Skip to main content
SpringerLink
Log in
Book cover

Theory of Slow Atomic Collisions pp 202–242Cite as

Approximate Calculation of a Multichannel Quasi-classical Scattering Matrix

  • Chapter

  • 265 Accesses

Part of the book series: Springer Series in Chemical Physics ((CHEMICAL,volume 30))

Abstract

An exact calculation of the scattering matrix calls for the numerical solution of a system of second-order scattering equations formulated using a basis of electronic functions. However, the basis functions and the corresponding interactions are usually known only approximately. The only exception is the interaction at large distances, where the general perturbation approach can be used (Chap. 4).

This is a preview of subscription content, 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   84.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   109.99
Price excludes VAT (USA)
  • Compact, lightweight 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

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. J. A. Gaunt: Proc. Cambridge Philos. Soc. 23, 732 (1927)

    MATH  Google Scholar 

  2. N. F. Mott: Proc. Cambridge Philos. Soc. 27, 553 (1931)

    Google Scholar 

  3. D. R. Bates: In Atomic and Molecular Processes, ed. by D.R. Bates ( Academic, New York 1962 ) p. 550

    Google Scholar 

  4. D. R. Bates: Comments At. Mol. Phys. 3, 23 (1971)

    Google Scholar 

  5. B. H. Bransden: Atomic Collision Theory (Benjamin, New York 1970 )

    Google Scholar 

  6. H. S. W. Massey, E.H.S. Burhop, H.B. Gilbody: Slow Collisions of Heavy Particles, 2nd ed., Electronic and Ionic Impact Phenomena, Vol. 3 ( Clarendon, Oxford 1971 )

    Google Scholar 

  7. M. R. C. McDowell, J.P. Coleman: Introduction to the Theory of Ion-Atom Collisions ( North-Holland, Amsterdam 1970 )

    Google Scholar 

  8. N. F. Mott, H. S. W. Massey: The Theory of Atomic Collisions ( Clarendon, Oxford 1965 )

    Google Scholar 

  9. B. M. Smirnov: Atomnye Stolknoveniya i Elementarnye Protesessy v Plazme ( Atomizdat, Moscow 1968 )

    Google Scholar 

  10. B. M. Smirnov: Asimptoticheskie Me tody v Teorii Atomnykh Stolknovenii ( Atomizdat, Moscow 1973 )

    Google Scholar 

  11. I. I. Sobelman, L. A. Vainshtein, E. A. Yukov: Excitation of Atoms and Broadening of Spectral Lines, Springer Ser. Chem. Phys., Vol. 7 ( Springer, Berlin, Heidelberg, New York 1981 )

    Google Scholar 

  12. R. B. Bernstein (ed.): Atom-Molecule Collision Theory. A Guide for Experimentalists ( Plenum, New York 1979 )

    Google Scholar 

  13. V. N. Kondratiev, E.E. Ni kitin: Gas-Phase Reactions. Kinetics and Mechanisms (Springer, Berlin, Heidelberg, New York 1981 )

    Google Scholar 

  14. E. E. Nikitin: Theory of Elementary Atomic and Molecular Processes in Gases ( Clarendon, Oxford 1974 )

    Google Scholar 

  15. G. Breit, R. L. Gluckstern: In Handbuch der Physik, Vol.41, ed. by S. Flügge (Springer, Berlin, Heidelberg, New York 1959 ) p. 496

    Google Scholar 

  16. W. Nörenberg, H. A. Weidenmüller: Introduction to the Tteory of Heavy- Ion Collisions, 2nd ed., Lecture Notes Phys., Vol. 51 ( Springer, Berlin, Heidelberg, New York 1980 )

    Google Scholar 

  17. J. W. Frame: Proc. Cambridge Philos. Soc. 27, 511 (1931)

    Google Scholar 

  18. B. L. Moiseiwitsch: Proc. Phys. Soc. London 87, 885 (1966)

    Article  Google Scholar 

  19. A. V. Vinogradov: Opt. Spektrosk. 22, 663 (1967)

    Google Scholar 

  20. F. W. Byron: Phys. Rev. A4, 1907 (1971)

    Article  ADS  Google Scholar 

  21. D. Campos, H. Krüger: J. Phys. B11, 687 (1978)

    Article  ADS  MathSciNet  Google Scholar 

  22. J. C. Y. Chen, T. Ishihara, V. H. Ponce, K. M. Watson: Phys. Rev. A8, 1334 (1973)

    Article  ADS  Google Scholar 

  23. J. C. Y. Chen, C. J. Joachain, K. M. Watson: Phys. Rev. A5, 1268 (1972)

    Article  ADS  Google Scholar 

  24. J. C. Y. Chen, C. S. Wang, K.M. Watson: Phys. Rev. AI, 1150 (1970)

    Google Scholar 

  25. J. C. Y. Chen, K. M. Watson: Phys. Rev. 174, 152 (1968)

    Article  ADS  Google Scholar 

  26. M.R. Flannery, K. J. McCann: Phys. Rev. A8, 2915 (1973)

    Article  ADS  Google Scholar 

  27. R. McCarroll: In Atoms, Molecules and Lasers, Lectures presented at the Int. Winter Colloquium in Trieste 1973 (Intern. Atomic Energy Agency, Vienna 1974 ) p. 471

    Google Scholar 

  28. M. R. Bates, D. S. F. Crothers: Proc. Roy. Soc. London A315, 465 (1970)

    Article  ADS  Google Scholar 

  29. I. Ya. Berson: Izv. Akad. Nauk Latv. SSSR, Ser. Fiz. Tekh. Nauk 4, 47 (1968)

    Google Scholar 

  30. I. Ya. Berson: Izv. Akad. Nauk Latv. SSSR, Ser. Fiz. Tekh. Nauk 4, 47 (1968)

    Google Scholar 

  31. M. S. Child: Mol. Phys. 20, 171 (1971)

    Article  ADS  Google Scholar 

  32. R. J. Cross, Jr.: J. Chem. Phys. 51, 5163 (1969)

    Article  ADS  Google Scholar 

  33. J. B. Delos, W. R. Thorson: Phys. Rev. Aß, 720 (1972)

    Google Scholar 

  34. J. B. Delos, W. R. Thorson, S.K. Knudson: Phys. Rev. A6, 709 (1972)

    Article  ADS  Google Scholar 

  35. G. V. Dubrovskii: Zh. Eksp. Teor. Fiz. 58, 1075 (1970) [English transl.: Sov. Phys. JETP 31(58), 577 (1970)]

    Google Scholar 

  36. Ch. Gaussorgues, C. Le Sech, F. Masnou-Seeuws, R. McCarroll, A. Riera: J. Phys. B8, 240 (1975)

    ADS  Google Scholar 

  37. K. P. Lawley, J. Ross: J. Chem. Phys. 43, 2930 (1965)

    Article  ADS  MathSciNet  Google Scholar 

  38. R. McCarroll: In Atomic Processes and Applications, ed. by P.G. Burke, B.L. Moiseiwitsch ( North-Holland, Amsterdam 1976 ) p. 469

    Google Scholar 

  39. B. L. Moisweiwitsch: Rep. Prog. Phys. 40, 843 (1977)

    Article  ADS  Google Scholar 

  40. M. E. Riley: Phys. Rev. A8, 742 (1973)

    Article  ADS  Google Scholar 

  41. S. D. Augustin, H. Rabitz: J. Chem. Phys. 69, 4195 (1978)

    Article  ADS  Google Scholar 

  42. M. H. Mittleman: Phys. Rev. 122, 499 (1961)

    Article  ADS  MathSciNet  Google Scholar 

  43. P. Pechukas: Phys. Rev. 181, 166 (1969)

    Article  ADS  Google Scholar 

  44. P. Pechukas: Phys. Rev. 181, 174 (1969)

    Article  ADS  Google Scholar 

  45. A. P. Penner, R. Wallace: Phys. Rev. A7, 1007 (1973)

    Article  ADS  Google Scholar 

  46. B. Corrigall, B. Kupers, R. Wallace: Phys. Rev. A4, 977 (1971)

    Article  ADS  Google Scholar 

  47. T. A. Green: Phys. Rev. A23, 532 (1981)

    ADS  Google Scholar 

  48. R. E. Turner, J.S. Dahler: J. Phys. B13, 161 (1980)

    Article  ADS  MathSciNet  Google Scholar 

  49. E. Gerjuoy: Case Stud. At. Phys. 3, 1 (1972)

    Google Scholar 

  50. R. Shakershaft: J. Phys. B5, 559 (1972)

    ADS  Google Scholar 

  51. R. Shakershaft, J. Macek, E. Gerjuoy: J. Phys. B6, 794 (1973)

    ADS  Google Scholar 

  52. R. J. Glauber: In Lectures in Theoretical Physics, Vol.1, ed. by W.E. Brittin, L.G. Dunham ( Interscience, New York 1959 ) p. 315

    Google Scholar 

  53. M. L. Goldberger, K.M. Watson: Collision Theory ( Wiley, New York 1964 )

    MATH  Google Scholar 

  54. R. G. Newton: Scattering Theory of Waves and Particles, 2nd ed., Texts and Monographs in Phys. (Springer, Berlin, Heidelberg, New York 1982 )

    MATH  Google Scholar 

  55. E. Gerjuoy, B. C. Thomas: Rep. Prog. Phys. 37, 1345 (1974)

    Article  ADS  Google Scholar 

  56. C. J. Joachim, C. Quigg: Rev. Mod. Phys. 46, 279 (1974)

    Article  ADS  Google Scholar 

  57. L. D. Landau, E. M. Lifshitz: Quantum Mechanics, 3rd rev. ed. ( Pergamon, Oxford 1977 )

    Google Scholar 

  58. N. Froman, P. O. Froman: JWKB Approximation: Contribution to the Theory ( North-Holland, Amsterdam 1965 )

    Google Scholar 

  59. A. H. Nayfeh: Perturbation Methods ( Wiley, New York 1973 )

    MATH  Google Scholar 

  60. B. C. Eu, N. Zaritsky: J. Chem. Phys. 70, 4986 (1979)

    Article  ADS  Google Scholar 

  61. T. A. Green, M.E. Riley: Phys. Rev. A8, 2938 (1973)

    Article  ADS  Google Scholar 

  62. B. R. Johnson: Chem. Phys. 2, 381 (1973); D. Campos: J. Phys. B14, 2585 (1981); M.F. Herman: J. Chem. Phys. 76, 2949 (1982); H. Nakamura: Phys. Rev. A26, 3125 (1982); M.F. Herman: J. Chem. Phys. 79, 2771 (1983)

    Google Scholar 

  63. E. J. Shipsey: J. Chem. Phys. 59, 5109 (1973)

    Article  ADS  Google Scholar 

  64. E. J. Shipsey: J. Chem. Phys. 60, 1589 (1974)

    Article  ADS  Google Scholar 

  65. E. J. Shipsey: MoT. Phys. 35, 81 (1978)

    Article  ADS  Google Scholar 

  66. E. J. Shipsey: J. Chem. Phys. 70, 5281 (1979)

    Article  ADS  MathSciNet  Google Scholar 

  67. L. Landau: Phys. T. Sowietunion 2, 46 (1932)

    MATH  Google Scholar 

  68. A. M. Dykhne: Zh. Eksp. Teor. Fiz. 41, 1324 (1961) [English transl.: Sov. Phys. JETP 14(41), 941 (1962)]

    Google Scholar 

  69. M. Matsuzawa: J. Phys. Soc. Jpn. 23, 1383 (1967)

    Article  ADS  Google Scholar 

  70. J. P. Davis, P. Pechukas: J. Chem. Phys. 64, 3129 (1976)

    Article  ADS  Google Scholar 

  71. Yu. N. Demkov, V.N. Ostrovskii, E.D. Solov’ev: Phys. Rev. A18, 2089 (1978)

    Google Scholar 

  72. E. A. Solov’ev: Vestn. Leningr. Univ. Fiz. Khim. 4, 10 (1976)

    Google Scholar 

  73. J. T. Hwang, P. Pechukas: J. Chem. Phys. 67, 4640 (1977)

    Article  ADS  MathSciNet  Google Scholar 

  74. F. J. McLafferty, T.F. George: J. Chem. Phys. 63, 2609 (1975)

    Article  ADS  Google Scholar 

  75. E. P. Gordeev, E.E. Niktin, A.I. Shushin: Mol. Phys. 33, 1611 (1977)

    Article  ADS  Google Scholar 

  76. E. A. Solov’ev: Teor. Mat. Fiz. 28, 115 (1976) [English transl.: Theor. Math. Phys. USSR 28, 669 (1976)]

    Google Scholar 

  77. T. F. George, K. Morokuma: Chem. Phys. 2, 129 (1973)

    Article  Google Scholar 

  78. R. L. Jaffe, A. D. Isaacson, J. R. Laing, K. Morokuma, T. F. George: Theor. Chim, Acta 40, 189 (1975)

    Article  Google Scholar 

  79. R. L. Jaffe, T. F. George, K. Morokuma: Mol. Phys. 28, 1489 (1974)

    Article  ADS  Google Scholar 

  80. K. D. Jordan: Chem. Phys. 9, 199 (1975)

    Article  ADS  Google Scholar 

  81. K. D. Jordan: Int. J. Quantum Chem. Symp. 9, 325 (1975)

    Article  Google Scholar 

  82. R. K. Preston, C. Sloane, W. H. Miller: J. Chem. Phys. 60, 4961 (1974)

    Article  ADS  Google Scholar 

  83. P. Pechukas, T. F. George, K. Morokuma, F. J. McLafferty, J. R. Laing: J. Chem. Phys. 64, 1099 (1976)

    Article  ADS  Google Scholar 

  84. W. N. Whitton: Mol. Phys. 36, 941 (1978)

    Article  ADS  MathSciNet  Google Scholar 

  85. R. M. Wilcox: J. Math. Phys. 8, 962 (1967)

    Article  MATH  ADS  MathSciNet  Google Scholar 

  86. A. I. Shushin: Chem. Phys. Lett. 55, 535 (1978)

    Article  ADS  Google Scholar 

  87. A. I. Shushin: Opt. Spektrosk. 49, 103 (1980) [English transl.: Opt. Spectrosc. USSR 49, 54 (1980)]

    Google Scholar 

  88. A. M. Dykhne, G. L. Yudin: Usp. Fiz. Nauk 125, 377 (1978) [English transl. Sov. Phys. Usp. 21, 549 (1978)]

    Google Scholar 

  89. E. I. Dashevskaya: Chem. Phys. Lett. 11, 184 (1971)

    Article  ADS  Google Scholar 

  90. E. I. Dashevskaya, N.A. Mokhova: Opt. Spektrosk. 33, 817 (1972) [English transl.: Opt. Spectrosc. USSR 33, 452 (1972)]

    Google Scholar 

  91. B. C. Eu: J. Chem. Phys. 56, 2507 (1972)

    Article  ADS  Google Scholar 

  92. B. C. Eu: J. Chem. Phys. 58, 472 (1973)

    Article  ADS  Google Scholar 

  93. B. C. Eu: J. Chem. Phys. 59, 4705 (1973)

    Article  ADS  Google Scholar 

  94. B. C. Eu, T. P. Tsien: Chem. Phys. Lett. 17, 256 (1972)

    Article  ADS  Google Scholar 

  95. T. Uzer, M. S. Child: Mol. Phys. 41, 1177 (1980); R. J. Bieniek: Phys. Rev. A23, 2826 (1981)

    Google Scholar 

  96. S. Bosanac: J. Math. Phys. 20, 396 (1979)

    Article  ADS  Google Scholar 

  97. R. D. Levine: Mol. Phys. 22, 497 (1971)

    Article  ADS  Google Scholar 

  98. U. I. Cho, B. C. Eu: Mol. Phys. 32, 19 (1976)

    Article  ADS  Google Scholar 

  99. B. C. Eu, T. P. Tsien: Phys. Rev. A7, 648 (1973); H. J. Korsch: Mol. Phys. 49, 325 (1983); B.C. Eu: Semiclassical Theories of Molecular Scattering, Springer Ser. Chem. Phys., Vol. 26 ( Sprinqer, Berlin, Heidelberq, New York, Tokyo 1984 )

    Google Scholar 

  100. C. H. Wang, W. J. Tomlison: Phys. Rev. 181, 115 (1969)

    Article  ADS  Google Scholar 

  101. M. Mori: J. Phys. Soc. Jpn. 23, 1086 (1967)

    Article  ADS  Google Scholar 

  102. P. Pechukas, J. C. Light: J. Chem. Phys. 44, 3897 (1966)

    Article  ADS  Google Scholar 

  103. D. Richards: J. Phys. B14, 1465 (1981)

    ADS  Google Scholar 

  104. J. Eichler: Phys. Rev. A15, 1856 (1977); R. E. Turner: J. Phys. A13, 2079 (1980)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Institute of Chemical Physics, Academy of Sciences of the USSR, Kosygin Street 4, V-334, Moscow, USSR

    Professor Evgenii E. Nikitin & Stanislav Ya. Umanskii

Authors
  1. Professor Evgenii E. Nikitin
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Stanislav Ya. Umanskii
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

Copyright information

© 1984 Springer-Verlag Berlin Heidelberg

About this chapter

Cite this chapter

Nikitin, E.E., Umanskii, S.Y. (1984). Approximate Calculation of a Multichannel Quasi-classical Scattering Matrix. In: Theory of Slow Atomic Collisions. Springer Series in Chemical Physics, vol 30. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-82045-8_6

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-82045-8_6

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-82047-2

  • Online ISBN: 978-3-642-82045-8

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation