Advertisement

Many-Body Theory of Photoabsorption in Atoms and Molecules

  • Cleanthes A. Nicolaides
  • Donald R. Beck
Chapter
Part of the NATO Advanced Study Institutes Series book series (ASIC, volume 46)

Abstract

We present an approach to the calculation of photoexcitation and photoionization transition probabilities which first derives, consistently, the important correlation effects and then computes them efficiently and accurately. The emphasis is on the correct evaluation of the transition matrix element and not of the exact Schrödinger equation for initial and final wave-functions. The theory is implemented through Configuration-Interaction techniques which allows the practical consideration of any type of state. Both initial and final states are treated at the same level of approximation due to the similarity of restrictions imposed upon them. The basic conceptual and computational characteristics of the theory are simple: The zeroth order vectors for initial and final states are the Fermi-Sea (FS) wave-functions. The transition operator is then applied to the FS vectors and selects the additional correlation effects in initial and final states which contribute to the transition amplitude the most. These correlations are expressed in terms of Hartree-Fock and variationally optimized virtual orbitals for each state. The resulting very small wave-functions are then employed for the calculation of the transition probabilities. This First Order Theory of Oscillator Strengths (FOTOS) is applicable to any system with a shell structure and symmetry (including nuclear transitions). Its application to a variety of atomic transitions has yielded accurate results, some of which are presented here. Also presented are brief discussions on the question of which form of the electric dipole operator is the appropriate one to use in computations, nonorthonormality, extraordinary absorption properties of certain systems, polarizability calculations within FOTOS and the extension of FOTOS to the relativistic domain.

Keywords

Oscillator Strength Correlation Effect Random Phase Approximation Electric Dipole Transition Transition Matrix Element 
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.
    D.R. Beck and C.A. Nicolaides, “Theory of the Electronic Structure of Excited States in Small Systems with Numerical Applications to Atomic States”, this volume.Google Scholar
  2. 2.
    C.A. Nicolaides and D.R. Beck, J. Chem. Phys. 66, 1982 (1977).CrossRefGoogle Scholar
  3. 3.
    C.M. Brown, S.G. Tilford and M.L. Ginter, J. Opt. Soc. Am. 65, 1404 (1975).CrossRefGoogle Scholar
  4. 4.
    A.W. Weiss, Phys. Rev. A9, 1524 (1974).Google Scholar
  5. 5.
    C.A. Nicolaides and D.R. Beck, J. Phys. B9, L259 (1976).Google Scholar
  6. 6.
    D.R. Beck and C.A. Nicolaides, Phys. Letts. 61A, 227 (1977).CrossRefGoogle Scholar
  7. 7.
    R.J. Buenker and S.D. Peyerimhoff, Chem. Phys. Letts. 34, 225 (1975).CrossRefGoogle Scholar
  8. 8.
    M. Yoshimine et al, J. Chem. Phys. 64, 2254 (1976).CrossRefGoogle Scholar
  9. 9.
    C.A. Nicolaides and D.R. Beck, Chem. Phys. Letts. 53, 87 (1978).CrossRefGoogle Scholar
  10. 10.
    D.R. Beck and C.A. Nicolaides, Chem. Phys. Letts. 53, 91 (1978).CrossRefGoogle Scholar
  11. 11.
    U. Gelius, J. El. Spect. 5, 985 (1974).CrossRefGoogle Scholar
  12. 12.
    S.P. Kowalczyk et al, Phys. Rev. B7, 4009 (1973).Google Scholar
  13. 13.
    F. Wuilleumier and M.O. Krause, Phys. Rev. A10, 242 (1974).Google Scholar
  14. 14.
    J.P. Connerade and M.W.D. Mansfield, Proc. Roy. Soc. A343, 415 (1975).Google Scholar
  15. 15.
    G.K. Wertheim and H.J. Guggenheim, Phys. Rev. Letts. 27, 479 (1971).CrossRefGoogle Scholar
  16. 16.
    G. Wendin and M. Ohno, Phys. Scripta 14, 148 (1976).CrossRefGoogle Scholar
  17. 17.
    P.S. Bagus and E.K. Viinikka, Phys. Rev. A15, 1486 (1977).Google Scholar
  18. 18.
    C.A. Nicolaides, Chem. Phys. Letts. 17, 436 (1972)CrossRefGoogle Scholar
  19. 18a.
    G. Nowak, W.L. Borst and J. Fricke, Phys. Rev. A17, 1921 (1978).Google Scholar
  20. 19.
    D.R. Beck, G. Aspromallis and C.A. Nicolaides, work in progress.Google Scholar
  21. 20.
    L. Goodman and B.J. Laurenzi, Adv. Qu. Chem. 4, 141 (1968).CrossRefGoogle Scholar
  22. 21.
    F.W. Byron and C.J. Joachain, Phys. Rev. 164, 1, (1967).CrossRefGoogle Scholar
  23. 22.
    T.N. Chang, T. Ishihara and R.T.Poe, Phys. Rev. Letts. 27, 838 (1971).CrossRefGoogle Scholar
  24. 23.
    S.L. Carter and H.P. Kelly, Phys. Rev. A16, 1525 (1977).Google Scholar
  25. 24.
    P.L. Altick, “Atomic Photoionization Cross-Sections” in this volume.Google Scholar
  26. 25.
    Y. Komninos, D.R. Beck and C.A. Nicolaides, work in progress.Google Scholar
  27. 26.
    C.A. Nicolaides and D.R. Beck, Phys. Rev. A17, 2116 (1978).Google Scholar
  28. 27.
    I. Martinson, “Experimental Determination of Lifetimes”, this volume.Google Scholar
  29. 28.
    H.G. Berry, Phys. Scr. 12, 5 (1975).CrossRefGoogle Scholar
  30. 29.
    P. Erman, Phys. Scr. 11, 65 (1975).CrossRefGoogle Scholar
  31. 30.
    J.M. Esteva, G. Mehlman-Balloffet and J. Romand, J. Quant. Spect. Rad. Trans. 12, 1291 (1972).CrossRefGoogle Scholar
  32. 31.
    P.M. Dehmer, J. Berkowitz and W.A. Chupka, J. Chem. Phys. 59, 5777 (1973).CrossRefGoogle Scholar
  33. 32.
    J.B. West and B.V. Marr, Proc. R. Soc. A349, 397 (1976).Google Scholar
  34. 33.
    M.J. Van der Wiel and G.R. Wright, Phys. Letts. 54A, 83 (1975).CrossRefGoogle Scholar
  35. 34.
    C. Laughlin and A. Dalgarno, Phys. Rev. A8, 39 (1973).Google Scholar
  36. 35.
    C.A. Nicolaides, D.R. Beck and O. Sinanoglu, J. Phys. B6, 62 (1973).Google Scholar
  37. 36.
    C.A. Nicolaides, Chem. Phys. Letts. 21, 242 (1973).CrossRefGoogle Scholar
  38. 37.
    D.R. Beck and O. Sinanoğlu, Phys. Rev. Letts. 28, 934 (1972).Google Scholar
  39. 38.
    P. Westhaus and O. Sinanoğlu, Phys. Rev. 183, 56 (1969).CrossRefGoogle Scholar
  40. 39.
    C.M. Moser, R.K. Nesbet and M.V. Gupta, Phys. Rev. A13, 17 (1976).Google Scholar
  41. 40.
    A. Hibbert, J. Phys. B7, 1417 (1974).Google Scholar
  42. 41.
    Z. Sibincic, Phys. Rev. A5, 1150 (1972).Google Scholar
  43. 42.
    J.S. Sims and R.C. Whitten, Phys. Rev. A8, 2220 (1973).Google Scholar
  44. 43.
    U.I. Safronova and Z.B. Rudzikas, J. Phys. B10, 7 (1977).Google Scholar
  45. 44.
    M. Ya. Amusia, V.K. Ivanov, N.A. Cherepkov and L.V. Chernysheva, Phys. Letts. 40A 361 (1972)CrossRefGoogle Scholar
  46. 44a.
    M. Ya. Amusia, V.K. Ivanov, N.A. Cherepkov and L.V. Chernysheva, Sov. Phys. JETP 39, 752 (1974).Google Scholar
  47. 45.
    S. Garpman, Phys. Scripta 12, 295 (1975).CrossRefGoogle Scholar
  48. 46.
    T.I. Shibuya and V. McKoy, Phys. Rev. A2, 2208 (1970).Google Scholar
  49. 47.
    L.S. Cederbaum, J. Phys. B8, 290 (1975).Google Scholar
  50. 48.
    W. Von Niessen, L.S. Cederbaum and W. Domcke, in this volume.Google Scholar
  51. 49.
    J. Oddershede, P. Jørgensen and N.H.F. Beebe, J. Phys. B11, 1 (1978).Google Scholar
  52. 50.
    J. Linderberg and Y. Ohrn, “Propagators in Quantum Chemistry”, Acad. Press (1973).Google Scholar
  53. 51.
    C. Froese-Fischer and J.E. Hansen, Phys. Rev. A17, 1956 (1978).Google Scholar
  54. 52.
    D.K. Watson, A. Dalgarno, and R.F. Stewart, Phys. Rev. A17, 1928 (1978).Google Scholar
  55. 53.
    K.T. Cheng and W.R. Johnson, Phys. Rev. A15, 1046 (1977).Google Scholar
  56. 54.
    C.A. Nicolaides and D.R. Beck, Chem. Phys. Letts. 36, 79 (1975).CrossRefGoogle Scholar
  57. 55.
    D.R. Beck and C.A. Nicolaides, Int. J. Qu. Chem. S10, 119 (1976).Google Scholar
  58. 56.
    D.R. Beck and C.A. Nicolaides, Phys. Letts. 56A, 265 (1976).CrossRefGoogle Scholar
  59. 57.
    D.R. Beck and C.A. Nicolaides, Phys. Letts. 65A, 293 (1978).CrossRefGoogle Scholar
  60. 58.
    B. Edlen, Encyclopaedia of Physics, S. Flügge ed., Springer Verlag, Berlin (1964), vol. 27.Google Scholar
  61. 59.
    A.W. Fliflet, R.L. Chase and H.P. Kelly, J. Phys. B: At. Mol. Phys. 7, L443 (1974).CrossRefGoogle Scholar
  62. 60.
    L.W. Bruch and A.P. Lehnen, J. Chem. Phys. 64, 2065 (1976).CrossRefGoogle Scholar
  63. 61.
    C.A. Nicolaides and D.R. Beck, Can. J. Phys. 53, 1224 (1975).CrossRefGoogle Scholar
  64. 62.
    C.A. Nicolaides, Phys. Rev. A6, 2078 (1972)Google Scholar
  65. 62a.
    C.A. Nicolaides, Nucl. Inst. Meth. 110, 231 (1973).CrossRefGoogle Scholar
  66. 63.
    C.A. Nicolaides and D.R. Beck, “Time Dependence, Complex Scaling and the Calculation of Resonances in Many-Electron Systems”, Int.J. Qu. Chem. 14, to be published.Google Scholar
  67. 64.
    T.N. Rescigno et al., J. Chem. Phys. 68, 970 (1978) and refs. therein.CrossRefGoogle Scholar
  68. 65.
    Y. Komninos, D.R. Beck and C.A. Nicolaides, work in progress.Google Scholar
  69. 66.
    H.F. King et al, J. Chem. Phys. 47, 1936 (1967).CrossRefGoogle Scholar
  70. 67.
    C.A. Nicolaides, O. Sinanoglu and P. Westhaus, Phys. Rev. A4, 1400 (1971).Google Scholar
  71. 68.
    M.W.D. Mansfield and J.P. Connerade, Proc. R. Soc. (Lond.) A359, 389 (1978).Google Scholar
  72. 69.
    R.J. Buenker and S.D. Peyerimhoff, Chem. Phys. Letts. 29, 253 (2974).CrossRefGoogle Scholar
  73. 70.
    J.A. Kernahan and P.H-L Pang, Can. J. Phys. 53, 455 (1975).CrossRefGoogle Scholar
  74. 71.
    C.A. Nicolaides and D.R. Beck, Chem. Phys. Lett. 35, 202 (1975).CrossRefGoogle Scholar
  75. 72.
    T. Shibuya, J. Rose and V. McKoy, J. Chem. Phys. 58, 500 (1973).CrossRefGoogle Scholar
  76. 73.
    W.L. Wiese and A.W. Weiss, Phys. Rev. 175, 50 (1968).CrossRefGoogle Scholar
  77. 74.
    Y.-K. Kim and J.P. Desclaux, Phys. Rev. Letts. 36, 139 (1976).CrossRefGoogle Scholar
  78. 75.
    L.E. Nitzsche and E.R. Davidson, J. Chem. Phys. 68, 3103 (1978).CrossRefGoogle Scholar
  79. 76.
    R.K. Nesbet, Phys. Rev. A14, 1065 (1976).Google Scholar
  80. 77.
    A.W. Weiss, Phys. Rev. 188, 119 (1969).CrossRefGoogle Scholar
  81. 78.
    J.A. Kernahan et al., Phys. Scripta 12, 319 (1975).CrossRefGoogle Scholar
  82. 79.
    I. Martinson et al., J. Opt. Soc. Am. 60, 1213 (1970).CrossRefGoogle Scholar
  83. 80.
    G.A. Victor and C Laughlin, Nucl. Inst. Meth. 110, 189 (1973).CrossRefGoogle Scholar
  84. 81.
    A.W. Weiss, quoted in ref. 80.Google Scholar
  85. 82.
    T. Andersen, et al., Phys. Scripta 4, 52 (1971).CrossRefGoogle Scholar
  86. 83.
    S. Bashkin and I. Martinson, J. Opt. Soc. Am. 61, 1686 (1971).CrossRefGoogle Scholar
  87. 84.
    P. Shorer and A. Dalgarno, Phys. Rev. A16, 1502 (1977).Google Scholar
  88. 85.
    P. Shorer, C.D. Lin and A. Dalgarno, Phys. Rev. A16, 1109 (1977).Google Scholar
  89. 86.
    J.L. Fox and A. Dalgarno, Phys. Rev. A16, 283 (1977).Google Scholar
  90. 87.
    J.P. Buchet et al., Phys. Rev. A7, 922 (1973).Google Scholar
  91. 88.
    T. Sberg, Phys. Rev. A4, 1735 (1971).Google Scholar
  92. 89.
    G.W.F. Drake, Astroph. J. 184, 145 (1973).CrossRefGoogle Scholar
  93. 90.
    D.R. Beck and C.A. Nicolaides, Chem. Phys. Letts. 48, 135 (1977).CrossRefGoogle Scholar
  94. 91.
    J.S. Sims and J.R. Rumble Jr., Phys. Rev. A8, 2231 (1973).Google Scholar
  95. 92.
    H. J. Werner and W. Meyer, Phys. Rev. A13, 13 (1976).Google Scholar
  96. 93.
    D.R. Beck and C.A. Nicolaides, Chem. Phys. Letts. 49, 357 (1977).CrossRefGoogle Scholar
  97. 94.
    G. Astner et al., Z. Physik, A279, 1, (1976).Google Scholar
  98. 95.
    J. Andra, private communication.Google Scholar
  99. 96.
    A.W. Weiss, Astroph. J. 138, 1262 (1963).CrossRefGoogle Scholar
  100. 97.
    A. Lindgard and S.E. Nielsen, J. Phys. B8, 1183 (1975); value using optimal cutoff.Google Scholar
  101. 98.
    R.A. Harris, J. Chem. Phys. 50, 3947 (1969).CrossRefGoogle Scholar
  102. 99.
    M.Ya. Amusia, N.A. Cherepkov and L.V. Shernysheva, Soviet Phys. (JETP) 33, 90 (1971).Google Scholar
  103. 100.
    D.L. Lin, Phys. Rev. A16, 600 (1977).Google Scholar
  104. 101.
    C.A. Nicolaides and D.R. Beck, J. Phys. B9, L259 (1976).Google Scholar
  105. 102.
    J. Oddershede and N. Elander, J. Chem. Phys. 65, 3495 (1976).CrossRefGoogle Scholar
  106. 103.
    G.W.F. Drake, J. Phys. B9, L169 (1976).Google Scholar
  107. 104.
    J. Migdalek, Can. J. Phys. 54, 2272 (1976).CrossRefGoogle Scholar
  108. 105.
    L. Armstrong Jr., W.R. Fielder and D.L. Lin, Phys. Rev. A14, 1114 (1976).Google Scholar
  109. 106.
    M. Aymar and E. Luc-Koenig, Phys. Rev. A15, 821 (1977).Google Scholar
  110. 107.
    D.R. Beck and C.A. Nicolaides, “Theory of one electron binding energies including correlation, relativistic and radiative effects: Application to free atoms and metals” in this volume.Google Scholar
  111. 108.
    J.P. Desclaux, Comp. Phys. Commun, 9, 31 (1975).CrossRefGoogle Scholar

Copyright information

© D. Reidel Publishing Company, Dordrecht, Holland 1978

Authors and Affiliations

  • Cleanthes A. Nicolaides
    • 1
  • Donald R. Beck
    • 1
  1. 1.Theoretical Chemistry InstituteNational Hellenic Research FoundationAthens 501/1Greece

Personalised recommendations