Variational methods have proven to be invaluable tools in theoretical physics and chemistry, both for bound state problems and for the study of collision phenomena. For collisional problems variational methods can be grouped into two types, those based on the Schrödinger equation and those based on the Lippmann-Schwinger equation. The Hulthén-Kohn1–3 method belongs to the first type, and their modern development for electron-molecule scattering, incorporating complex boundary conditions, is reported in chapter 1 of this book by Rescigno et al.4 An offshoot of the Hulthén-Kohn variational method is the variational R-matrix method.5, 6 In chapter 8 of this book Schneider7 presents a general discussion of the R-matrix method, including the variational R-matrix.


Trial Function Closed Channel Continuum Electron Correct Boundary Condition Vibrational Excitation Cross Section 
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  1. 1.
    L. Hulthén, Kgl. Fysiograf. Sälbkap. Lund. Fröh. 14, 257 (1944).Google Scholar
  2. 2.
    W. Kohn, Phys. Rev. 74, 1763 (1948).ADSzbMATHCrossRefGoogle Scholar
  3. 3.
    S.I. Rubinow, Phys. Rev. 96, 218 (1954).MathSciNetADSzbMATHCrossRefGoogle Scholar
  4. 4.
    T.N. Rescigno, C.W. McCurdy, A.E. Orel, and B.H. Lengsfield III, “The Complex Kohn Variational Method,” chapter 1 in this book.Google Scholar
  5. 5.
    J.L. Jackson, Phys. Rev. 83, 301 (1951).ADSzbMATHCrossRefGoogle Scholar
  6. 6.
    R.K. Nesbet, Variational Methods in Electron-Atom Scattering Theory, Plenum Press, New York (1980).CrossRefGoogle Scholar
  7. 7.
    B.I. Schneider, “An R-Matrix Approach to Electron Molecule Collisions,” chapter 8 in this book.Google Scholar
  8. 8.
    J. Schwinger, Phys. Rev. 56, 750 (1947).Google Scholar
  9. 9.
    R.R. Lucchese, K. Takatsuka, and V. McKoy, Phys. Rep. 131, 147 (1986).ADSCrossRefGoogle Scholar
  10. 10.
    D.K. Watson, Adv. At. Mol. Phys. 25, 221 (1988).ADSCrossRefGoogle Scholar
  11. 11.
    M.A.P. Lima, T.L. Gibson, L.M. Brescansin, V. McKoy, and W.M. Huo, “Studies of Elastic and Electronically Inelastic Electron-Molecule Collisions,” in Swarm Studies and Inelastic Electron-Molecule Collisions, ed. L.C. Pitchford, B.V. McKoy, A. Chutjian, and S. Trajmar, Springer-Verlag, New York (1987), pp 239–264.CrossRefGoogle Scholar
  12. 12.
    C. Winstead and V. McKoy, “Studies of Electron-Molecule Collisions on Highly Parallel Computers,” in Modern Electronic Structure Theory Vol. 2, ed. D. Yarkony, World Scientific, Singapore (1994).Google Scholar
  13. 13.
    D.K. Watson and V. McKoy, Phys. Rev. A 20, 1474 (1979).ADSCrossRefGoogle Scholar
  14. 14.
    R.R. Lucchese, G. Raseev, and V. McKoy, Phys. Rev. A 25, 2572 (1982).ADSCrossRefGoogle Scholar
  15. 15.
    See, for example, G. Bandarage and R.R. Lucchese, Phys. Rev. A 47, 1989 (1993)ADSCrossRefGoogle Scholar
  16. M.-T. Lee, K. Wang, and V. McKoy, J. Chem. Phys. 97, 3108 (1992).ADSCrossRefGoogle Scholar
  17. 16.
    M.-T. Lee, M.M. Fujimoto. S.E. Michelin, L.E. Machado, and L.M. Brescansin, J. Phys. B. 25, L505 (1992).ADSCrossRefGoogle Scholar
  18. 17.
    M.-T. Lee, S.E. Michelin, L.M. Brescansin, G.D. Meneses, and L.E. Machado, J. Phys. B. 26, L477 (1993).ADSCrossRefGoogle Scholar
  19. 18.
    K. Takatsuka and V. McKoy, Phys. Rev. A 24, 2473 (1981).MathSciNetADSCrossRefGoogle Scholar
  20. 19.
    K. Takatsuka and V. McKoy, Phys. Rev. A 30, 1734 (1981).MathSciNetADSCrossRefGoogle Scholar
  21. 20.
    W.M. Huo and J.A. Sheehy (to be published).Google Scholar
  22. 21.
    C. Winstead, Q. Sun, and V. McKoy, J. Chem. Phys. 97, 9483 (1992).ADSCrossRefGoogle Scholar
  23. 22.
    W.M. Huo and J.A. Sheehy, “Theoretical Study of Electron Scattering by Small Clusters and Adsorbates,” in Electron Collisions with Molecules, Clusters, and Surfaces, ed. H. Ehrhardt and L.A. Morgan, Plenum, New York (1994), pp 171–182.Google Scholar
  24. 23.
    W. Domcke, Phys. Rep. 208, 97 (1991).ADSCrossRefGoogle Scholar
  25. 24.
    R.G. Newton, Scattering Theory of Waves and Particles, Springer-Verlag, New York (1982).zbMATHGoogle Scholar
  26. 25.
    B.H. Bransden, R. Hewitt, and M. Plummer, J. Phys. B 21, 2645 (1988).ADSCrossRefGoogle Scholar
  27. 26.
    S.K. Adhikari and I.H. Sloan, Phys. Rev. C 11, 1133 (1975).ADSCrossRefGoogle Scholar
  28. 27.
    K. Takatsuka, R.R. Lucchese, and V. McKoy, Phys. Rev. A 24, 1812 (1981).MathSciNetADSCrossRefGoogle Scholar
  29. 28.
    J.T. Taylor, Scattering Theory, R. E. Krieger Publishing, FL (1983), pp. 274–279.Google Scholar
  30. 29.
    H. Feshbach Ann. Phys. 5. 357 (1958); ibid 19, 287 (1962).MathSciNetADSzbMATHCrossRefGoogle Scholar
  31. 30.
    M.A.P. Lima and V. McKoy, Phys. Rev. A 38, 501 (1988).ADSCrossRefGoogle Scholar
  32. 31.
    W.M. Huo and C.A. Weatherford, BuU. Am. Phys. Soc. 36, 1265 (1991).Google Scholar
  33. 32.
    C. Winstead and V. McKoy, Phys. Rev. A 47, 1514 (1993).ADSCrossRefGoogle Scholar
  34. 33.
    T. Helgaker and P.R. Taylor, “Gaussian Basis Sets and Molecular Integrals” in Modern Electronic Structure Theory Vol. 2, ed. D. Yarkony, World Scientific, Singapore (1994).Google Scholar
  35. 34.
    T.H. Dunning, J. Chem. Phys. 53, 2823 (1970).ADSCrossRefGoogle Scholar
  36. 35.
    T.H. Dunning, J. Chem. Phys. 90, 1007 (1989)ADSCrossRefGoogle Scholar
  37. and D.E. Woon and T.H. Dunning, J. Chem. Phys. 98, 1358 (1993).ADSCrossRefGoogle Scholar
  38. 36.
    As an example of valence excitation calculations which neglected Rydberg states in the open channel configurations, see Q. Sun, C. Winstead, V. McKoy, J.S.E. Germano, and M.A.P. Lima, Phys. Rev. A 46, 2462 (1992).ADSCrossRefGoogle Scholar
  39. 37.
    W.M. Huo, M.A.P. Lima, T.L. Gibson, and V. McKoy, Phys. Rev. A 36, 1642 (1987).ADSCrossRefGoogle Scholar
  40. 38.
    B.H. Lengsfield, T.N. Rescigno, and C.W. McCurdy, Phys. Rev. A 44, 4296 (1991).ADSCrossRefGoogle Scholar
  41. 39.
    W.M. Huo, T.L. Gibson, M.A.P. Lima, and V. McKoy, Phys. Rev. A 36, 1632 (1987).ADSCrossRefGoogle Scholar
  42. 40.
    A.J.R. da Silva, M.A.P. Lima, L.M. Brescansin, and V. McKoy, Phys. Rev. A 41, 2903 (1991).CrossRefGoogle Scholar
  43. 41.
    T.L. Gibson, M.A.P. Lima, V. McKoy, and W.M. Huo, Phys. Rev. A 35, 2473 (1987).ADSCrossRefGoogle Scholar
  44. 42.
    N.S. Ostlund, Chem. Phys. Letters, 34, 419 (1975).ADSCrossRefGoogle Scholar
  45. 43.
    W.M. Huo and J.A. Sheehy (to be published). See also J.A. Sheehy and W.M. Huo, “Low-Energy Elastic Electron Scattering from Carbon Tetrafluoride” in ICPEAC Abstracts Vol. I, ed. T. Andersen, B. Fastrup, F. Folkmann, H. Knudsen, (1993), p. 259.Google Scholar
  46. 44.
    C. Winstead, Q. Sun, and V. McKoy, J. Chem. Phys. 98, 1105 (1993).ADSCrossRefGoogle Scholar
  47. 45.
    W.M. Huo, Phys. Rev. A 38, 3303 (1988).ADSCrossRefGoogle Scholar
  48. 46.
    A. Mann and F. Linder, J. Phys. B 25, 545 (1992).ADSCrossRefGoogle Scholar
  49. 47.
    L. Boesten, H. Tanaka, A. Kobayashi, M.A. Dillon, and M. Kimura, J. Phys. B 25, 1607 (1992).ADSCrossRefGoogle Scholar
  50. 48.
    D.W. Norcross and N.T. Padial, Phys. Rev. A 25, 226 (1982).ADSCrossRefGoogle Scholar
  51. 49.
    S. Chung and C.C. Lin, Phys. Rev. A 17, 1874 (1978).ADSCrossRefGoogle Scholar
  52. 50.
    A.W. Fliflet and V. McKoy, Phys. Rev. A 21, 1863 (1980).ADSCrossRefGoogle Scholar
  53. 51.
    T.N. Rescigno, C.W. McCurdy, Jr., and V. McKoy, J. Phys. B 7, 2396 (1974).ADSCrossRefGoogle Scholar
  54. 52.
    S.K. Srivastava and S. Jensen, J. Phys. B 10, 3341 (1977).ADSCrossRefGoogle Scholar
  55. See S. Trajmar, D.F. Register, and A. Chutjian, Phys. Rep. 97, 219 (1983) for renormalization of this data.ADSCrossRefGoogle Scholar
  56. 53.
    M.A. Khakoo and S. Trajmar, Phys. Rev A 34, 146 (1986).ADSCrossRefGoogle Scholar
  57. 54.
    T.N. Rescigno, B.H. Lengsfield, C.W. McCurdy, and S.D. Parker, Phys. Rev. A 45, 7800 (1992).ADSCrossRefGoogle Scholar
  58. 55.
    H.J.R. Walters, J. Phys. B 4, 437 (1971).ADSCrossRefGoogle Scholar
  59. 56.
    E.J. Heller and W.P. Reinhardt, Phys. Rev. A 7, 365 (1973).MathSciNetADSCrossRefGoogle Scholar
  60. 57.
    M.A.P. Lima, L.M. Brescansin, A.J.R. da Silva, C. Winstead, and V. McKoy, Phys. Rev. A 41, 327 (1990).ADSCrossRefGoogle Scholar
  61. 58.
    C. Winstead, P.G. Hipes, M.A.P. Lima, and V. McKoy, J. Chem. Phys. 94, 5455 (1991).ADSCrossRefGoogle Scholar
  62. 59.
    D.A. Levin, A.W. Fliflet, M. Ma, and V. McKoy, J. Comp. Phys. 28, 416 (1978).ADSCrossRefGoogle Scholar
  63. 60.
    B.I. Schneider, Phys. Rev. A 31, 2188 (1985).ADSCrossRefGoogle Scholar
  64. 61.
    M.H.F. Bettega, L.G. Ferreira, and M.A.P. Lima, Phys. Rev. A 47 1111 (1993).ADSCrossRefGoogle Scholar
  65. 62.
    B.H. Lengsfield III and T.N. Rescigno, Phys. Rev. A 44, 2913 (1991).ADSCrossRefGoogle Scholar
  66. 63.
    T.N. Rescigno, B.H. Lengsfield III, and A.E. Orel, J. Chem. Phys. 99, 5097 (1993).ADSCrossRefGoogle Scholar
  67. 64.
    C.J. Gillan, O. Nagy, P.G. Burke, L.A. Morgan and C.J. Noble, J. Phys. B 20, 4585 (1987).ADSCrossRefGoogle Scholar
  68. 65.
    S.E. Branchett and J. Tennyson, Phys. Rev. Letts. 64, 2889 (1990).ADSCrossRefGoogle Scholar
  69. 66.
    W.M. Huo, V. McKoy, M.A.P. Lima, and T.L. Gibson, “Electron-Nitrogen Molecule Collisions in High-Temperature Nonequilibrium Air,” in Thermalphysical Aspects of Re-entry Flows, ed. J.N. Moss and CD. Sott, AIAA, New York (1986), pp. 152-196.Google Scholar
  70. 67.
    M. Berman, H. Estrada, L.S. Cederbaum, and W. Domcke, Phys. Rev. A 28, 1363 (1983).ADSCrossRefGoogle Scholar
  71. 68.
    S.F. Wong, J.A. Michejda, and A. Stamatovic, unpublished data.Google Scholar

Copyright information

© Springer Science+Business Media New York 1995

Authors and Affiliations

  • Winifred M. Huo
    • 1
  1. 1.NASA Ames Research CenterMoffett FieldUSA

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