Many-Electron, Many-Photon Theory of Atoms in Strong Fields

  • C. A. Nicolaides
  • Th. Mercouris
Part of the NATO ASI Series book series (NSSB, volume 212)


This article treats the many-electron, many-photon (MEMP) problem for weak or strong fields under the assumption of monochromaticity and adiabaticity. We emphasize the efficient and reliable solution of a non Hermitian, complex eigenvalue Schrödinger equation which yields the energy width (ionization rate) and shift of an atomic or molecular ground or excited state due to the perturbation of an ac- or a dc-field. Thus far, applications have been made on the negative ions H and Li, whose zeroth order structures are different, for ac-fields up to 1011 W/cm2, with and without a dc-field (ref.14). A number of results have been obtained and analyzed in terms of electronic structure and final state effects. For some of them, comparison is possible with recent experiments as well as with previous less sophisticated theories.


Schrodinger Equation Complex Eigenvalue Multiphoton Ionization Giant Resonance Hilbert Space Quantum 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    H.J. Silverstone, article in this book.Google Scholar
  2. 2.
    J. Silverman and C.A. Nicolaides, article in this book.Google Scholar
  3. 3.
    Y. Gontier, N.K. Rahman and M. Trahin, Phys. Rev. A24, 3102 (1981).ADSCrossRefGoogle Scholar
  4. Y. Gontier, N.K. Rahman and M. Trahin, Phys.Rev. A34, 1112 (1986).ADSCrossRefGoogle Scholar
  5. E. Karule, J.Phys. B11, 441(1978).ADSGoogle Scholar
  6. E. Karule, J.Phys. B21, 1997(1988).ADSGoogle Scholar
  7. 4.
    P. Lambropoulos, Adv.At.Mol.Phys. 12, 87(1976).ADSCrossRefGoogle Scholar
  8. 5.
    J. Morellec, D. Normand and G. Petite, Adv.At.Mol.Phys. 18, 96 (1982).ADSGoogle Scholar
  9. 6.
    N.C. Manakov, V.D. Oviannikov and L.P. Rapoport, Phys.Rep. 141, 319 (1986).CrossRefADSGoogle Scholar
  10. 7.
    F.H.M. Faisal, “Theory and Multiphoton Processes”, Plenum Pr.(1987).Google Scholar
  11. 8.
    R. Shakeshaft, J.Opt.Soc.Am. B4, 705 (1987).ADSCrossRefGoogle Scholar
  12. 9.
    “Multiphoton processes” eds.S.J. Smith and P.L. Knight, Cambridge Univ.(1988).Google Scholar
  13. 10.
    Y. Gontier and M. Trahin, J.Phys. B13, 4381 (1980).For atoms with one valence electron, semiemprirical model potential calculations have been carried out beyond the LOPT, by assuming a pseudo-one-electron atom, e.g.see the pioneering calculations of.ADSGoogle Scholar
  14. M. Aymar and M. Crance, J.Phys. B14, 3585 (1981).ADSGoogle Scholar
  15. 11.
    M.S. Pindzola and H.P. Kelly (1975), Phys.Rev. A11 1543.ADSCrossRefGoogle Scholar
  16. 12.
    T. FJiang and A.F. Starace, Phys.Rev. A38, 2347 (1988).ADSGoogle Scholar
  17. A. L’Huillier and G. Wendin, J.Phys. B21, L247 (1988).Google Scholar
  18. 13.
    R. Moccia and P. Spizzo, J.Phys. B21, 1145 (1988).ADSGoogle Scholar
  19. 14.
    Th. Mercouris and C.A. Nicolaides, J.Phys. B21, L285 (1988).ADSGoogle Scholar
  20. C.A. Nicolaides and Th. Mercouris, Chem.Phys.Lett. 159 45 (1989); Th.Mercouris and C.A.Nicolaides, J.Phys.B, to be published.ADSCrossRefGoogle Scholar
  21. 15.
    Magnitudes of laser intensities characterizing the word “very strong” in the present context cannot be defined yet. They are expected to have peak strengths of the order of an atomic unit. As stated in the text, possible effects on observables of the pulse shape is a question which in not treated here.Google Scholar
  22. 16a.
    A. Dalgarno and G.A. Victor, Proc.Roy.Soc.(London) A291, 26 (1988).Google Scholar
  23. 16b.
    A. Maquet, P. Martin and V. Veniard, Phys.Lett. A129, 26 (1988).MathSciNetADSCrossRefGoogle Scholar
  24. 17.
    G. Petite, F. Fabre, P. Agostini, M. Crance and M. Aymar, Phvs.Rev. A29, 2677 (1984).ADSCrossRefGoogle Scholar
  25. 18.
    P. Lambropoulos, Phys.Rev.Lett. 55, 2141 (1985).ADSCrossRefGoogle Scholar
  26. 19.
    G. Petite and P. Agostini, J.Physique 47, 795 (1986).CrossRefGoogle Scholar
  27. 20.
    P. Lambropoulos and X. Tang, J.Opt.Soc. B4, 821 (1987).ADSCrossRefGoogle Scholar
  28. 21.
    K. Boyer, T.S. Luk, C.Rhodes, A.Szöke et al, in ref.9, p.58.Google Scholar
  29. 22.
    C.A. Nicolaides and D.R. Beck, in “Excited States in Quantum Chemistry” eds. C.A. Nicolaides and D.R. Beck, Reidel (1978), p. 143.Google Scholar
  30. Y. Komninos and C.A. Nicolaides, Phys.Rev. A34, 1995 (1986).ADSCrossRefGoogle Scholar
  31. Y. Komninos and C.A. Nicolaides, Z.Physik D4, 301 (1987).ADSGoogle Scholar
  32. 23.
    H.P. Kelly and S.L. Carter, Phys.Scripta 21, 448 (1980).ADSCrossRefGoogle Scholar
  33. 24.
    P.C. Burke, J.Physique 39, C4–27 (1978).ADSGoogle Scholar
  34. 25.
    A. W. Weiss, Phys.Rev. A9, 1524 (1974).ADSCrossRefGoogle Scholar
  35. 26.
    C. A. Nicolaides, in “Giant Resonances in Atoms, Molecules and Solids” eds.J.P. Connerade, J.M. Esteva and R.C. Karnatak, Plenum (1987), p.213.Google Scholar
  36. 27.
    C.A. Nicolaides and D.R. Beck, Chem.Phys.Lett. 36, 79 (1975).ADSCrossRefGoogle Scholar
  37. 28.
    C.A. Nicolaides, Chem.Phys.Lett. 101, 435 (1983); C.A. Nicolaides, Y. Komninos, M. Chrysos and G. Aspromallis, article in this book.ADSCrossRefGoogle Scholar
  38. 29.
    M. YaAmusia, Adv.At.Mol.Phys. 17, 1 (1981).CrossRefGoogle Scholar
  39. 30.
    F. Wuilleumier, M. YAdam, N. Sandner and V. Schmidt, J.Phys.Lett. 41, 373 (1980).CrossRefGoogle Scholar
  40. 31.
    C.A. Nicolaides and D.R. Beck, Can.J.Phys. 53, 1224 (1975).ADSCrossRefGoogle Scholar
  41. 32.
    C. A. Nicolaides, in “Advanced Theories and Computational Approaches to the Electronic Structure of Molecules”, ed.C.E. Dykstra, Reidel (1984), p.161; in “Quantum Chemistry, Basic Aspects, Actual Trends” ed. R. Carbo, Elsevier (1989).Google Scholar
  42. 33.
    C.A. Nicolaides and D.R. Beck, J.Phys. B9, L259 (1976).ADSGoogle Scholar
  43. 34.
    A.W. Fliflet, R.L. Chase and H.P. Kelly, J.Phys. B7, L443 (1974).ADSGoogle Scholar
  44. 35.
    For the reader who is not familiar with details of atomic theory: The effect of the exchange operator (which, to a large extent, is absent in local potential models) on the orbitals, can be large-with consequences on the calculation of properties. The best known example in that of the term dependence of the Be 1s22s2p 3,1p0 2p orbitals, first computed by D.R. Hartree and W. Hartree, Proc.Roy.Soc.(London) 154, 588 (1936). Many such situations exist for other open shell configurations (with a bound or a scattering orbital) throughout the periodic table. One such case is that which was pointed out by Fliflet et al (ref.34) to explain the “collective” interpretations ofADSCrossRefGoogle Scholar
  45. G. Wendin, Phys.Lett. 46A, 119 (1973).ADSCrossRefGoogle Scholar
  46. 36.
    G. Wendin, Phys.Lett. 46A, 119 (1973).ADSCrossRefGoogle Scholar
  47. S. Lundquist and G. Wendin, J.Elect Spect. 5, 513 (1974).CrossRefGoogle Scholar
  48. U. Gelius, J.Elect.Spect. 5, 985 (1974).CrossRefGoogle Scholar
  49. 37.
    A. Zangwill and P. Soven, Phys.Rev. A21, 1561 (1980).ADSCrossRefGoogle Scholar
  50. 38.
    C. K. Rhodes, in “Giant Resonances in Atoms, Molecules and Solids” eds J.P. Connerade, J.M. Esteva and R.C. Karnatak, Plenum(1987), p.533.Google Scholar
  51. 39.
    L. A. Lompré and G. Mainfray, in “Fundamentals of Laser Interactions” ed.F. Ehlotzky, Springer-Verlag (1985).Google Scholar
  52. 40.
    C.A. Nicolaides and D.R. Beck, Phys.Lett. 65A, 11 (1978).ADSCrossRefGoogle Scholar
  53. 41.
    C.A. Nicolaides and D.R. Beck, Int J.Qu.Chem. 14, 457 (1978).CrossRefGoogle Scholar
  54. 42.
    C.A. Nicolaides, Y. Komninos and Th. Mercouris, Int J.Qu.Chem. S15, 355 (1981).Google Scholar
  55. C.A. Nicolaides, Y. Komninos and Th. Mercouris, Int J.Qu.Chem. 26, 1017 (1984).CrossRefGoogle Scholar
  56. 43.
    C.A. Nicolaides and Th. Mercouris, Phys.Rev. A36, 390 (1987).ADSCrossRefGoogle Scholar
  57. C.A. Nicolaides and Th. Mercouris, Phys.Rev. A32, 3247 (1985).ADSCrossRefGoogle Scholar
  58. 44.
    J.H. Shirley, Phys.Rev. 138, B979 (1965).ADSCrossRefGoogle Scholar
  59. GJ. Pert, IEEE J.Qu.Elect. QE8, 623 (1972).ADSCrossRefGoogle Scholar
  60. Ya.B. Zeldovich, Sov.Phys.JETP 24, 1006 (1967).ADSGoogle Scholar
  61. 45.
    L. Armstrong Jr., B.L. Beers and S. Feneuille, Phys.Rev. A12, 1903 (1975).ADSCrossRefGoogle Scholar
  62. 46.
    H. Feshbach, Ann.Phys.(N.Y) 5, 357 (1958).MathSciNetADSCrossRefMATHGoogle Scholar
  63. H. Feshbach, Ann.Phys.(N.Y) 19, 287 (1962).MathSciNetADSCrossRefMATHGoogle Scholar
  64. 47.
    U. Fano, Phys.Rev. 124, 1866 (1961).ADSCrossRefMATHGoogle Scholar
  65. 48.
    T. F. O’Malley and S. Geltman, Phys.Rev. 137, A1344 (1965).CrossRefGoogle Scholar
  66. 49.
    C.A. Nicolaides, Phys.Rev. A6 2078 (1972).ADSCrossRefGoogle Scholar
  67. 50.
    W. Heitler, “Quantum Theory of Radiation”, 3rd ed. Oxford U.P. (1954), p.163.Google Scholar
  68. M. Schönberg, Nuovo Cimento 8, 817 (1951).MathSciNetCrossRefGoogle Scholar
  69. 51.
    L. Lipsky and A. Russek, Phys.Rev. 142, 59 (1966).ADSCrossRefGoogle Scholar
  70. 52.
    Y. Komninos, N. Makri and C.A. Nicolaides, Z.Phys. D2, 105 (1986).ADSGoogle Scholar
  71. 53.
    M.L. Goldberger and K.M. Watson, “Collision Theory” Wiley (N.Y.) (1964).MATHGoogle Scholar
  72. 54.
    C.A. Nicolaides and D.R. Beck, Phys.Rev.Letts. 38, 683 (1977).ADSCrossRefGoogle Scholar
  73. 55.
    P.T. Greenland, Nature 335, 298 (1988).ADSCrossRefGoogle Scholar
  74. 56.
    K. Rzazewski, L. Lewenstein and J.H. Eberly, J.Phys. B15, L661 (1982).ADSGoogle Scholar
  75. S.L. Haan and JJ. Cooper, J.Phys. B17, 3481 (1986).ADSGoogle Scholar
  76. 57.
    Y. Komninos and C.A. Nicolaides, Chem.Phys.Lett. 78, 347 (1981).ADSCrossRefGoogle Scholar
  77. 58.
    G. Gamow, in “Constitution of Atomic Nuclei and Radioactivity” Oxford Press, 1931.Google Scholar
  78. A.F.J. Siegert, Phys.Rev. 56, 750 (1939).ADSCrossRefGoogle Scholar
  79. 59.
    The non-Hermiticity of eq.15 is a result of the outgoing boundary condition (eq.11) that the eigenfunction Ψ(r1.rN;zO) satisfies. In other words, this type of non-square-integrability is responsible for the complex eigenvalue and for the fact that eq.15 cannot be treated directly with the usual methods of Hilbert space quantum mechanics. We note that non-Hermiticity is an intrinsic property of decaying systems, i.e. of nonstationary states with a flux, when they are described by time-independent Schrödinger equations. It can be introduced abinitio to the physics either through the appropriate boundary conditions or through non-Hermitian operators which are defined in the Hilbert space of square integrable functions/e.g. see refs.41 and 60/. A clear discussion of the formalism of non-Hermitian Schrödinger equations with application to multiphoton ionization of atoms has been published by F.H.M. Faisal and J.V. Moloney, J.Phys. B14, 3603 (1981).MathSciNetADSGoogle Scholar
  80. 60.
    T. Berggren, Nucl.Phvs. A109, 265 (1968).ADSCrossRefGoogle Scholar
  81. 61.
    A.M. Dykhne and A.V. Chaplik, Sov.PhysJETP 13, 1002 (1961).Google Scholar
  82. 62.
    The spectral properties of rotated, non-Hermitian Hamiltonians-whose importance was revealed after the mathematical results ofGoogle Scholar
  83. J. Aquilar, E. Balslev and J.M. Combes, Comm.Math.Phys. 22, 269, (1971)-have formed the impetus for a phethora of brute-force configuration-interaction calculations based on H(Ú) where H(Ú) may correspond to the free atom Hamiltonian matrix in the case of autoionization.MathSciNetADSCrossRefGoogle Scholar
  84. (G.D. Doolen, J.Phys. B8 525(1975)) or to atoms in external ac-or static fields.ADSGoogle Scholar
  85. [W.P. Reinhardt, Int J.Qu.Chem. S10, 359 (1976).Google Scholar
  86. S.I. Chu and W.P. Reinhardt Phys.Rev.Lett. 39, 1195 (1977).ADSCrossRefGoogle Scholar
  87. M. Crance and Aymar, J.Phys. B18, 3529 (1985)]. The computational method has been named the complex-coordinate rotation (CCR) and reviews together with applications can be found in refs./63–66/. The theory of this paper and the related computational methods are developed along the lines of N-electron eigenvalue equations with appropriate boundary conditions and with state-specific functions spaces which are characteristic of the physics of decay, and not along the lines of the CCR (i.e. of repeated diagonalization of H(Ú) in a large square-integrable basis set). Therefore, it has been possible to tackle the MEMP problem reliably/14/ and to compute properties of multichannel N-electron resonances such as partial widths /41–43/.ADSGoogle Scholar
  88. 63.
    B.R. Junker, in Adv.At.Mol.Phys. 18, 207 (1982).ADSCrossRefGoogle Scholar
  89. 64.
    W.P. Reinhardt, Ann.Rev.Phys.Chem. 33, 223 (1982).ADSCrossRefGoogle Scholar
  90. 65.
    Y.K. Ho, Phys.Rev. 99, 1 (1983).Google Scholar
  91. 66.
    S.-I. Chu, Adv.At.Mol.Phys. 21, 197 (1985).ADSCrossRefGoogle Scholar
  92. 67.
    B. Simon, Phys.Lett. 71A, 211 (1979).ADSCrossRefGoogle Scholar
  93. 68.
    S. Graffi and K. Yajima, Commun.Math.Phys. 89, 277 (1983).MathSciNetADSCrossRefMATHGoogle Scholar
  94. 69.
    D. R. Beck and C.A. Nicolaides, in “Excited States in Quantum Chemistry” eds.C.A. Nicolaides and D.R. Beck, Reidel (1978).Google Scholar
  95. 70.
    C. Froese-Fischer, Comp.Phys.Comm. 4, 107 (1972).ADSCrossRefGoogle Scholar
  96. 71.
    J.T. Broad, Phys.Rev. A3L 1494 (1985).ADSCrossRefGoogle Scholar
  97. 72.
    See also T.N. Rescigno, C.W. McCurdy and A.E. Orel, Phys.Rev. A17, 1931 (1978) for the case of the single channel calculation of the Be−(1S + e)2P0 shape resonance.ADSCrossRefGoogle Scholar
  98. 73.
    R. Bruch, S. Datz, P.D. Miller, P.L. Pepmiller, H.F. Kranse and N. Stolterfoht, Phys.Rev. A36, 394 (1987).ADSCrossRefGoogle Scholar
  99. 74.
    P. Agostini, F. Fabre, G. Mainfray, G. Petite and N. Rahman, Phys.Rev.Lett. 42, 1127 (1979).ADSCrossRefGoogle Scholar
  100. Y. Gontier, M. Poirier and M. Trahin, J.Phys. B13, 1381 (1980).ADSGoogle Scholar
  101. 75.
    P. Kruit, J. Kimman and M. van der Wiel, J.Phys. B14, L597 (1981).ADSGoogle Scholar
  102. 76.
    W. Zernik and R.W. Klopfenstein, J.Math.Phys. 6, 262 (1965).ADSCrossRefGoogle Scholar
  103. 77.
    S.H. Autler and C.H. Townes, Phys.Rev. 100, 703 (1955).ADSCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 1990

Authors and Affiliations

  • C. A. Nicolaides
    • 1
  • Th. Mercouris
    • 1
  1. 1.Theoretical and Physical Chemistry InstituteNational Hellenic Research FoundationAthensGreece

Personalised recommendations