The Complex Kohn Variational Method

  • T. N. Rescigno
  • C. W. McCurdy
  • A. E. Orel
  • B. H. LengsfieldIII

Abstract

Though substantial progress has been made in the theoretical study of electron collisions with molecules and molecular ions, most work has been restricted to diatomic or linear targets. Electron- and photon-molecule collision cross sections are needed in such diverse areas such as advanced laser development, pollution control, the design of highspeed space re-entry vehicles, the manufacture of semiconductor devices and plasma driven chemical synthesis. For example, the photoionization of polyatomic radicals, which plays an important role in combustion1, requires a description of electron scattering from a polyatomic molecular ion. Such studies are scarce. In the area of plasma enhanced chemical vapor deposition and etching2, studies indicate a subtle interplay between the neutrals, ions, electrons, and the surface. A critical lack of fundamental cross sections is hindering our understanding of these processes. Reliable theoretical methods are exceptionally important because of the extreme difficulty of experiments in this area.

Keywords

Wave Function Differential Cross Section Trial Function Elastic Cross Section Dissociative Recombination 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    A. B. Ehrhardt and W. D. Larger, Collisional Processes of Hydrocarbons in Hydrogen Plasmas, PPPL-2477 (Sept. 1987).Google Scholar
  2. 2.
    A. Gallagher, “Materials Issues in Amorphous-Semiconductor Technology Symposium,” Palo Alto, 1986 (Mater. Res. Soc, Pittsburgh, PA1986), p. 3.Google Scholar
  3. 3.
    J. B. A. Mitchell, Phys. Repts. 186, 216 (1990).ADSGoogle Scholar
  4. 4.
    M. A. Biondi, in Principles of Laser Plasmas, ed. by G. Bekefi (Wiley, New York, 1976) p. 125.Google Scholar
  5. 5.
    See, for example, Excimer Lasers, ed. by C. K. Rhodes (Springer-Verlag, New York, 1979).Google Scholar
  6. 6.
    A. Dalgarno and J. H. Black, Rep. Prog. Phys., 39, 573 (1976).ADSCrossRefGoogle Scholar
  7. 7.
    For a recent review, see D. R. Bates, M. F. Guest and R. A. Kendall, Planet. Space Sci. 41, 9 (1993).ADSCrossRefGoogle Scholar
  8. 8.
    J. Z. H. Zhang and W. H. Miller, J. Chem. Phys. 91, 1528 (1989).ADSCrossRefGoogle Scholar
  9. 9.
    T. Kato, Prog. Theo. Phys. 6, 394 (1951).ADSMATHCrossRefGoogle Scholar
  10. 10.
    W. Kohn, Phys. Rev. 74, 1763 (1948).ADSMATHCrossRefGoogle Scholar
  11. 11.
    R. K. Nesbet, Variational Methods in Electron-Atom Scattering Theory (Plenum, New York, 1980).CrossRefGoogle Scholar
  12. 12.
    R. K. Nesbet, Phys. Rev. 175, 134 (1968); 179, 60 (1969).ADSCrossRefGoogle Scholar
  13. 13.
    Y. Mito and M. Kamimura, Prog. Theo. Phys. 56, 583 (1976).ADSCrossRefGoogle Scholar
  14. 14.
    W. H. Miller and B. M. D. D. Jansen op de Haar, J. Chem Phys. 86, 6213 (1987).MathSciNetADSCrossRefGoogle Scholar
  15. 15.
    C. W. McCurdy, T. N. Rescigno and B. I. Schneider Phys. Rev. A 36, 2061 (1987).ADSCrossRefGoogle Scholar
  16. 16.
    T. N. Rescigno and B. I. Schneider, Phys. Rev. A 37, 1044 (1988).ADSCrossRefGoogle Scholar
  17. 17.
    C. W. McCurdy and T. N. Rescigno, Phys. Rev. A 39, 4487 (1989).ADSCrossRefGoogle Scholar
  18. 18.
    A. D. Becke, J. Chem. Phys. 88, 2547 (1988).ADSCrossRefGoogle Scholar
  19. 19.
    T. N. Rescigno, B. H. Lengsfield III and C. W. McCurdy, in Modern Electronic Structure, edited by D. Yarkony (World Scientific, 1994).Google Scholar
  20. 20.
    J. N. Bardsley, in Electron-Molecule and Photon-Molecule Collisions, edited by T. N. Rescigno, V. McKoy and B. I. Schneider (Plenum, New York, 1979), p. 267CrossRefGoogle Scholar
  21. 21.
    M. A. Morrison, Adv. At. Molec. Phys. 24, 51 (1988).ADSCrossRefGoogle Scholar
  22. 22.
    A. U. Hazi, T. N. Rescigno and M. Kurilla, Phys. Rev. A 23, 1089 (1981)ADSCrossRefGoogle Scholar
  23. A. U. Hazi, A. E. Orel and T. N. Rescigno, Phys. Rev. Letts. 46, 918 (1981).ADSCrossRefGoogle Scholar
  24. 23.
    A. E. Orel and K. C. Kulander, Phys. Rev. Letts. 71, 4315 (1993).ADSCrossRefGoogle Scholar
  25. 24.
    P. G. Burke, Potential Scattering in Atomic Physics, (Plenum, New York, 1977).CrossRefGoogle Scholar
  26. 25.
    M. Abramowitz and I. A. Stegun, Handbook of Mathematical Functions, (Dover, New York, 1965).Google Scholar
  27. 26.
    D. Lyons and R. K. Nesbet, J. Comp. Phys. 11, 166 (1973)MathSciNetADSMATHCrossRefGoogle Scholar
  28. R. L. Smith and D. G. Truhlar, Comp. Phys. Commun. 5, 80 (1973)ADSCrossRefGoogle Scholar
  29. J. Abdallah and D. G. Truhlar, ibid. 9, 327 (1975).Google Scholar
  30. 27.
    T. N. Rescigno and A. E. Orel, Phys. Rev. A 43, 1625 (1991).ADSCrossRefGoogle Scholar
  31. 28.
    Y. Sun, D. J. Kouri, D. G. Truhlar and D. W. Schwenke, Phys. Rev. A 41, 4857 (1990).ADSCrossRefGoogle Scholar
  32. 29.
    B. I. Schneider and T. N. Rescigno, Phys. Rev. A 37, 3749 (1988).ADSCrossRefGoogle Scholar
  33. 30.
    A. E. Orel. T. N. Rescigno and B. H. Lengsfield III, Phys. Rev. A 44, 4328 (1991).ADSCrossRefGoogle Scholar
  34. 31.
    B. H. Lengsfield III, T. N. Rescigno and C. W. McCurdy, Phys. Rev. A 44, 4296 (1991).ADSCrossRefGoogle Scholar
  35. 32.
    B. H. Lengsfield III and T. N. Rescigno, Phys. Rev. A 44, 2913 (1991).ADSCrossRefGoogle Scholar
  36. 33.
    H. E. Saraph, M. J. Seaton and J. Shemming, Proc. Phys. Soc. London 89, 27 (1966).ADSCrossRefGoogle Scholar
  37. 34.
    P. G. Burke, A. Hibbert and W. D. Robb, J. Phys. B 4, 153 (1971).ADSCrossRefGoogle Scholar
  38. 35.
    T. N. Rescigno, B. H. Lengsfield III and A. E. Orel, J. Chem. Phys. 99, 5097 (1993).ADSCrossRefGoogle Scholar
  39. 36.
    H. Feshbach, Ann. Phys. (N. Y.) 5, 357 (1958); 19, 287 (1962).MathSciNetADSMATHCrossRefGoogle Scholar
  40. 37.
    B. H. Lengsfield III and B. Liu, J. Chem. Phys. 75, 478 (1981).ADSCrossRefGoogle Scholar
  41. 38.
    J. A. Pople, R. Krishnam, H. B. Schlegel and J. S. Binkley, Int. J. Quan. Chem. Symp. 13, 225 (1979).Google Scholar
  42. 39.
    E. R. Davidson, J. Comp. Phys. 17, 87 (1975)ADSMATHCrossRefGoogle Scholar
  43. P. E. M. Siegbahn, J. Chem. Phys. 70, 5391 (1980); 72, 1647 (1980).MathSciNetADSCrossRefGoogle Scholar
  44. 40.
    T. N. Rescigno and A. E. Orel, Phys. Rev. A 23, 1134 (1981); 24, 1267 (1981)ADSCrossRefGoogle Scholar
  45. B. Gyarmati, A. T. Kruppa and J. Revai, Nucl. Phys. A 326, 119 (1979).MathSciNetADSCrossRefGoogle Scholar
  46. 41.
    C. W. Murray, N. C. Handy and G. J. Laming, Molec. Phys. 78, 997 (1993).ADSCrossRefGoogle Scholar
  47. 42.
    J. D. Jackson, Classical Electrodynamics, (Wiley, New York, 1962), p. 69.Google Scholar
  48. 43.
    A. D. Becke and R. M. Dickson, J. Chem. Phys. 89, 2993 (1988).ADSCrossRefGoogle Scholar
  49. 44.
    W. Eissner and M. J. Seaton, J. Phys. B 5, 2187 (1972).ADSCrossRefGoogle Scholar
  50. 45.
    R. K. Nesbet, Comp. Phys. Comm. 6, 275 (1973).ADSCrossRefGoogle Scholar
  51. 46.
    P. G. Burke, Comp. Phys. Comm. 6, 288 (1973).ADSCrossRefGoogle Scholar
  52. 47.
    S. Chung and C. C. Lin, Phys. Rev. A 17, 1874 (1978).ADSCrossRefGoogle Scholar
  53. 48.
    C. Weatherford, Phys. Rev. A 22, 2519 (1980).ADSCrossRefGoogle Scholar
  54. 49.
    A. E. Orel, T. N. Rescigno and B. H. Lengsfield, Phys. Rev. A 42, 5292 (1990).ADSCrossRefGoogle Scholar
  55. 50.
    T. N. Rescigno and B. I. Schneider, Phys. Rev. A 45, 2894 (1992).ADSCrossRefGoogle Scholar
  56. 51.
    T. N. Rescigno, “Low energy electron collision processes in molecular chlorine”, Phys. Rev. A XX, xxxx (1994)Google Scholar
  57. 52.
    T. J. Gil, C. W. McCurdy, T. N. Rescigno and B. H. Lengsfield III, Phys. Rev. A 47, 255 (1993).ADSCrossRefGoogle Scholar
  58. 53.
    D. E. Golden, N. F. Lane, A. Temkin and E. Gerjuoy, Rev. Mod. Phys. 43 642 (1971)ADSCrossRefGoogle Scholar
  59. 54.
    M. A. Morrison, Adv. Atom. Mol. Phys. 24, 51 (1988)ADSCrossRefGoogle Scholar
  60. 55.
    A. M. Arthurs and A. Dalgarno, Proc. R. Soc. A 256, 540 (1960).MathSciNetADSMATHCrossRefGoogle Scholar
  61. 56.
    N. Chandra and A. Temkin, Phys. Rev. A 13, 188 (1976).ADSCrossRefGoogle Scholar
  62. 57.
    M. Shugard and A.U. Hazi, Phys. Rev. A 12, 1895 (1975).ADSCrossRefGoogle Scholar
  63. 58.
    M.A. Morrison, J. Phys. B 19, L707 (1986)ADSCrossRefGoogle Scholar
  64. M.A. Morrison, M. Abdolsalami and B. K. Elza, Phys. Rev. A 43, 3440 (1991); B. K. Elza, University of Oklahoma, PhD Thesis, (1992, unpublished).ADSCrossRefGoogle Scholar
  65. 59.
    R. G. Newton, Scattering Theory of Waves and Particles, (McGraw-Hill, New York, 1966), p. 188.Google Scholar
  66. 60.
    E. Gerjouy, A. Rau and L. Spruch, J. Math. Phys. 13, 1797 (1972).ADSCrossRefGoogle Scholar
  67. 61.
    A. E. Orel and T. N. Rescigno, Phys. Rev. A 41, 1695 (1990).ADSCrossRefGoogle Scholar
  68. 62.
    D. M. Chase, Phys. Rev. 104, 838 (1956).ADSCrossRefGoogle Scholar
  69. 63.
    T. N. Rescigno, B. K. Elza and B. H. Lengsfield III, J. Phys. B 26, L567 (1993).ADSCrossRefGoogle Scholar
  70. 64.
    M.J. Brunger, S.J. Buckman, D.S. Newman and D.T. Alle, J. Phys. B 24, 1435 (1991).ADSCrossRefGoogle Scholar
  71. 65.
    J.P. England, M.T. Elford and R.W. Crompton, Aust. J. Phys. 41, 573 (1988).ADSCrossRefGoogle Scholar
  72. 66.
    S.J. Buckman, M.J. Brunger, D.S. Newman, G. Snitchler, S. Alston, D.W. Norcross, M.A. Morrison, B.C. Saha, G. Danby and W.K. Trail, Phys. Rev. Letts. 65, 3253 (1990).ADSCrossRefGoogle Scholar
  73. 67.
    F. Linder and H. Schmidt, Z. Naturforsch. 26a, 1603 (1971).ADSGoogle Scholar
  74. 68.
    H. Ehrhardt, L. Langhans, F. Linder and H.S. Taylor, Phys. Rev. 173, 222 (1968).ADSCrossRefGoogle Scholar
  75. 69.
    K. Rohr and F. Linder, J. Phys. B 9, 2521 (1976).ADSCrossRefGoogle Scholar
  76. 70.
    L. A. Morgan and P. G. Burke, J. Phys. B 21, 2091 (1988)ADSCrossRefGoogle Scholar
  77. G. Snitchler, D. Norcross, A. Jain and S. Alston, Phys. Rev. A 42, 671 (1990).ADSCrossRefGoogle Scholar
  78. 71.
    K. Rohr, J. Phys. B 13, 4897 (1980).ADSCrossRefGoogle Scholar
  79. 72.
    W. Sohn, K. Jung and H. Ehrhardt, J. Phys. B 16, 891 (1983).ADSCrossRefGoogle Scholar
  80. 73.
    T. N. Rescigno, A. E. Orel and C. W. McCurdy (unpublished).Google Scholar
  81. 74.
    W. Sohn, K. H. Kochern, K. M. Scheuerlein, K. Jung and H. Ehrhardt, J. Phys. B 19, 3625 (1986).ADSCrossRefGoogle Scholar
  82. 75.
    O. H. Crawford, A. Dalgarno and P. B. Hays, Molec. Phys. 13, 181 (1967).ADSCrossRefGoogle Scholar
  83. 76.
    W. R. Garrett, Molec. Phys. 24, 465 (1972).ADSCrossRefGoogle Scholar
  84. 77.
    See, for example, N. F. Lane, Rev. Mod. Phys. 52, 29 (1980).ADSCrossRefGoogle Scholar
  85. 78.
    M. E. Rose, Elementary Theory of Angular Momentum (Wiley, New York, 1967) pp. 62–65.Google Scholar
  86. 79.
    See, for example, M. J. Seaton, Proc. Phys. Soc. London 79, 1105 (1962).ADSCrossRefGoogle Scholar
  87. 80.
    See, for example, L. A. Collins and D. W. Norcross, Phys. Rev. A 18, 467 (1978). This paper gives a clear treatment of the subject and also contains many references to earlier work.ADSCrossRefGoogle Scholar
  88. 81.
    D. W. Norcross and N. T. Padial, Phys. Rev. A 25, 226 (1982).ADSCrossRefGoogle Scholar
  89. 82.
    T. N. Rescigno and B. H. Lengsfield III, Z. Phys. D 24, 117 (1992).ADSCrossRefGoogle Scholar
  90. 83.
    T. N. Rescigno, B. H. Lengsfield III, C. W. McCurdy and S. D. Parker, Phys. Rev. A 45, 7800 (1992).ADSCrossRefGoogle Scholar
  91. 84.
    B. H. Lengsfield III and T. N. Rescigno, (unpublished).Google Scholar
  92. 85.
    R. J. Gulley, M. J. Brunger and S. A. Buckman, Phys. B 26, 2913 (1993).CrossRefGoogle Scholar
  93. 86.
    R. R. Lucchese and V. McKoy, Phys. Rev. A 24, 770 (1981)MathSciNetADSCrossRefGoogle Scholar
  94. R. R. Lucchese, G. Raseev and V. McKoy, Phys. Rev. A 25, 2572 (1982).ADSCrossRefGoogle Scholar
  95. 87.
    J. C. Tully, R. S. Berry and B. J. Dalton, Phys. Rev. 176, 95 (1968).ADSCrossRefGoogle Scholar
  96. 88.
    B. Basden and R. R. Lucchese, Phys. Rev. A 37, 89 (1988).ADSCrossRefGoogle Scholar
  97. 89.
    E. W. Plummer, T. Gustafsson, W. Gudat and D. E. Eastman, Phys. Rev. A 15, 2339 (1977).ADSCrossRefGoogle Scholar
  98. 90.
    C. W. McCurdy and J. L. Turner, J. Chem. Phys. 78, 6773 (1983).ADSCrossRefGoogle Scholar
  99. 91.
    E. J. Heller, J. Chem. Phys. 68, 3891 (1978).ADSCrossRefGoogle Scholar
  100. 92.
    K. C. Kulander and E. J. Heller, J. Chem. Phys. 69, 2439 (1978).ADSCrossRefGoogle Scholar
  101. 93.
    G. Herzberg, Electronic Spectra of Polyatomic Molecules, (Van Nostrand Reinhold Company, New York), pg. 289 (1966).Google Scholar
  102. 94.
    M. Larssen, H. Danared, J. R. Mowat, P. Sigray, G. Sundström, L. Broström, A. Filevich, A. Källberg, S. Mannervik, K. G. Rensfelt and S. Datz, Phys. Rev. Lett.Google Scholar

Copyright information

© Springer Science+Business Media New York 1995

Authors and Affiliations

  • T. N. Rescigno
    • 1
  • C. W. McCurdy
    • 2
  • A. E. Orel
    • 3
  • B. H. LengsfieldIII
    • 4
  1. 1.Physics DepartmentLawrence Livermore National LaboratoryUSA
  2. 2.National Energy Research Supercomputer CenterUSA
  3. 3.Department of Applied ScienceUniversity of California DavisLivermoreUSA
  4. 4.IBM Almaden Research CenterSan JoseUSA

Personalised recommendations