Skip to main content
SpringerLink
Log in

How to Calculate Rotational and Vibrational Cross Sections for Low-Energy Electron Scattering from Diatomic Molecules using Close-Coupling Techniques

  • Chapter
Computational Methods for Electron—Molecule Collisions

Abstract

This chapter is not a review; electron-molecule dynamics is already replete with fine reviews, many of which appear in books devoted entirely to this topic.1–6 These reviews discuss the applied importance of this field,7–10 survey the status of electron-molecule collision data,11–40 and address specialized topics such as resonance scattering,15 vibrational excitation,16 near-threshold scattering,17–18 particular theoretical approaches such as the R-matrix method,19 numerical methods for solving the Schrödinger equation,20–22 and scattering from polar23,24 and polyatomic25,26 targets. Neither is this chapter primarily pedagogical; readers can find elsewhere a wealth of pedagogically useful tutorial introductions and reviews that narrate the major developments in the field’s long rich history and survey recent advances that have made it the focus of intense activity during the last 20 years.27–30 Rather, this chapter is a “ready reference” of the key equations for the application of one very widely used theoretical strategy—the eigenfunction-expansion or “close-coupling“ method— to one very important class of problems: quantum scattering (at incident energies less than about 10 eV) from a closed-shell diatomic molecule accompanied, perhaps, by rotational and/or vibrational (but not electronic) excitation of the target. As exemplary of an extremely powerful method for reducing multi-variable integro-differential equations to more tractable sets of fewer-variable equations, this class of problems illustrates strategies used in many other theoretical contexts, both within and outside of electron-molecule collisions.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 129.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 169.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 169.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Electron Molecule and Photon-Molecule Collisions, edited by T. N. Rescigno, V. McKoy and B. I. Schneider, (New York, Plenum 1979).

    Google Scholar 

  2. Electron-Molecule Collisions and Photoionization Processes, edited by V. McKoy, H. Suzuki, K. Takayanagi, and S. Trajmar (Deerfield Beach, Florida: Verlag Chemie International, 1983).

    Google Scholar 

  3. Wavefunctions and Mechanisms for Electron Scattering Processes, edited by F. A. Gianturco and G. Stefani (Springer-Verlag, 1984).

    Google Scholar 

  4. Electron-Molecule Interactions and their Applications, Volume 1, edited by L. G. Christophorou (Academic Press, New York, 1984).

    Google Scholar 

  5. Electron-Molecule Collisions, edited by I. Shimamura and K. Takayanagi (New York, Plenum, 1984).

    Google Scholar 

  6. Swarm Studies and Inelastic Electron-Molecule Collisions, edited by L. C. Pitchford, V. McKoy, A. Chutjian, and S. Trajmar (New York: Springer-Verlag, 1986).

    Google Scholar 

  7. G. J. Schulz in Principles of Laser Plasmas, edited by G. Bekite (Wiley, New York, 1976), Chap. 2.

    Google Scholar 

  8. A. V. Phelps in Electron-Molecule Scattering, edited by S. C. Brown (Wiley-Interscience, New York, 1979), Chap. 2.

    Google Scholar 

  9. J. N. Bardsley, in Electron-Molecule Collisions and Photoionization Processes, edited by V. McKoy, H. Suzuki, K. Takayanagi, and S. Trajmar (Deerfield Beach. Fl: Verlag Chemie International, 1983), p.235.

    Google Scholar 

  10. G. S. Willet, Introduction to Gas Lasers—Population Inversion Mechanisms (New York: Pergammon, 1984).

    Google Scholar 

  11. S. Trajmar, D. F. Register, and A. J. Chutjian, Phys. Rept. 97, 220 (1983).

    Article  ADS  Google Scholar 

  12. J. W. McConkey, S. Trajmar, and G. C. M. King, Comments At. Mol. Phys. 22, 17 (1988).

    Google Scholar 

  13. M. Kimura and M. Inokuti, Comments At. Mol. Phys. 24, 269 (1990).

    Google Scholar 

  14. W. L. Morgan, Plasma Chemistry and Plasma Processing 12, 449 (1992); JILA Data Center Report No. 34 (1991).

    Article  Google Scholar 

  15. G. J. Schulz, Rev. Mod. Phys. 45, 423 (1962).

    Article  ADS  Google Scholar 

  16. D. G. Thompson, Adv. At. Mol. Phys. 19, 309 (1984).

    Article  ADS  Google Scholar 

  17. E. Enhardt and L. Frost, Comments At. Mol. Phys. 29, 123 (1993).

    Google Scholar 

  18. M. A. Morrison, Adv. At. Mol. Phys. 24, 51 (1988).

    Article  ADS  Google Scholar 

  19. P. G. Burke, in Quantum Dynamics of Molecules, ed. by R. G. Wooley (New York: Plenum, 1980), pp. 483.

    Chapter  Google Scholar 

  20. M. A. Morrison, in Electron-and Photon-Molecule Collisions edited by T. N. Rescigno, B. V. McKoy and B. I. Schneider (Plenum Press, New York, 1979).

    Google Scholar 

  21. B. D. Buckley, P. G. Burke, and C. J. Noble in Electron-Molecule Collisions edited by I. Shimamura and K. Takayanagi (Plenum, New York, 1984) page 495.

    Chapter  Google Scholar 

  22. L. A. Collins and B. I. Schneider, in Electron-Molecule Scattering Processes and Photoionization, edited by P. G. Burke and J. B. West (New York: Plenum, 1988).

    Google Scholar 

  23. Y. Itikawa, Phys. Rept. 46, 117 (1978).

    Article  ADS  Google Scholar 

  24. L. A. Collins and D. W. Norcross, Adv. At. Mol. Phys. 18, 341 (1983).

    Google Scholar 

  25. D. G. Thompson and F. A. Gianturco, Comments At. Mol. Phys. 16, 307 (1985).

    Google Scholar 

  26. F. A. Gianturco and A. Jain, Phys. Rept. 143, 347 (1986).

    Article  ADS  Google Scholar 

  27. D. E. Golden, N. F. Lane, A. Temkin, and E. Gerjuoy, Rev. Mod. Phys. 43, 642 (1971).

    Article  ADS  Google Scholar 

  28. P. G. Burke, Adv. At. Mol. Phys. 15, 471 (1979).

    Article  ADS  Google Scholar 

  29. N. F. Lane, Rev. Mod. Phys. 52, 29 (1980).

    Article  ADS  Google Scholar 

  30. M. A. Morrison, Aust. J. Phys. 36, 239 (1983).

    Article  ADS  Google Scholar 

  31. M. Born and J. R. Oppenheimer, Ann. Phys. (Leipzig) 84, 457 (1927).

    ADS  MATH  Google Scholar 

  32. M. A. Morrison, T. L. Estle, and N. F. Lane, Quantum States of Atoms, Molecules, and Solids (Prentice-Hall, Englewood Cliffs, New Jersey, 1977).

    Google Scholar 

  33. A primary resource for electron-molecule codes is the program library of Computer Physics Communcations. Information is available from Department of Applied Mathematics and Theoretical Physics, The Queen’s University of Belfast, Belfast BT7 INN, Northern Ireland.

    Google Scholar 

  34. M. A. Morrison and G. A. Parker, Aust. J. Phys. 40, 465 (1987).

    Article  ADS  Google Scholar 

  35. M. E. Rose, Elementary Theory of Angular Momentum (New York, Wiley, 1957).

    MATH  Google Scholar 

  36. D. A. Varshalovich, A. N. Moskalev and V. K. Khersonskii, Quantum Theory of Angular Momentum (World Scientific, Singapore, 1988).

    Google Scholar 

  37. R. N. Zare, Angular Momentum: Understanding Spatial Aspects in Chemistry and Physics (Wiley, New York, 1988).

    Google Scholar 

  38. D. M. Brink and G. R. Satchler, Angular Momentum (Third Edition) (New York: Oxford, 1993).

    Google Scholar 

  39. B. I. Schneider and L. A. Collins, J. Phys. B: At. Mol. Phys. 15, L335 (1982); Phys. Rev. A 27, 2847 (1983).

    Article  ADS  Google Scholar 

  40. H. D. Meyer, J. Phys. B: At. Mol. Phy. 25, 2657 (1992).

    Article  ADS  Google Scholar 

  41. T. L. Gibson and M. A. Morrison, Phys. Rev. A 29, 2497 (1984).

    Article  ADS  Google Scholar 

  42. J. K. O’Connell and N. F. Lane, Phys. Rev. A 27, 1893 (1983).

    Article  ADS  Google Scholar 

  43. A. Jain and D. W. Norcross, Phys. Rev. A 34, 739 (1986).

    Google Scholar 

  44. M. A. Morrison and W. K. Trail, Phys. Rev. A 48, 2874 (1993).

    Article  ADS  Google Scholar 

  45. M. J. Seaton, Comments At. Mol. Phys. 1, 184 (1970).

    ADS  Google Scholar 

  46. M. A. Morrison, and L. A. Collins, Phys. Rev. A 23, 127 (1981).

    Article  ADS  Google Scholar 

  47. L. A. Collins, W. D. Robb, and M. A. Morrison, Phys. Rev. A 21, 488 (1980).

    Article  ADS  Google Scholar 

  48. B. I. Schneider and L. A. Collins, Comput. Phys. Rpt. 10, 51 (1989).

    ADS  Google Scholar 

  49. E. R. Cohen and B. N. Taylor, Rev. Mod. Phys. 59, 1121 (1987).

    Article  ADS  Google Scholar 

  50. N. F. Mott and H. S. W. Massey, The Theory of Atomic Collisions (Third Edition) (Oxford: Clarendon Press, 1965).

    Google Scholar 

  51. J. R. Taylor, Scattering Theory, (New York: Wiley, 1972).

    Google Scholar 

  52. S. Hara, J. Phys. Soc. Jpn. 27, 1592 (1969).

    Article  ADS  Google Scholar 

  53. A. Temkin and K. V. Vasavada, Phys. Rev. A 160, 190 (1967).

    Google Scholar 

  54. N. Chandra and A. Temkin, Phys. Rev. A 13, 188 (1976).

    Article  ADS  Google Scholar 

  55. M. A. Morrison, A. N. Feldt, and D. A. Austin, Phys. Rev. A 29, 2518 (1984).

    Article  ADS  Google Scholar 

  56. A. N. Feldt and M. A. Morrison, Phys. Rev. A 29, 401 (1984).

    Article  ADS  Google Scholar 

  57. M. A. Morrison, Understanding Quantum Physics: A User’s Manual (Prentice-Hall Inc., Englewood Cliffs, NJ, 1990).

    Google Scholar 

  58. A. M. Arthurs and A. Dalgarno, Proc. R. Soc. London Ser. A 256, 540 (1960).

    Article  MathSciNet  ADS  MATH  Google Scholar 

  59. W. K. Trail, M. A. Morrison, W. A. Isaacs, and B. C. Saha, Phys. Rev. A 41, 4868 (1990).

    Article  ADS  Google Scholar 

  60. R. G. Newton, Scattering Theory of Waves and Particles (Second Edition), (New York: Springer-Verlag, 1982).

    MATH  Google Scholar 

  61. S. Geltman, Topics in Atomic Collision Theory (New York: Academic Press, 1969).

    Google Scholar 

  62. L. S. Rodberg and R. M. Thaler, Introduction to the Quantum Theory of Scattering (New York: Academic Press, 1967).

    Google Scholar 

  63. M. A. Morrison, N. F. Lane, and L. A. Collins, Phys. Rev. A 15, 2186 (1977).

    Article  ADS  Google Scholar 

  64. D. T. Birtwistle and A. Herzenberg, J. Phys. B 4, 53 (1971).

    Article  ADS  Google Scholar 

  65. B. K. Elza, Ph. D. thesis, University of Oklahoma, 1992.

    Google Scholar 

  66. R. K. Nesbet, Variational Methods in Electron-Atom Scattering Theory (New York: Plenum, 1980).

