University Press, Princeton, New Jersey (1957).

    Google Scholar 

  76. M. Jacob and G.C. Wick, On the general theory of collisions of particles with spin, Ann. Phys. (N.Y.) 7, 404–428 (1959).

    Google Scholar 

  77. J.O. Hirschfelder, C.F. Curtiss, and R.B. Bird, Molecular Theory of Gases and Liquids, Wiley, New York (1965).

    Google Scholar 

  78. U. Fano, Pressure broadening as a prototype of relaxation, Phys. Rev. 131, 259–268 (1963).

    Google Scholar 

  79. A. Ben-Reuven, Impact broadening of microwave spectra, Phys. Rev. 145, 7–22 (1966).

    CAS  Google Scholar 

  80. R. Shafer and R.G. Gordon, Quantum scattering theory of rotational relaxation and spectral line shapes in H2-He gas mixtures, J. Chem. Phys. 58, 5422–5443 (1973).

    CAS  Google Scholar 

  81. W.K. Liu and R.A. Marcus, On the theory of the relaxation matrix and its application to microwave transient phenomena, J. Chem. Phys. 63, 272–289 (1975).

    CAS  Google Scholar 

  82. A.E. De Pristo and M. Alexander, Rotationally inelastic scattering of two HF molecules, J. Chem. Phys. 66, 1334–1342 (1977).

    Google Scholar 

  83. M.H. Alexander and A.E. De Pristo, Symmetry considerations in the quantum treatment of collisions of two diatomic molecules, J. Chem. Phys. 66, 2166–2172 (1977).

    CAS  Google Scholar 

  84. S.I. Drozdov, The scattering of fast neutrons by non-spherical nuclei, JETP 1, 591–592 (1955).

    CAS  Google Scholar 

  85. D.M. Chase, Adiabatic approximation for scattering processes, Phys. Rev. 104, 838–842 (1956).

    CAS  Google Scholar 

  86. K. Adler and A. Winther, On the theory of multiple Coulomb excitation with heavy ions, Mat. Fys. Medd. Dan. Vid. Selsk. 32, 1–72 (1960).

    Google Scholar 

  87. L. Monchick and E.A. Mason, Transport properties of polar gases, J. Chem. Phys. 35, 1676–1697 (1961).

    CAS  Google Scholar 

  88. K. Takayanagi, Vibrational and rotational transitions in molecular collisions, Prog. Theor. Phys. Suppl. 25, 1–98 (1963).

    Google Scholar 

  89. K.H. Kramer and R.B. Bernstein, Sudden approximation applied to rotational excitation of molecules by atoms. I, J. Chem. Phys. 40, 200–203 (1964).

    CAS  Google Scholar 

  90. R.B. Bernstein and K.H. Kramer, Sudden approximation applied to rotational excition of molecules by atoms. II. Scattering of polar diatomics, J. Chem. Phys. 44, 4473–4485 (1966).

    CAS  Google Scholar 

  91. R.J. Cross and D.R. Herschbach, Classical scattering of an atom from a diatomic rigid rotor, J. Chem. Phys. 43, 3530–3540 (1965).

    CAS  Google Scholar 

  92. R.J. Cross, Jr., Classical small-angle scattering from anisotropic potentials, J. Chem. Phys. 46, 609–618 (1967).

    CAS  Google Scholar 

  93. C.F. Curtiss, Molecular collisions. VI. Diagrammatic methods, J. Chem. Phys. 48, 1725–1731 (1968).

    Google Scholar 

  94. C.F. Curtiss, Molecular collisions. VIII, J. Chem. Phys. 49, 1952–1957 (1968).

    CAS  Google Scholar 

  95. R.J. Cross, Quenching of glory undulations in the total cross section by anisotropy in the intermolecular potential, J. Chem. Phys. 49, 1976–1977 (1968).

    CAS  Google Scholar 

  96. R.D. Levine, Opacity analysis of inelastic molecular collisions: I. The quantum mechanical sudden approximation, Chem. Phys. Lett. 4, 211–213 (1969).

    CAS  Google Scholar 

  97. R.D. Levine, Opacity analysis of inelastic molecular collisions. VI. The sudden approximation for rotational excitation, J. Chem. Phys. 54, 997–1004 (1971).

    CAS  Google Scholar 

  98. R.J. Cross, Jr., Effects of anisotropy in the potential on molecular scattering, J. Chem. Phys. 52, 5703–5707 (1970).

    CAS  Google Scholar 

  99. T.P. Tsien and R.T Pack, Rotational excitation in molecular collisions: A strong coupling approximation, Chem. Phys. Lett. 6, 54–56 (1970).

    CAS  Google Scholar 

  100. C.F. Curtiss, Molecular collisions. XII. Generalized phase shifts, J. Chem. Phys. 52, 4832–4841 (1970).

    CAS  Google Scholar 

  101. M.A. Wartell and R.J. Cross, Jr., Semiclassical theory of vibrationally inelastic scattering in three dimensions, J. Chem. Phys. 55, 4983–4991 (1971).

    CAS  Google Scholar 

  102. T.P. Tsien and R.T Pack, Rotational excitation in molecular collisions: A many- state test of the strong coupling approximation, Chem. Phys. Lett. 8, 579–581 (1971).

    CAS  Google Scholar 

  103. E.S. Chang and U. Fano, Theory of electron-molecule collisions by frame transformations, Phys. Rev. A 6, 173–185 (1972).

    Google Scholar 

  104. P.G. Burke and N. Chandra, Electron-molecule interactions. III. A pseudo-potential method for e¯-N2 scattering, J. Phys. B 5, 1696–1711 (1972).

    CAS  Google Scholar 

  105. D.E. Golden, N.F. Lane, A. Temkin, and E. Gerjuoy, Low energy electron-molecule scattering experiments and the theory of rotational excitation, Rev. Mod. Phys. 43, 642–678 (1971).

    CAS  Google Scholar 

  106. M.A. Brandt and D.G. Truhlar, Importance of long-range forces and short-range forces in electron scattering: Elastic scattering by N2 at 10 and 30 eV, Chem. Phys. Lett. 23, 48–52 (1973).

    CAS  Google Scholar 

  107. T.P. Tsien, G.A. Parker, and R.T Pack, Rotational inelastic molecular scattering: Computational tests of some simple solutions of the strong coupling problem, J. Chem. Phys. 59, 5373–5381 (1973).

    CAS  Google Scholar 

  108. L.W. Hunter, On infinite order sudden approximations for an arbitrary potential energy, J. Chem. Phys. 62, 2855–2859 (1975).

    CAS  Google Scholar 

  109. C.F. Curtiss, Semiclassical theory of rotational excitation in collisions of diatomic molecules, Chem. Phys. 63, 2738–2744 (1975).

    CAS  Google Scholar 

  110. F.S. Collins and R.J. Cross, Jr., Vibrationally inelastic scattering at high energies: H+-H2, J. Chem. Phys. 65, 644–652 (1976).

    CAS  Google Scholar 

  111. C.F. Curtiss, Rotational and vibrational excitation in the scattering of atoms by diatomic molecules, preprint.

    Google Scholar 

  112. D.G. Truhlar, R.E. Poling, and M.A. Brandt, Infinite order sudden approximation for rotational excitation of hydrogen molecules by electrons in the energy range 10–40 eV, J. Chem. Phys. 64, 826–829 (1976).

    CAS  Google Scholar 

  113. J.M. Bowman and J. Arruda, Static rotation and quasiclassical total cross sections for atom-rigid rotor scattering: 4He + I2*2(j = 12)→ 4He + I2*(j’), Chem. Phys. Lett. 41, 43–45 (1976).

    CAS  Google Scholar 

  114. J.M. Bowman and S.C. Leasure, Sudden rotation calculations of atom-molecule scattering, J. Chem. Phys. 66, 288–295 (1977).

    CAS  Google Scholar 

  115. Erratum: Sudden rotation calculations of atom-molecule scattering [J. Chem. Phys. 66, 288 (1977)], J. Chem. Phys. 66, 4724 (1977).

    Google Scholar 

  116. J.M. Bowman, Sudden rotation total rotational inelastic cross sections for 4He + I2, J. Chem. Phys. 66, 296–297 (1977).

    CAS  Google Scholar 

  117. S.C. Leasure and J.M. Bowman, Fully converged sudden rotation total integral cross sections for 4He + H2(v = 0,J = 0)→ 4He + H2(v’ = 1,j’), Chem. Phys. Lett. 48, 179–183 (1977).

    CAS  Google Scholar 

  118. R.T Pack, Effect of partial wave parameter identification on IOS opacities and integral cross sections for rotationally inelastic collisions, J. Chem. Phys. 66, 1557–1561 (1977).

    CAS  Google Scholar 

  119. C.F. Curtiss, Semiclassical theory of rotational transitions in collisions of diatomic molecules, J. Chem. Phys. 67, 5770–5774 (1977).

    CAS  Google Scholar 

  120. R. Goldflam, S. Green, and D.J. Kouri, Infinite order sudden approximation for rotational energy transfer in gaseous mixtures, J. Chem. Phys. 67, 4149–4161 (1977).

    CAS  Google Scholar 

  121. R. Goldflam, D.J. Kouri, and S. Green, On the factorization and fitting of molecular scattering information, J. Chem. Phys. 67, 5661–5675 (1977).

    CAS  Google Scholar 

  122. G.A. Parker and R.T Pack, Rotationally and vibrationally inelastic scattering in the rotational IOS approximation: Ultrasimple calculation of total (differential, integral and transport) cross sections for nonspherical molecules, J. Chem. Phys. 68, 1585–1601 (1978).

    CAS  Google Scholar 

  123. R. Schinke and P. McGuire, On the sudden centrifugal potential in the space-fixed system: Dependence of proton-H2 cross sections on the choice of angular momentum parameter, Chem. Phys. 28, 129–145 (1978).

    CAS  Google Scholar 

  124. D.A. Varshalovich and V.K. Khersonsky, Collisional excitations of interstellar molecules, Astrophys. Lett. 18, 167–172 (1977).

    CAS  Google Scholar 

  125. A.S. Dickinson and D. Richards, Sudden atom-molecule collisions: CsF scattered by Ne, Ar, Kr and Xe, J. Phys. B 11, 1085–1103 (1978).

    CAS  Google Scholar 

  126. D.E. Fitz, A study of reorientation effects in CsF-Ar using approximate quantum methods, Chem. Phys. 24, 133–142 (1977).

    CAS  Google Scholar 

  127. Z.H. Top and D.J. Kouri, Numerical tests of the factorization of cross section data, Chem. Phys. (in press).

    Google Scholar 

  128. D.E. Fitz, On the choice of partial wave parameter for IOS calculations of m-dependent rotationally inelastic cross sections, Chem. Phys. Lett. 55, 202–205 (1978).

    CAS  Google Scholar 

  129. S. Green, On the relation between microwave transient T1 and T2 relaxation times, J. Chem. Phys. 69, 4076–4082 (1978).

    CAS  Google Scholar 

  130. R. Schinke and P. McGuire, Combined rotationally sudden and vibrationally exact quantum treatment of proton-H2 collisions, Chem. Phys. 31, 391–412 (1978).

    CAS  Google Scholar 

  131. I.C. Percival and M.J. Seaton, The partial wave theory of electron-hydrogen atom collisions, Proc. Camb. Philos. Soc. 53, 654–662 (1957).

    CAS  Google Scholar 

  132. R.P. Srivastava and H.R. Zaidi, Intermolecular forces revealed by Raman scattering, in Contemporary Raman Spectroscopy, Topics in Current Physics Series, Springer-Verlag, New York (1977).

    Google Scholar 

  133. H. Rabitz, Rotation and rotation-vibration pressure-broadened spectral lineshapes, in Ann. Rev. Phys. Chem., H. Eyring, C.J. Christensen, and H.S. Johnston, editors, Vol. 25, Annual Reviews, Inc., Palo Alto (1974), pp. 155–177.

    Google Scholar 

  134. L. Monchick, K.S. Yun, and E.A. Mason, Formal kinetic theory of transport phenomena in polyatomic gas mixtures, J. Chem. Phys. 39, 654–669 (1963).

    Google Scholar 

  135. L. Monchick and S. Green, Validity of central field approximations in molecular scattering: Low energy CO-He collisions, J. Chem. Phys. 6–2000–2009 (1975).

    Google Scholar 

  136. A. Messiah, Quantum Mechanics, Wiley, New York (1961).

    Google Scholar 

  137. V. Khare, On the l z-conserving energy sudden approximation for atom-diatom scattering, J. Chem. Phys. 68, 4631–4640 (1978).

    CAS  Google Scholar 

  138. A.E. De Pristo and M.H. Alexander, A decoupled l-dominant approximation for ion-molecule and atom-molecule collisions, J. Chem. Phys. 64, 3009–3013 (1976).

    Google Scholar 

  139. A.E. De Pristo and M.H. Alexander, Limits of validity of the decoupled l-dominant approximation, Chem. Phys. Lett. 44, 214–218 (1976).

    Google Scholar 

  140. A.E. De Pristo and M.H. Alexander, Decoupling approximations for rotationally inelastic collisions between ions and polar molecules: H+-CN, J. Phys. B 9, 2713–2721 (1976).

    Google Scholar 

  141. G.G. Balint-Kurti, The theory of rotationally inelastic molecular collisions, in Int. Rev. of Science, Physical Chemistry, A.D. Buckingham and C.A. Coulson, editors, Series Two, Butterworths, Boston (1975), pp. 283–326.

    Google Scholar 

  142. W.H. Miller, Classical-limit quantum mechanics and the theory of molecular collisions, in Advances in Chemical Physics, I. Prigogine and S.A. Rice, editors, Vol. 25, Interscience, New York (1974), pp. 69–177.

    Google Scholar 

  143. A.P. Clark, A.S. Dickinson, and D. Richards, The correspondence principle in heavy- particle collisions, in Advances in Chemical Physics, I. Prigogine and S.A. Rice, editors, Vol. 36, Interscience, New York (1977), pp. 63–139.

    Google Scholar 

  144. W.H. Miller, Semiclassical theory of atom-diatom collisions: Path integrals and the classical S matrix, J. Chem. Phys. 53, 1949–1959 (1970).

    CAS  Google Scholar 

  145. R.A. Marcus, Extension of the WKB method to wave functions and transition probability amplitudes (S-matrix) for inelastic or reactive collisions, Chem. Phys. Lett. 7, 525–532 (1970).

    CAS  Google Scholar 

  146. R.A. Marcus, Theory of semiclassical transition probabilities (S matrix) for inelastic and reactive collisions, J. Chem. Phys. 54, 3965–3979 (1971).

    CAS  Google Scholar 

  147. I.C. Percival and D. Richards, A correspondence principle for strongly coupled states, J. Phys. B 3, 1035–1046 (1970).

    Google Scholar 

  148. A.S. Dickinson and D. Richards, A semiclassical study of the body-fixed approximation for rotational excitation in atom-molecule collisions, J. Phys. B 10, 323–343 (1977).

    CAS  Google Scholar 

  149. R.D. Levine and B.R. Johnson, On the classical and semi-classical limits in collision theory, Chem. Phys. Lett. 7, 404–408 (1970).

    CAS  Google Scholar 

  150. Y. Shimoni, D.J. Kouri, and A. Kumar, Close coupling calculations of magnetic transitions for He + H2 in an uncoupled space frame, Chem. Phys. Lett. 52, 299–304 (1977).

    CAS  Google Scholar 

  151. G. Pfeffer and D. Secrest, The rotational sudden approximation at low energies, J. Chem. Phys. 67, 1394–1404 (1977).

    CAS  Google Scholar 

  152. I.C. Percival, A variational principle for scattering phases, Proc. Phys. Soc. (London) 76, 206–216 (1960).

    Google Scholar 

  153. M.J. Seaton, Strong coupling in optically allowed atomic transitions produced by electron impact, Proc. Phys. Soc. (London) 77, 174–183 (1961).

    CAS  Google Scholar 

  154. G.G. Balint-Kurti and R.D. Levine, Opacity analysis of inelastic molecular collisions: Computational studies of the exponential Born approximation for rotational excitation, Chem. Phys. Lett. 7, 107–111 (1970).

    CAS  Google Scholar 

  155. R.D. Levine, Exponential approximations in collision theory, Mol. Phys. 22, 497–523 (1971).

    CAS  Google Scholar 

  156. S. Bosanac and G.G. Balint-Kurti, Cross sections for the rotationally inelastic scattering of Ne + N2: Application of the exponential semi-classical distorted wave approximation, Mol. Phys. 29, 1797–1811 (1975).

    CAS  Google Scholar 

  157. A.S. Dickinson and D. Richards, Rotational excitation of diatomic molecules by atoms, J. Phys. B 7, 1916–1936 (1974).

    CAS  Google Scholar 

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  1. Departments of Chemistry and Physics, University of Houston, Houston, Texas, 77004, USA

    Donald Jack Kouri

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  1. Columbia University, New York, New York, USA

    Richard B. Bernstein

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© 1979 Plenum Press, New York

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Kouri, D.J. (1979). Rotational Excitation II: Approximation Methods. In: Bernstein, R.B. (eds) Atom - Molecule Collision Theory. Springer, Boston, MA. https://doi.org/10.1007/978-1-4613-2913-8_9

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