    Book  Google Scholar 

  67. U. Fano, Comments At. Mol. Phys. 1, 140 (1970).

    Google Scholar 

  68. E. S. Chang and U. Fano, Phys. Rev. A 6, 173 (1972).

    Article  ADS  Google Scholar 

  69. K. A. Jerjian and R. J. W. Henry, Phys. Rev. A 31, 585 (1985).

    Article  ADS  Google Scholar 

  70. M. A. Morrison, B. C. Saha, and A. N. Feldt, Phys. Rev. A 30, 2811 (1984).

    Article  ADS  Google Scholar 

  71. A. Temkin and F. H. M. Faisal, Phys. Rev. A 3, 520 (1971).

    Article  ADS  Google Scholar 

  72. M. Shugard, and A. Hazi, Phys. Rev. A 12, 1895 (1975).

    Article  ADS  Google Scholar 

  73. M. A. Morrison, M. Abdolsalami, and B. K. Elza, Phys. Rev. A 43, 3440 (1991).

    Article  ADS  Google Scholar 

  74. A. C. Allison, Adv. At. Mol. Phys. 25, 323 (1988).

    Article  ADS  Google Scholar 

  75. W. N. Sams and D. J. Kouri, J. Chem. Phys. 51, 4809 (1969).

    Article  MathSciNet  ADS  Google Scholar 

  76. N. F. Lane and S. Geltman, Phys. Rev. 160, 53 (1967).

    Article  ADS  Google Scholar 

  77. T. N. Rescigno and A. E. Orel, Phys. Rev. A 25, 2402 (1982).

    Article  ADS  Google Scholar 

  78. M. A. Morrison, Comput. Phys. Commun. 21, 63 (1980).

    Article  ADS  Google Scholar 

  79. L. A. Collins, D. W. Norcross, and G. B. Schmid, Comput. Phys. Commun. 79, 63 (1980).

    Google Scholar 

  80. M. A. Morrison and L. A. Collins, J. Phys. B 10, L119 (1977).

    Article  ADS  Google Scholar 

  81. W. M. Huo, T. L. Gibson, M. A. P. Lima, and V. McKoy, Phys. Rev. A 36, 1632 (1987).

    Article  ADS  Google Scholar 

  82. H.-D. Meyer, Phys. Rev. A 40, 5605 (1989).

    Article  ADS  Google Scholar 

  83. L. Castillejo, I. C. Percival, and M. J. Seaton, Proc. R. Soc. London, Ser. A 254, 259 (1960).

    Article  MathSciNet  ADS  MATH  Google Scholar 

  84. M. A. Morrison and P. J. Hay, Phys. Rev. A 20, 740 (1979).

    Article  ADS  Google Scholar 

  85. C. A. Weatherford, K. Onda, and A. Temkin, J. Phys. B 31, 3620 (1985).

    Google Scholar 

  86. B. K. Elza, T. L. Gibson, M. A. Morrison, and B. C. Saha, J. Phys. B 22, 113 (1989).

    Article  ADS  Google Scholar 

  87. I. C. Percival and M. J. Seaton, Prof. Cambridge Phil. Soc. 53, 654 (1957).

    Article  ADS  MATH  Google Scholar 

  88. H. S. W. Massey, and I. C. Percival, Proc. Roy. Soc. A 274, 427 (1963).

    Article  ADS  Google Scholar 

  89. G. Herzberg, Molecular Spectra and Molecular Structure I: Spectra of Diatomic Molecules (Second Edition) (Van Nostrand, New York, 1950).

    Google Scholar 

  90. K. P. Huber, and G. Herzberg, Molecular Spectra and Molecular Structure IV. Constants of Diatomic Molecules (Van Nostrand, New York, 1979).

    Google Scholar 

  91. A. A. Radzig and B. Smirnov, Reference Data on Atoms, Molecules, and Ions (Springer-Verlag, New York, 1986).

    Google Scholar 

  92. P. M. Morse, Phys. Rev. 34, 57 (1929).

    Article  ADS  MATH  Google Scholar 

  93. M. Abramowitz and I. A. Stegun, Pocketbook of Mathematical Functions (Frankfurt: Deutsch, 1984).

    MATH  Google Scholar 

  94. J. Spanier and K. B. Oldham, An Atlas of Functions (New York: Hemisphere, 1987).

    MATH  Google Scholar 

  95. G. A. Korn and T. M. Korn, Mathematical Handbook for Scientists and Engineers (Second Edition), (New York: McGraw Hill, 1968).

    Google Scholar 

  96. S. Wolfram, Mathematica: A System for Doing Mathematics by Computer (Second Edition) (New York: Adison-Wesley, 1991).

    Google Scholar 

  97. Y. P. Varshni, Rev. Mod. Phys. 29, 664 (1957).

    Article  ADS  Google Scholar 

  98. D. Steele, E. R. Lippincott, and J. T. Vanderslice, Rev. Mod. Phys. 34, 239 (1962).

    Article  ADS  Google Scholar 

  99. G. Simons, R. G. Parr, and J. M. Finlan, J. Chem. Phys. 59, 3229 (1973).

    Article  ADS  Google Scholar 

  100. J. M. Finlan and G. Simons, J. Mol. Spectrosc. 57, 1 (1975).

    Article  ADS  Google Scholar 

  101. D. W. Norcross and N. T. Padial, Phys. Rev. A 25, 226 (1982).

    Article  ADS  Google Scholar 

  102. L. A. Collins and D. W. Norcross Phys. Rev. A 18, 467 (1978).

    Article  ADS  Google Scholar 

  103. N. Chandra, Phys. Rev. A 16, 80 (1977).

    Article  ADS  Google Scholar 

  104. E. Gerjuoy, and S. Stein Phys. Rev. 97, 1671 (1955).

    Article  ADS  Google Scholar 

  105. A. Dalgarno and R. J. Moffett, Proc. Natl. Acad. Sci. India 33, 511 (1963).

    Google Scholar 

  106. L. G. H. Huxley and R. W. Crompton, The Diffusion and Drift of Electrons in Gases (Wiley: New York, 1974).

    Google Scholar 

  107. U. Fano and D. Dill, Phys. Rev. A 6, 185 (1972).

    Article  ADS  Google Scholar 

  108. W. A. Isaacs and M. A. Morrison, J. Phys. B 25, 703 (1992).

    Article  ADS  Google Scholar 

  109. I. I. Fabrikant, J. Phys. B 17, 4223 (1984).

    Article  ADS  Google Scholar 

  110. M. A. Morrison, R. W. Crompton, B. C. Saha, and Z. LjPetrovic, Aust. J. Phys. 40, 239 (1987).

    Article  ADS  Google Scholar 

  111. A. U. Hazi, Phys. Rev. A 19, 920 (1979).

    Article  ADS  Google Scholar 

  112. C. W. Clark, Phys. Rev. A 30, 750 (1984).

    Article  ADS  Google Scholar 

  113. G. Forsythe and C. B. Moler, Computational Solutions of Linear Algebraic Systems (Englewood Cliffs, NJ: Prentice-Hall, 1967).

    Google Scholar 

  114. M. A. Morrison, and N. F. Lane, Chem. Phys. Lett. 66, 527 (1979).

    Article  ADS  Google Scholar 

Download references

Author information

Author notes

  1. Weiguo Sun

    Present address: Department of Chemistry, The Sichuan Union University, Chengdu, Sichuan, 610065, People’s Republic of China

Authors and Affiliations

  1. Department of Physics and Astronomy, University of Oklahoma, Norman, Oklahoma, 73019, USA

    Michael A. Morrison & Weiguo Sun

Authors
  1. Michael A. Morrison
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Weiguo Sun
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. NASA Ames Research Center, Moffet Field, California, USA

    Winifred M. Huo

  2. University of Rome, City of Rome, Rome, Italy

    Franco A. Gianturco

Rights and permissions

Reprints and permissions

Copyright information

© 1995 Springer Science+Business Media New York

About this chapter

Cite this chapter

Morrison, M.A., Sun, W. (1995). How to Calculate Rotational and Vibrational Cross Sections for Low-Energy Electron Scattering from Diatomic Molecules using Close-Coupling Techniques. In: Huo, W.M., Gianturco, F.A. (eds) Computational Methods for Electron—Molecule Collisions. Springer, Boston, MA. https://doi.org/10.1007/978-1-4757-9797-8_6

Download citation

  • DOI: https://doi.org/10.1007/978-1-4757-9797-8_6

  • Publisher Name: Springer, Boston, MA

  • Print ISBN: 978-1-4757-9799-2

  • Online ISBN: 978-1-4757-9797-8

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation