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The European Physical Journal Special Topics

, Volume 223, Issue 2, pp 177–336 | Cite as

Time-dependent multiconfiguration methods for the numerical simulation of photoionization processes of many-electron atoms

  • D. Hochstuhl
  • C.M. Hinz
  • M. Bonitz
Review
Part of the following topical collections:
  1. Time-Dependent Multiconfiguration Methods for the Numerical Simulation of Photoionization Processes of Many-Electron Atoms

Abstract

Numerical simulations present an indispensable way to the understanding of complex physical processes. In quantum mechanics where the theoretical description is given in terms of the time-dependent Schrödinger equation the road is, however, difficult for any but the simplest systems. This is particularly true if one considers photoionization processes of atoms and molecules which, at the same time, require an accurate description of bound and continuum states and, therefore, an extensive region of space to be sampled during the calculation. As a consequence, direct simulations of photoionization processes are currently only feasible for systems containing up to three electrons. Despite this fundamental restriction, many physical effects can be essentially described by single- and two-electron models, among them are high-order harmonic generation and non-sequential double-ionization of atoms and molecules. A plethora of numerical investigations have been performed on atomic and molecular hydrogen and helium in the last two decades, and these have had a strong impact on the current understanding of photoionization. On the other hand, there are processes which are characterized by the interplay of a larger number of electrons, such as tunnel ionization, the Auger effect and, to give a more recent example, the temporal delay between the photo-emission of electrons from different shells of neon and krypton. The many-electron character of these effects complicates the accurate, time-resolved simulation and, so far, no universally applicable method exists. This review presents two theoretical methods which are promising candidates for closing this gap–the multiconfigurational time-dependent Hartree-Fock (MCTDHF) method and the time-dependent restricted active space configuration interaction (TD-RASCI) method. Both represent the wavefunction in a linear subspace of the many-body Hilbert space and follow particular strategies to avoid the exponential problem. This makes it possible to treat a much larger number of electrons than with the direct techniques mentioned above.

Keywords

European Physical Journal Special Topic Slater Determinant Orbital Equation Photoionization Process Discrete Variable Representation 
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.

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References

  1. 1.
    A. Einstein, Phys. Z. 18, 121 (1917)Google Scholar
  2. 2.
    J.P. Gordon, H.J. Zeiger, C.H. Townes, Phys. Rev. 99, 1264 (1955)ADSGoogle Scholar
  3. 3.
    A.L. Schawlow, C.H. Townes, Phys. Rev. 112, 1940 (1958)ADSGoogle Scholar
  4. 4.
    T.H. Maiman, Nature 187, 493 (1960)ADSGoogle Scholar
  5. 5.
    P.A. Franken, A.E. Hill, C.W. Peters, G. Weinreich, Phys. Rev. Lett. 7, 118 (1961)ADSGoogle Scholar
  6. 6.
    M.J. Weber, Handbook of Lasers (CRC Press, 2000)Google Scholar
  7. 7.
    D.A.G. Deacon, L.R. Elias, J.M.J. Madey, GJ Ramian, HA Schwettman, T.I. Smith, Phys. Rev. Lett. 38, 892 (1977)ADSGoogle Scholar
  8. 8.
    J. Ullrich, A. Rudenko, R. Moshammer, Ann. Rev. Phys. Chem. 63, 635 (2012)ADSGoogle Scholar
  9. 9.
    F. Grüner, S. Becker, U. Schramm, T. Eichner, M. Fuchs, R. Weingartner, D. Habs, J. Meyer-ter Vehn, M. Geissler, M. Ferrario, et al., App. Phys. B: Lasers Opt. 86, 431 (2007)ADSGoogle Scholar
  10. 10.
    A.A. Sorokin, M. Wellhöfer, S.V. Bobashev, K. Tiedtke, M. Richter, Phys. Rev. A 75, 051402 (2007)ADSGoogle Scholar
  11. 11.
    J.P. Cryan, J.M. Glownia, J. Andreasson, A. Belkacem, N. Berrah, C.I. Blaga, C. Bostedt, J. Bozek, C. Buth, L.F. DiMauro, L. Fang, O. Gessner, M. Guehr, J. Hajdu, M.P. Hertlein, M. Hoener, O. Kornilov, J.P. Marangos, A.M. March, B.K. McFarland, H. Merdji, V.S. Petrović, C. Raman, D. Ray, D. Reis, F. Tarantelli, M. Trigo, J.L. White, W. White, L. Young, P.H. Bucksbaum, R.N. Coffee, Phys. Rev. Lett. 105, 083004 (2010)ADSGoogle Scholar
  12. 12.
    H.N. Chapman, P. Fromme, A. Barty, T.A. White, R.A. Kirian, A. Aquila, M.S. Hunter, J. Schulz, D.P. DePonte, U. Weierstall, et al., Nature 470, 73 (2011)ADSGoogle Scholar
  13. 13.
    J. Ullrich, R. Moshammer, A. Dorn, R. Dörner, L.P.H. Schmidt, H. Schmidt-Böcking, Reports Progr. Phys. 66, 1463 (2003)ADSGoogle Scholar
  14. 14.
    P.M. Paul, E.S. Toma, P. Breger, G. Mullot, F. Augé, P. Balcou, H.G. Muller, P. Agostini, Science 292, 1689 (2001)ADSGoogle Scholar
  15. 15.
    M. Hentschel, R. Kienberger, C. Spielmann, GA Reider, N. Milosevic, T. Brabec, P. Corkum, U. Heinzmann, M. Drescher, F. Krausz, Nature 414, 509 (2001)ADSGoogle Scholar
  16. 16.
    L. Gallmann, C. Cirelli, U. Keller, Ann. Rev. Phys. Chem. 63, 447 (2012)ADSGoogle Scholar
  17. 17.
    M. Drescher, M. Hentschel, R. Kienberger, M. Uiberacker, V. Yakovlev, A. Scrinzi, T. Westerwalbesloh, U. Kleineberg, U. Heinzmann, F. Krausz, Nature 419, 803 (2002)ADSGoogle Scholar
  18. 18.
    E. Goulielmakis, M. Uiberacker, R. Kienberger, A. Baltuska, V. Yakovlev, A. Scrinzi, T. Westerwalbesloh, U. Kleineberg, M. Drescher, Science 305, 1267 (2004)ADSGoogle Scholar
  19. 19.
    M. Uiberacker, T. Uphues, M. Schultze, A.J. Verhoef, V. Yakovlev, M.F. Kling, J. Rauschenberger, N.M. Kabachnik, H. Schröder, M. Lezius, Nature 446, 627 (2007)ADSGoogle Scholar
  20. 20.
    P.B. Corkum, Phys. Rev. Lett. 71, 1994 (1993)ADSGoogle Scholar
  21. 21.
    M. Lewenstein, Ph. Balcou, M.Yu. Ivanov, A. L’Huillier, P.B. Corkum, Phys. Rev. A 49, 2117 (1994)ADSGoogle Scholar
  22. 22.
    R. Santra, A. Gordon, Phys. Rev. Lett. 96, 73906 (2006)ADSGoogle Scholar
  23. 23.
    M.F. Kling, M.J.J. Vrakking, Ann. Rev. Phys. Chem. 59, 463 (2008)ADSGoogle Scholar
  24. 24.
    E. Goulielmakis, M. Schultze, M. Hofstetter, V.S. Yakovlev, J. Gagnon, M. Uiberacker, A.L. Aquila, E.M. Gullikson, D.T. Attwood, R. Kienberger, F. Krausz, U. Kleineberg, Science 320, 1614 (2008)ADSGoogle Scholar
  25. 25.
    K. Zhao, Q. Zhang, M. Chini, Y. Wu, X. Wang, Z. Chang, Opt. Lett. 37, 3891 (2012)ADSGoogle Scholar
  26. 26.
    S. Bauch, M. Bonitz, Phys. Rev. A 78, 043403 (2008)ADSGoogle Scholar
  27. 27.
    P. Tzallas, E. Skantzakis, L.A.A. Nikolopoulos, G.D. Tsakiris, D. Charalambidis, Nat. Phys. 7, 781 (2011)Google Scholar
  28. 28.
    B. Schütte, S. Bauch, U. Frühling, M. Wieland, M. Gensch, E. Plönjes, T. Gaumnitz, A. Azima, M. Bonitz, M. Drescher, Phys. Rev. Lett. 108, 253003 (2012)ADSGoogle Scholar
  29. 29.
    S. Bauch, M. Bonitz, Phys. Rev. A 85, 053416 (2012)ADSGoogle Scholar
  30. 30.
    M. Schultze, M. Fieß, N. Karpowicz, J. Gagnon, M. Korbman, M. Hofstetter, S. Neppl, A.L. Cavalieri, Y. Komninos, T. Mercouris, et al., Science 328, 1658 (2010)ADSGoogle Scholar
  31. 31.
    A.S. Kheifets, I.A. Ivanov, Phys. Rev. Lett. 105, 233002 (2010)ADSGoogle Scholar
  32. 32.
    S. Nagele, R. Pazourek, J. Feist, K. Doblhoff-Dier, C. Lemell, K. Tokési, J. Burgdörfer, J. Phys. B: Atomic, Molec. Opt. Phys. 44, 081001 (2011)ADSGoogle Scholar
  33. 33.
    L.R. Moore, M.A. Lysaght, J.S. Parker, H.W. van der Hart, K.T. Taylor, Phys. Rev. A 84, 061404 (2011)ADSGoogle Scholar
  34. 34.
    P. Eckle, A.N. Pfeiffer, C. Cirelli, A. Staudte, R. Dörner, H.G. Muller, M. Büttiker, U. Keller, Science 322, 1525 (2008)ADSGoogle Scholar
  35. 35.
    E. Goulielmakis, Z.H. Loh, A. Wirth, R. Santra, N. Rohringer, V.S. Yakovlev, S. Zherebtsov, T. Pfeifer, A.M. Azzeer, M.F. Kling, et al., Nature 466, 739 (2010)ADSGoogle Scholar
  36. 36.
    E.E. Krasovskii, M. Bonitz, Phys. Rev. Lett. 99, 247601 (2007)ADSGoogle Scholar
  37. 37.
    E.E. Krasovskii, M. Bonitz, Phys. Rev. A 80, 053421 (2009)ADSGoogle Scholar
  38. 38.
    F.H.M. Faisal, J. Phys. B: Atomic Mol. Phys. 6, L89 (1973)ADSGoogle Scholar
  39. 39.
    H.R. Reiss, Phys. Rev. A 22, 1786 (1980)ADSGoogle Scholar
  40. 40.
    M.V. Ammosov, N.B. Delone, V.P. Krainov, Soviet. Phys. JETP 23, 924 (1986)Google Scholar
  41. 41.
    N. Camus, B. Fischer, M. Kremer, V. Sharma, A. Rudenko, B. Bergues, M. Kübel, N.G. Johnson, M.F. Kling, T. Pfeifer, J. Ullrich, R. Moshammer. Phys. Rev. Lett. 108, 073003 (2012)ADSGoogle Scholar
  42. 42.
    P. Krause, T. Klamroth, P. Saalfrank, J. Chem. Phys. 123, 074105 (2005)ADSGoogle Scholar
  43. 43.
    J. Feist, S. Nagele, R. Pazourek, E. Persson, B.I. Schneider, L.A. Collins, J. Burgdörfer, Phys. Rev. A 77, 043420 (2008)ADSGoogle Scholar
  44. 44.
    M. Rontani, C. Cavazzoni, D. Bellucci, G. Goldoni, J. Chem. Phys. 124, 124102 (2006)ADSGoogle Scholar
  45. 45.
    R. Bellman, Adaptive Control Processes: A Guided Tour (Princeton University Press, 1961)Google Scholar
  46. 46.
    J. Colgan, M.S. Pindzola, Phys. Rev. Lett. 108, 053001 (2012)ADSGoogle Scholar
  47. 47.
    E. Foumouo, G.L. Kamta, G. Edah, B. Piraux, Phys. Rev. A 74, 063409 (2006)ADSGoogle Scholar
  48. 48.
    M. Walter, J. Briggs, J. Phys. B: Atomic, Molec. Optical Phys. 32, 2487 (1999)ADSGoogle Scholar
  49. 49.
    J. Feist, S. Nagele, C. Ticknor, B.I. Schneider, L.A. Collins, J. Burgdörfer, Phys. Rev. Lett. 107, 93005 (2011)ADSGoogle Scholar
  50. 50.
    A. Palacios, T.N. Rescigno, C.W. McCurdy, Phys. Rev. Lett. 103, 253001 (2009)ADSGoogle Scholar
  51. 51.
    S. Bauch, K. Balzer, M. Bonitz, EPL 91, 53001 (2010)ADSGoogle Scholar
  52. 52.
    R. van Leeuwen, Phys. Rev. Lett. 82, 3863 (1999)ADSGoogle Scholar
  53. 53.
    K. Pernal, O. Gritsenko, E.J. Baerends, Phys. Rev. A 75, 012506 (2007)ADSGoogle Scholar
  54. 54.
    M. Bonitz, D. Semkat (eds.), Introduction to Computational Methods in Many Body Physics (Rinton Press, Princeton, 2006)Google Scholar
  55. 55.
    N.E. Dahlen, R. van Leeuwen, Phys. Rev. Lett. 98, 153004 (2007)ADSGoogle Scholar
  56. 56.
    D.A. Mazziotti, Phys. Rev. Lett. 93, 213001 (2004)ADSGoogle Scholar
  57. 57.
    K.C. Kulander, Phys. Rev. A 38, 778 (1988)ADSGoogle Scholar
  58. 58.
    S. Kvaal, J. Chem. Phys. 136, 194109 (2012)ADSGoogle Scholar
  59. 59.
    T. Helgaker, P. Joergensen, J. Olsen, Molecular Electronic Structure Theory (Wiley, New York, 2000)Google Scholar
  60. 60.
    S.R. White, A.E. Feiguin, Phys. Rev. Lett. 93, 76401 (2004)ADSGoogle Scholar
  61. 61.
    K.H. Marti, B. Bauer, M. Reiher, M. Troyer, F. Verstraete, New J. Phys. 12, 103008 (2010)ADSGoogle Scholar
  62. 62.
    G.H. Booth, A.J.W. Thom, A. Alavi, J. Chem. Phys. 131, 054106 (2009)ADSGoogle Scholar
  63. 63.
    K.C. Kulander, B.W. Shore, J. Optical Soc. Amer. B 7, 502 (1990)ADSGoogle Scholar
  64. 64.
    L. Greenman, P.J. Ho, S. Pabst, E. Kamarchik, D.A. Mazziotti, R. Santra, Phys. Rev. A 82, 023406 (2010)ADSGoogle Scholar
  65. 65.
    P.G. Burke, K.T. Taylor, J. Phys. B: Atomic, Molec. Optical Phys. 8, 2620 (1975)ADSGoogle Scholar
  66. 66.
    D. Hochstuhl, Multiconfiguration Methods for the Numerical Simulation of Photoionization Processes of Many-Electron Atoms, Ph.D. thesis, University of Kiel, 2013Google Scholar
  67. 67.
    M.A. Lysaght, P.G. Burke, H.W. van der Hart, Phys. Rev. Lett. 101, 253001 (2008)ADSGoogle Scholar
  68. 68.
    X. Guan, O. Zatsarinny, K. Bartschat, B.I. Schneider, J. Feist, C.J. Noble, Phys. Rev. A 76, 053411 (2007)ADSGoogle Scholar
  69. 69.
    X. Guan, C.J. Noble, O. Zatsarinny, K. Bartschat, B.I. Schneider, Phys. Rev. A 78, 053402 (2008)ADSGoogle Scholar
  70. 70.
    J. Caillat, J. Zanghellini, M. Kitzler, O. Koch, W. Kreuzer, A. Scrinzi, Phys. Rev. A 71, 012712 (2005)ADSGoogle Scholar
  71. 71.
    T. Kato, H. Kono, Chem. Phys. Lett. 392, 533 (2004)ADSGoogle Scholar
  72. 72.
    M. Nest, T. Klamroth, P. Saalfrank, J. Chem. Phys. 122, 124102 (2005)ADSGoogle Scholar
  73. 73.
    D.J. Haxton, K.V. Lawler, C.W. McCurdy, Phys. Rev. A 83, 063416 (2011)ADSGoogle Scholar
  74. 74.
    D.J. Haxton, K.V. Lawler, C.W. McCurdy, Phys. Rev. A 86, 013406 (2012)ADSGoogle Scholar
  75. 75.
    D. Hochstuhl, M. Bonitz, Phys. Rev. A 86, 053424 (2012)ADSGoogle Scholar
  76. 76.
    D. Hochstuhl, M. Bonitz, J. Chem. Phys. 134, 084106 (2011)ADSGoogle Scholar
  77. 77.
    D. Hochstuhl, M. Bonitz, J. Phys. Conf. Ser. 427, 012007 (2013)ADSGoogle Scholar
  78. 78.
    E. Schrödinger, Ann. Physik 385, 437 (1926)Google Scholar
  79. 79.
    C.C. Gerry, P.L. Knight, Introductory Quantum Optics, Vol. 73 (Cambridge University Press, 2004)Google Scholar
  80. 80.
    I. Hertel, C. Schulz, Atome, Moleküle und Optische Physik 1 (Springer, Berlin Heidelberg, 2008)Google Scholar
  81. 81.
    M. Born, R. Oppenheimer, Ann. Physik 389, 457 (1927)ADSGoogle Scholar
  82. 82.
    H.J. Kull, Laserphysik: Physikalische Grundlagen des Laserlichts und Seine Wechselwirkung mit Materie (Oldenbourg Wissenschaftsverlag, 2010)Google Scholar
  83. 83.
    P. Pyykko, Chem. Rev. 88, 563 (1988)Google Scholar
  84. 84.
    R. Pauncz, Spin Eigenfunctions: Construction and Use (Plenum Press, New York, 1979)Google Scholar
  85. 85.
    J. Von Neumann, Mathematical Foundations of Quantum Mechanics, Vol. 2 (Princeton University Press, 1996)Google Scholar
  86. 86.
    G. Teschl, Mathematical methods in quantum mechanics: with applications to Schrödinger operators, Vol. 99 (American Mathematical Society, 2009)Google Scholar
  87. 87.
    A.L. Fetter, J.D. Walecka, Quantum Theory of Many-Particle Systems (Dover Publications, 2003)Google Scholar
  88. 88.
    M.H. Beck, A. Jäckle, GA Worth, H.D. Meyer, Phys. Rep. 324, 1 (2000)ADSGoogle Scholar
  89. 89.
    J.C. Slater, Phys. Rev. 34, 1293 (1929)zbMATHADSGoogle Scholar
  90. 90.
    E.U. Condon, Phys. Rev. 36, 1121 (1930)zbMATHADSGoogle Scholar
  91. 91.
    P.O. Löwdin, Phys. Rev. 97, 1474 (1955)zbMATHMathSciNetADSGoogle Scholar
  92. 92.
    R.K. Nesbet, Variational Principles and Methods in Theoretical Physics and Chemistry (Cambridge University Press, 2003)Google Scholar
  93. 93.
    P. Kramer, M. Saraceno, Geometry of the Time-Dependent Variational Principle in Quantum Mechanics Geometry of the Time-Dependent Variational Principle in Quantum Mechanics, Vol. 140 (1981)Google Scholar
  94. 94.
    P.A.M. Dirac, Note on exchange phenomena in the Thomas atom Mathematical Proceedings of the Cambridge Philosophical Society, Vol. 26 (Cambridge University Press, 1930)Google Scholar
  95. 95.
    J. Frenkel, Wave Mechanics (Clarendon Press, Oxford, 1934)Google Scholar
  96. 96.
    A.D. McLachlan, Molec. Phys. 8, 39 (1964)MathSciNetADSGoogle Scholar
  97. 97.
    O.E. Alon, A.I. Streltsov, L.S. Cederbaum, J. Chem. Phys. 127, 154103 (2007)ADSGoogle Scholar
  98. 98.
    I. Shavitt, Mole. Phys. 94, 3 (1998)ADSGoogle Scholar
  99. 99.
    J. Olsen, P. Jørgensen, J. Simons, Chem. Phys. Lett. 169, 463 (1990)ADSGoogle Scholar
  100. 100.
    E. Rossi, G.L. Bendazzoli, S. Evangelisti, D. Maynau, Chem. Phys. Lett. 310, 530 (1999)ADSGoogle Scholar
  101. 101.
    F. Becca, A. Parola, S. Sorella, Phys. Rev. B 61, 16287 (2000)ADSGoogle Scholar
  102. 102.
    F. Deuretzbacher, K. Bongs, K. Sengstock, D. Pfannkuche, Phys. Rev. A 75, 013614 (2007)ADSGoogle Scholar
  103. 103.
    G.D. Purvis III, R.J. Bartlett, J.Chem. Phys. 76, 1910 (1982)ADSGoogle Scholar
  104. 104.
    S.R. White, R.L. Martin, J. Chem. Phys. 110, 4127 (1999)ADSGoogle Scholar
  105. 105.
    S. Laulan, H. Bachau, Phys. Rev. A 68, 013409 (2003)ADSGoogle Scholar
  106. 106.
    J. Colgan, M.S. Pindzola, F. Robicheaux, J. Phys. B: Atom., Molec. Opt. Phys. 37, L377 (2004)ADSGoogle Scholar
  107. 107.
    S. Laulan, H. Bachau, Phys. Rev. A 69, 033408 (2004)ADSGoogle Scholar
  108. 108.
    F.L. Yip, C.W. McCurdy, T.N. Rescigno, Phys. Rev. A 81, 053407 (2010)ADSGoogle Scholar
  109. 109.
    D. Hochstuhl, S. Bauch, M. Bonitz, J. Phys.: Conf. Ser. 220, 012019 (2010)ADSGoogle Scholar
  110. 110.
    B. Roos, Chem. Phys. Lett. 15, 153 (1972)ADSGoogle Scholar
  111. 111.
    J.C. Slater, Quantum Theory of Molecules and Solids (McGraw-Hill, 1967)Google Scholar
  112. 112.
    M. Tinkham, Group Theory and Quantum Mechanics (Dover Publications, 2003)Google Scholar
  113. 113.
    G.B. Arfken, H.J. Weber, Mathematical Methods for Physicists, Sixth edition (New York Academic, 2005)Google Scholar
  114. 114.
    P.O. Löwdin, Rev. Mod. Phys. 36, 966 (1964)ADSGoogle Scholar
  115. 115.
    R.K. Nesbet, J. Math. Phys. 2, 701 (1961)zbMATHMathSciNetADSGoogle Scholar
  116. 116.
    W. Duch, J. Karwowski. Comput. Phys. Rep. 2, 93 (1985)ADSGoogle Scholar
  117. 117.
    H.F. Schaefer, F.E. Harris, J. Comput. Phys. 3, 217 (1968)MathSciNetADSGoogle Scholar
  118. 118.
    C.B. Mendl, G. Friesecke, Angular Momentum and Spin Diagonalization on Atomic Subshells: Algorithm and Complexity (2011)Google Scholar
  119. 119.
    A. Szabo, N.S. Ostlund, Modern Quantum Chemistry: Introduction to Advanced Electronic Structure Theory (Courier Dover Publications, 1996)Google Scholar
  120. 120.
    S.A. Blundell, K. Joshi, Phys. Rev. B 81, 115323 (2010)ADSGoogle Scholar
  121. 121.
    T. Vänskä, D. Sundholm, M. Lindberg, Phys. Rev. A 75, 023621 (2007)ADSGoogle Scholar
  122. 122.
    J. Olsen, B.O. Roos, P. Jørgensen, H.J.A. Jensen, J. Chem. Phys. 89, 2185 (1988)ADSGoogle Scholar
  123. 123.
    C.B. Mendl, Comput. Phys. Comm. 182, 1327 (2011)zbMATHADSGoogle Scholar
  124. 124.
    K.J. Schafer, B. Yang, L.F. DiMauro, K.C. Kulander, Phys. Rev. Lett. 70, 1599 (1993)ADSGoogle Scholar
  125. 125.
    C.I. Blaga, F. Catoire, P. Colosimo, G.G. Paulus, H.G. Muller, P. Agostini, L.F. DiMauro, Nat. Phys. 5, 335 (2009)Google Scholar
  126. 126.
    M. Awasthi, Y.V. Vanne, A. Saenz, A. Castro, P. Decleva, Phys. Rev. A 77, 063403 (2008)ADSGoogle Scholar
  127. 127.
    M. Lein, Phys. Rev. Lett. 94, 53004 (2005)ADSGoogle Scholar
  128. 128.
    G. Lagmago Kamta, A.F. Starace, Phys. Rev. A 65, 053418 (2002)ADSGoogle Scholar
  129. 129.
    N. Rohringer, A. Gordon, R. Santra, Phys. Rev. A 74, 043420 (2006)ADSGoogle Scholar
  130. 130.
    A. Gordon, F.X. Kärtner, N. Rohringer, R. Santra, Phys. Rev. Lett. 96, 223902 (2006)ADSGoogle Scholar
  131. 131.
    S. Pabst, L. Greenman, P.J. Ho, D.A. Mazziotti, R. Santra, Phys. Rev. Lett. 106, 053003 (2011)ADSGoogle Scholar
  132. 132.
    M. Spanner, S. Patchkovskii, Phys. Rev. A 80, 063411 (2009)ADSGoogle Scholar
  133. 133.
    X.M. Tong, C.D. Lin, J. Phys. B: Atom., Molec. Opt. Phys. 38, 2593 (2005)ADSGoogle Scholar
  134. 134.
    J. Mauritssen, M.B. Gaarde, K.J. Schafer, Phys. Rev. A 72, 13401 (2005)ADSGoogle Scholar
  135. 135.
    A.K. Kazansky, N.M. Kabachnik, J. Phys. B: Atom., Molec. Opt. Phys. 43, 035601 (2010)ADSGoogle Scholar
  136. 136.
    A.K. Kazansky, N.M. Kabachnik, Phys. Rev. A 72, 052714 (2005)ADSGoogle Scholar
  137. 137.
    F. Jensen, Introduction to Computational Chemistry, Vol. 2 (Wiley, New York, 1999)Google Scholar
  138. 138.
    J.S. Parker, E.S. Smyth, K.T. Taylor, J. Phys. B: Atom., Molec. Opt. Phys. 31, L571 (1998)ADSGoogle Scholar
  139. 139.
    H. Bachau, E. Cormier, P. Decleva, J.E. Hansen, F. Martin, Reports Progr. Phys. 64, 1815 (2001)ADSGoogle Scholar
  140. 140.
    S. Goedecker, O.V. Ivanov, Solid State Comm. 105, 665 (1998)ADSGoogle Scholar
  141. 141.
    C. McKenna, H.W. van der Hart, J. Phys. B: Atom., Molec. Opt. Phys. 37, 457 (2003)ADSGoogle Scholar
  142. 142.
    A.C. Brown, S. Hutchinson, M.A. Lysaght, H.W. van der Hart, Phys. Rev. Lett. 108, 063006 (2012)ADSGoogle Scholar
  143. 143.
    D.R. Hartree, W. Hartree, B. Swirles, Phil. Trans. Royal Soc. London. Ser A, Math. Phys. Sci. 238, 229 (1939)Google Scholar
  144. 144.
    C.F. Fischer, The Hartree-Fock Method for Atoms. A Numerical Approach (Wiley, New York, 1977)Google Scholar
  145. 145.
    H.P. Saha, C.D. Caldwell, Phys. Rev. A 40, 7020 (1989)ADSGoogle Scholar
  146. 146.
    S. Fritzsche, A.N. Grum-Grzhimailo, E.V. Gryzlova, N.M. Kabachnik, J. Phys. B: Atom Molec. Optical Phys. 41, 165601 (2008)ADSGoogle Scholar
  147. 147.
    E. Dalgaard, J. Chem. Phys. 72, 816 (1980)MathSciNetADSGoogle Scholar
  148. 148.
    D.L. Yeager, P. Jørgensen, Chem. Phys. Lett. 65, 77 (1979)ADSGoogle Scholar
  149. 149.
    R. McWeeny, Inter. J. Quant. Chem. 23, 405 (1983)Google Scholar
  150. 150.
    H.D. Meyer, U. Manthe, L.S. Cederbaum, Chem. Phys. Lett. 165, 73 (1990)ADSGoogle Scholar
  151. 151.
    U. Manthe, H.-D. Meyer, L.S. Cederbaum, J. Chem. Phys. 97, 3199 (1992)ADSGoogle Scholar
  152. 152.
    H.D. Meyer, F. Gatti, G.A. Worth, Multidimensional Quantum Dynamics (Wiley-VCH, 2010)Google Scholar
  153. 153.
    J. Zanghellini, M. Kitzler, T. Brabec, A. Scrinzi, J. Phys. B: Atom Molec. Opt. Phys. 37, 763 (2004)ADSGoogle Scholar
  154. 154.
    O.E. Alon, A.I. Streltsov, L.S. Cederbaum, Phys. Rev. A 77, 033613 (2008)ADSGoogle Scholar
  155. 155.
    T. Tung Nguyen-Dang, M. Peters, Sen-Ming Wang, E. Sinelnikov, F. Dion, J. Chem. Phys. 127, 174107 (2007)ADSGoogle Scholar
  156. 156.
    G.A. Worth, H.D. Meyer, L.S. Cederbaum, W. Domcke, D.R. Yarkony, H. Köppel, Conical Intersections: Electr. Struc. Dyn. Spectr., 583 (2004)Google Scholar
  157. 157.
    H.-D. Meyer, Wiley Interdisciplinary Rev: Comput. Molec. Sci. 2, 351 (2012)Google Scholar
  158. 158.
    H. Miyagi, L.B. Madsen, Phys. Rev. A 87, 062511 (2013)ADSGoogle Scholar
  159. 159.
    G. Jordan, J. Caillat, C. Ede, A. Scrinzi, J. Phys. B: Atom. Molec. Optical Phys. 39, S341 (2006)ADSGoogle Scholar
  160. 160.
    M. Nest, R. Padmanaban, P. Saalfrank, J. Chem. Phys. 126, 214106 (2007)ADSGoogle Scholar
  161. 161.
    T. Klamroth, M. Nest, Phys. Chem. Chem. Phys. 11, 349 (2009)Google Scholar
  162. 162.
    T. Kato, H. Kono, J. Chem. Phys. 128, 184102 (2008)ADSGoogle Scholar
  163. 163.
    T. Kato, H. Kono, M. Kanno, Y. Fujimura, K. Yamanouchi, Laser Phys. 19, 1712 (2009)ADSGoogle Scholar
  164. 164.
    T. Nguyen-Dang, M. Peters, S. Wang, F. Dion, Laser Phys. 19, 1521 (2009)ADSGoogle Scholar
  165. 165.
    M. Nest, Chem. Phys. Lett. 472, 171 (2009)ADSGoogle Scholar
  166. 166.
    S. Kvaal, Phys. Rev. A 84, 022512 (2011)ADSGoogle Scholar
  167. 167.
    M. Bonitz, D. Hochstuhl, S. Bauch, K. Balzer, Contrib. Plasma Phys. 50, 54 (2010)ADSGoogle Scholar
  168. 168.
    S. Bauch, D. Hochstuhl, K. Balzer, M. Bonitz, J. Phys.: Conf. Ser. 220, 012013 (2010)ADSGoogle Scholar
  169. 169.
    J.W. Abraham, K. Balzer, D. Hochstuhl, M. Bonitz, Phys. Rev. B 86, 125112 (2012)ADSGoogle Scholar
  170. 170.
    C. McDonald, G. Orlando, J.W. Abraham, D. Hochstuhl, M. Bonitz, T. Brabec, Phys. Rev. Lett. 111, 256801 (2013)ADSGoogle Scholar
  171. 171.
    J.W. Abraham, M. Bonitz, C. McDonald, G. Orlando, T. Brabec, New J. Phys. 16, 013001 (2014)Google Scholar
  172. 172.
    C.D. Sherrill, M.S. Lee, M. Head-Gordon, Chem. Phys. Lett. 302, 425 (1999)ADSGoogle Scholar
  173. 173.
    M. Heimsoth, M. Bonitz, Physica E: Low-dimensional Syst. Nanostr. 42, 420 (2010)ADSGoogle Scholar
  174. 174.
    A. Dalgarno, G.A. Victor, Proc. Royal Soc. London Series A. Math. Phys. Sci. 291, 291 (1966)ADSGoogle Scholar
  175. 175.
    K.L. Schuchardt, B.T. Didier, T. Elsethagen, L. Sun, V. Gurumoorthi, J. Chase, J. Li, T.L. Windus, J. Chem. Info. Model. 47, 1045 (2007)Google Scholar
  176. 176.
    R.L. DeKock, H.B. Gray, Chem. Structure and Bonding (University Science Books, 1989)Google Scholar
  177. 177.
    J.C. Slater, Phys. Rev. 36, 57 (1930)zbMATHADSGoogle Scholar
  178. 178.
    T. Kato, Comm. Pure Appl. Math. 10, 151 (1957)zbMATHMathSciNetGoogle Scholar
  179. 179.
    S.F. Boys, Proc. Royal Soc. London. Ser. A. Math. Phys. Sci. 200, 542 (1950)zbMATHADSGoogle Scholar
  180. 180.
    S. Huzinaga, Comput. Phys. Reports 2, 281 (1985)ADSGoogle Scholar
  181. 181.
    A. Faure, J.D. Gorfinkiel, L.A. Morgan, J. Tennyson, Comput. Phys. Comm. 144, 224 (2002)zbMATHADSGoogle Scholar
  182. 182.
    X. Li, S.M. Smith, A.N. Markevitch, D.A. Romanov, R.J. Levis, H.B. Schlegel, Phys. Chem. Chem. Phys. 7, 233 (2005)Google Scholar
  183. 183.
    P. Krause, T. Klamroth, P. Saalfrank, J. Chem. Phys. 127, 034107 (2007)ADSGoogle Scholar
  184. 184.
    H.G. Muller, Laser Phys. 9, 138 (1999)Google Scholar
  185. 185.
    C.W. McCurdy, F. Martín, J. Phys. B: Atomic, Molec. Optical Phys. 37, 917 (2004)ADSGoogle Scholar
  186. 186.
    L. Füsti-Molnar, P. Pulay, J. Chem. Phys. 116, 7795 (2002)ADSGoogle Scholar
  187. 187.
    J.V. Lill, G.A. Parker, J.C. Light, J. Chem. Phys. 85, 900 (1986)ADSGoogle Scholar
  188. 188.
    D.T. Colbert, W.H. Miller, J. Chem. Phys. 96, 1982 (1992)ADSGoogle Scholar
  189. 189.
    L.Y. Peng, A.F. Starace, J. Chem. Phys. 125, 154311 (2006)ADSGoogle Scholar
  190. 190.
    C.W. McCurdy, M. Baertschy, T.N. Rescigno, J. Phys. B: Atom, Molec. Optical Phys. 37, R137 (2004)ADSGoogle Scholar
  191. 191.
    S. Sukiasyan, H.D. Meyer, J. Phys. Chem. A 105, 2604 (2001)Google Scholar
  192. 192.
    D.J. Haxton, J. Phys. B: Atomic, Molec. Optical Phys. 40, 4443 (2007)ADSGoogle Scholar
  193. 193.
    V.I. Lebedev, D.N. Laikov, Doklady Math. 59 (1999)Google Scholar
  194. 194.
    L. Tao, C.W. McCurdy, T.N. Rescigno, Phys. Rev. A 79, 012719 (2009)ADSGoogle Scholar
  195. 195.
    L. Tao, C.W. McCurdy, T.N. Rescigno, Phys. Rev. A 82, 023423 (2010)ADSGoogle Scholar
  196. 196.
    J.N. Hurley, D.L. Huestis, W.A. Goddard III, J. Phys. Chem. 92, 4880 (1988)Google Scholar
  197. 197.
    A. Jäckle, H.D. Meyer, J. Chem. Phys. 104, 7974 (1996)ADSGoogle Scholar
  198. 198.
    N.H.F. Beebe, J. Linderberg, Inter. J. Quant. Chem. 12, 683 (1977)Google Scholar
  199. 199.
    S. Wilson, Comput. Phys. Comm. 58, 71 (1990)ADSGoogle Scholar
  200. 200.
    F. Aquilante, L. Gagliardi, T.B. Pedersen, R. Lindh, J. Chem. Phys. 130, 154107 (2009)ADSGoogle Scholar
  201. 201.
    U. Benedikt, A.A. Auer, M. Espig, W. Hackbusch, J. Chem. Phys. 134, 4118 (2011)ADSGoogle Scholar
  202. 202.
    R.C. Raffenetti, J. Chem. Phys. 59, 5936 (1973)ADSGoogle Scholar
  203. 203.
    A.D. Becke, R.M. Dickson, J. Chem. Phys. 89, 2993 (1988)ADSGoogle Scholar
  204. 204.
    W.H. Press, S.A. Teukolsky, W.T. Vetterling, B.P. Flannery, Numerical Recipes Third Edition: The Art of Scientific Computing (Cambridge University Press, 2007)Google Scholar
  205. 205.
    P.J. Knowles, N.C. Handy, Chem. Phys. Lett. 111, 315 (1984)ADSGoogle Scholar
  206. 206.
    A.I. Streltsov, O.E. Alon, L.S. Cederbaum, Phys. Rev. A. 81, 022124 (2010)ADSGoogle Scholar
  207. 207.
    T. Fließbach, Lehrbuch zur Theoretischen Physik. 3. Quantenmechanik (Spektrum Akademischer Verlag, 2000)Google Scholar
  208. 208.
    S. Blanes, F. Casas, J.A. Oteo, J. Ros, Phys. Rep. 470, 151 (2009)MathSciNetADSGoogle Scholar
  209. 209.
    M. Klaiber, D. Dimitrovski, J.S. Briggs, Phys. Rev. A. 79, 043402 (2009)ADSGoogle Scholar
  210. 210.
    U. Peskin, N. Moiseyev, J. Chem. Phys. 99, 4590 (1993)ADSGoogle Scholar
  211. 211.
    M. Heimsoth, C.E. Creffield, L.D. Carr, F. Sols, New J. Phys. 14, 075023 (2012)ADSGoogle Scholar
  212. 212.
    M. Ndong, H. Tal-Ezer, R. Kosloff, C.P. Koch, J. Chem. Phys. 132, 064105 (2010)ADSGoogle Scholar
  213. 213.
    H. Tal-Ezer, R. Kosloff, J. Chem. Phys. 81, 3967 (1984)ADSGoogle Scholar
  214. 214.
    W. van Dijk, F.M. Toyama, Phys. Rev. E 75, 036707 (2007)MathSciNetADSGoogle Scholar
  215. 215.
    S.A. Chin, C.R. Chen, J. Chem. Phys. 117, 1409 (2002)ADSGoogle Scholar
  216. 216.
    C. Leforestier, R.H. Bisseling, C. Cerjan, M.D. Feit, R. Friesner, A. Guldberg, A. Hammerich, G. Jolicard, W. Karrlein, H.D. Meyer, N. Lipkin, O. Roncero, R. Kosloff, J. Comput. Phys. 94, 59 (1991)zbMATHMathSciNetADSGoogle Scholar
  217. 217.
    E. Hairer, S.P. Nørsett, G. Wanner, Solving Ordinary Differential Equations: Nonstiff Problems, Vol. 1 (Springer Verlag, 1993)Google Scholar
  218. 218.
    J.C. Tremblay, T. Carrington Jr., J. Chem. Phys. 121, 11535 (2004)ADSGoogle Scholar
  219. 219.
    K. Kormann, S. Holmgren, H.O. Karlsson, J. Chem. Phys. 128, 184101 (2008)ADSGoogle Scholar
  220. 220.
    Th. Monovasilis, Z. Kalogiratou, T.E. Simos, Comput. Phys. Commu. 181, 1251 (2010)zbMATHMathSciNetADSGoogle Scholar
  221. 221.
    Tae Jun Park, J.C. Light, J. Chem. Phys. 85, 5870 (1986)ADSGoogle Scholar
  222. 222.
    Q. Jie, D. Liu, J. Phys. A: Math., General 39, 1691 (2006)zbMATHMathSciNetGoogle Scholar
  223. 223.
    C. Moler, C. Van Loan, SIAM Rev. 45, 3 (2003)zbMATHMathSciNetADSGoogle Scholar
  224. 224.
    M. Abramowitz, I.A. Stegun, Handbook of Mathematical Functions: With Formulas, Graphs, Mathematical Tables (Dover Publications, 1965)Google Scholar
  225. 225.
    Y. Saad, Numerical Methods for Large Eigenvalue Problems (Manchester University Press, 1992)Google Scholar
  226. 226.
    L. Lehtovaara, J. Toivanen, J. Eloranta, J. Comput. Phys. 221, 148 (2007)zbMATHADSGoogle Scholar
  227. 227.
    S. Hermanns, K. Balzer, M. Bonitz, Phys. Scr. 2012, 014036 (2012)Google Scholar
  228. 228.
    A. Scrinzi, B. Piraux, Phys. Rev. A. 58, 1310 (1998)ADSGoogle Scholar
  229. 229.
    M. Førre, S. Selstø, Raymond Nepstad, Phys. Rev. Lett. 105, 163001 (2010)ADSGoogle Scholar
  230. 230.
    A. Palacios, T.N. Rescigno, C.W. McCurdy, Phys. Rev. A. 77, 032716 (2008)ADSGoogle Scholar
  231. 231.
    J.S. Parker, L.R. Moore, K.J. Meharg, D. Dundas, K.T. Taylor, J. Phys. B: Atom. Molec. Optical Phys. 34, L69 (2001)ADSGoogle Scholar
  232. 232.
    L.B. Madsen, L.A.A. Nikolopoulos, T.K. Kjeldsen, J. Fernández, Phys. Rev. A. 76, 063407 (2007)ADSGoogle Scholar
  233. 233.
    L.A.A. Nikolopoulos, T.K. Kjeldsen, L.B. Madsen, Phys. Rev. A. 75, 063426 (2007)ADSGoogle Scholar
  234. 234.
    W. Martin, P. Flandrin, Acoust, Speech, Signal Proc. IEEE Trans. 33, 1461 (1985)Google Scholar
  235. 235.
    A. Jäckle, H.D. Meyer, J. Chem. Phys. 105, 6778 (1996)ADSGoogle Scholar
  236. 236.
    D. Vanfleteren, D. Van Neck, P.W. Ayers, R.C. Morrison, P. Bultinck, J. Chem. Phys. 130, 194104 (2009)ADSGoogle Scholar
  237. 237.
    D.W. Smith, O.W. Day, J. Chem. Phys. 62, 113 (1975)ADSGoogle Scholar
  238. 238.
    C. Hinz, Investigation of many-particle processes in Beryllium using the Multiconfigurational time-dependent Hartree-Fock method, Master’s thesis, University of Kiel, 2013Google Scholar
  239. 239.
    P.E. Gill, W. Murray, M.H. Wright, Practical Optimization (Academic Press, 1981)Google Scholar
  240. 240.
    L.B. Rall, Automatic Differentiation: Techniques and Applications, Vol. 120, Lect. Notes Computer Sci. (Springer, Berlin, 1981)Google Scholar
  241. 241.
    M. Jerosolimski, L. Levacher, A new method for fast calculation of Jacobian matrices: automatic differentiation for power system simulation. In Power Industry Computer Application Conference, Conference Proceedings, 411 (1993)Google Scholar
  242. 242.
    J.L. Gustafson, Commun. ACM 31, 532 (1988)Google Scholar
  243. 243.
    A.H. Karp, H.P. Flatt, Commun. ACM 33, 539 (1990)Google Scholar
  244. 244.
    G.M. Amdahl, In Proc. of the April 18-20, 1967, Spring Joint Computer conference, ACM, 483 (1967)Google Scholar
  245. 245.
    B. Walker, B. Sheehy, L.F. DiMauro, P. Agostini, K.J. Schafer, K.C. Kulander, Phys. Rev. Lett. 73, 1227 (1994)ADSGoogle Scholar
  246. 246.
    J.S. Briggs, V. Schmidt, J. Phys. B: Atom. Molec. Optical Phys. 33, R1 (2000)ADSGoogle Scholar
  247. 247.
    L. Avaldi, A. Huetz, J. Phys. B: Atom. Molec. Optical Phys. 38, S861 (2005)ADSGoogle Scholar
  248. 248.
    S. Chen, C. Ruiz, A. Becker, Phys. Rev. A. 82, 033426 (2010)ADSGoogle Scholar
  249. 249.
    T. Birkeland, R. Nepstad, M. Førre, Phys. Rev. Lett. 104, 163002 (2010)ADSGoogle Scholar
  250. 250.
    R. Pazourek, J. Feist, S. Nagele, J. Burgdörfer, Phys. Rev. Lett. 108, 163001 (2012)ADSGoogle Scholar
  251. 251.
    E.A. Hylleraas, Z. Phys. A Hadrons Nuclei 54, 347 (1929)zbMATHGoogle Scholar
  252. 252.
    J.S. Sims, S.A. Hagstrom, Inter. J. Quan. Chem. 90, 1600 (2002)Google Scholar
  253. 253.
    J.C. Slater, Quantum Theory of Atomic Structure (McGraw-Hill, 1964)Google Scholar
  254. 254.
    C. Schwartz, Inter. J. Mod. Phys. E 15, 877 (2006)ADSGoogle Scholar
  255. 255.
    P.O. Löwdin, Phys. Rev. 97, 1509 (1955)MathSciNetADSGoogle Scholar
  256. 256.
    S.D. Bergeson, A. Balakrishnan, K.G.H. Baldwin, T.B. Lucatorto, J.P. Marangos, T.J. McIlrath, T.R. O’Brian, S.L. Rolston, C.J. Sansonetti, J. Wen, et al., Phys. Rev. Lett. 80, 3475 (1998)ADSGoogle Scholar
  257. 257.
    H. Tatewaki, T. Koga, Y. Sakai, A.J. Thakkar, J. Chem. Phys. 101, 4945 (1994)ADSGoogle Scholar
  258. 258.
    M. Yan, H.R. Sadeghpour, A. Dalgarno, Astrophys. J. 496, 1044 (1998)ADSGoogle Scholar
  259. 259.
    R. Mitzner, A.A Sorokin, B. Siemer, S. Roling, M. Rutkowski, H. Zacharias, M. Neeb, T. Noll, F. Siewert, W. Eberhardt, et al., Phys. Rev. A. 80, 025402 (2009)ADSGoogle Scholar
  260. 260.
    R. Moshammer, Th. Pfeifer, A. Rudenko, Y.H. Jiang, L. Foucar, M. Kurka, K.U. Kühnel, C.D. Schröter, J. Ullrich, O. Herrwerth, M.F. Kling, X.-J. Liu, K. Motomura, H. Fukuzawa, A. Yamada, K. Ueda, K.L. Ishikawa, K. Nagaya, H. Iwayama, A. Sugishima, Y. Mizoguchi, S. Yase, M. Yao, N. Saito, A. Belkacem, M. Nagasono, A. Higashiya, M. Yabashi, T. Ishikawa, H. Ohashi, H. Kimura, T. Togashi, Optics Exp. 19, 21698 (2011)ADSGoogle Scholar
  261. 261.
    P.W. Langhoff, C.T. Corcoran, J. Chem. Phys. 61, 146 (1974)ADSGoogle Scholar
  262. 262.
    A. Scrinzi, N. Elander, J. Chem. Phys. 98, 3866 (1993)ADSGoogle Scholar
  263. 263.
    A. Stark, A. Saenz, J. Phys. B: Atom., Molec. Optical Phys. 44, 035004 (2011)ADSGoogle Scholar
  264. 264.
    J.A.R. Samson, Z.X. He, L. Yin, A. Haddad, J. Phys. B: Atom., Molec. Optical Phys. 27, 887 (1994)ADSGoogle Scholar
  265. 265.
    P. Lambropoulos, L.A.A. Nikolopoulos, New J. Phys. 10, 025012 (2008)ADSGoogle Scholar
  266. 266.
    R.P. Madden, K. Codling, Phys. Rev. Lett. 10, 516 (1963)ADSGoogle Scholar
  267. 267.
    U. Fano, Phys. Rev. 124, 1866 (1961)zbMATHADSGoogle Scholar
  268. 268.
    M. Domke, C. Xue, A. Puschmann, T. Mandel, E. Hudson, D.A. Shirley, G. Kaindl, C.H. Greene, H.R. Sadeghpour, H. Petersen, Phys. Rev. Lett. 66, 1306 (1991)ADSGoogle Scholar
  269. 269.
    K. Schulz, G. Kaindl, M. Domke, J.D. Bozek, P.A. Heimann, A.S. Schlachter, J.M. Rost, Phys. Rev. Lett. 77, 3086 (1996)ADSGoogle Scholar
  270. 270.
    A. Bürgers, D. Wintgen, J.M. Rost, J. Phys. B: Atom., Molec. Optical Phys. 28, 3163 (1995)ADSGoogle Scholar
  271. 271.
    E.J. Heller, Accounts Chem. Res. 14, 368 (1981)Google Scholar
  272. 272.
    H. Hasegawa, E.J. Takahashi, Y. Nabekawa, K.L. Ishikawa, K Midorikawa, Phys. Rev. A 71, 023407 (2005)ADSGoogle Scholar
  273. 273.
    M. Kurka, J. Feist, D.A. Horner, A. Rudenko, Y.H. Jiang, K.U. Kühnel, L. Foucar, T.N. Rescigno, C.W. McCurdy, R. Pazourek, S. Nagele, M. Schulz, O. Herrwerth, M. Lezius, M.F. Kling, M. Schöer, A. Belkacem, S. Düsterer, R. Treusch, B.I. Schneider, L.A. Collins, J. Burgdörfer, C.D. Schröter, R. Moshammer, J. Ullrich, New J. Phys. 12, 073035 (2010)ADSGoogle Scholar
  274. 274.
    R. Nepstad, T. Birkeland, M. Førre, Phys. Rev. A 81, 063402 (2010)ADSGoogle Scholar
  275. 275.
    L.A.A. Nikolopoulos, P. Lambropoulos, J. Phys. B: Atom., Molec. Optical Phys. 34, 545 (2001)ADSGoogle Scholar
  276. 276.
    L.A.A. Nikolopoulos, P. Lambropoulos, J. Phys. B: Atom. Molec. Optical Phys. 40, 1347 (2007)ADSGoogle Scholar
  277. 277.
    D.A. Horner, F. Morales, T.N. Rescigno, F. Martin, C.W. McCurdy, Phys. Rev. A 76, 030701 (2007)ADSGoogle Scholar
  278. 278.
    D.A. Horner, C.W. McCurdy, T.N. Rescigno, Phys. Rev. A 78, 043416 (2008)ADSGoogle Scholar
  279. 279.
    I.A. Ivanov, A.S. Kheifets, Phys. Rev. A 75, 033411 (2007)ADSGoogle Scholar
  280. 280.
    L. Feng, H.W. van der Hart, J. Phys. B: Atom. Molec. Optical Phys. 36, L1 (2002)Google Scholar
  281. 281.
    A. Palacios, T.N. Rescigno, C.W. McCurdy, Phys. Rev. A 79, 033402 (2009)ADSGoogle Scholar
  282. 282.
    N.E. Dahlen, R. van Leeuwen, Phys. Rev. A 64, 023405 (2001)ADSGoogle Scholar
  283. 283.
    A. Scrinzi, Phys. Rev. A. 81, 053845 (2010)ADSGoogle Scholar
  284. 284.
    U.V. Riss, H.D. Meyer, J. Phys. B: Atom. Molec. Optical Phys. 28, 1475 (1995)ADSGoogle Scholar
  285. 285.
    H. Bauke, C.H. Keitel, Phys. Rev. E 80, 016706 (2009)MathSciNetADSGoogle Scholar
  286. 286.
    A. Kramida, W.C. Martin, J. Phys. Chem. Ref. Data 26, 1185 (1997)ADSGoogle Scholar
  287. 287.
    D.S. Kim, S.S. Tayal, H.L. Zhou, S.T. Manson, Phys. Rev. A 61, 062701 (2000)ADSGoogle Scholar
  288. 288.
    H.C. Chi, K.N. Huang, Phys. Rev. A 43, 4742 (1991)ADSGoogle Scholar
  289. 289.
    B. Zhou, C.D. Lin, Phys. Rev. A 51, 1286 (1995)ADSGoogle Scholar
  290. 290.
    J. Colgan, M.S. Pindzola, F.J. Robicheaux, D.C. Griffin, M. Baertschy, Phys. Rev. A 65, 042721 (2002)ADSGoogle Scholar
  291. 291.
    J. Komasa, W. Cencek, J. Rychlewski, Phys. Rev. A 52, 4500 (1995)ADSGoogle Scholar
  292. 292.
    J. Komasa, W. Cencek, J. Rychlewski, Phys. Rev. A 52, 4500 (1995)ADSGoogle Scholar
  293. 293.
    R. Wehlitz, J.B. Bluett, S.B. Whitfield, Phys. Rev. A 66, 012701 (2002)ADSGoogle Scholar
  294. 294.
    R. Wehlitz, D. Lukić, J.B. Bluett, Phys. Rev. A 71, 012707 (2005)ADSGoogle Scholar
  295. 295.
    L. Voky, H.E. Saraph, W. Eissner, Z.W. Liu, H.P. Kelly, Phys. Rev. A 46, 3945 (1992)ADSGoogle Scholar
  296. 296.
    T.N. Chang, Phys. Rev. A. 16, 1171 (1977)ADSGoogle Scholar
  297. 297.
    K.G. Sewell, Phys. Rev. 138, A418 (1965)ADSGoogle Scholar
  298. 298.
    W.R. Johnson, K.T. Cheng, Phys. Rev. A 20, 978 (1979)ADSGoogle Scholar
  299. 299.
    K. Gokhberg, V. Vysotskiy, L.S. Cederbaum, L. Storchi, F. Tarantelli, V. Averbukh, J. Chem. Phys. 130, 064104 (2009)ADSGoogle Scholar
  300. 300.
    G.V. Marr, J.B. West, Atom. Data Nucl. Data Tables 18, 497 (1976)ADSGoogle Scholar
  301. 301.
    W.F. Chan, G. Cooper, X. Guo, C.E. Brion, Phys. Rev. A 45, 1420 (1992)ADSGoogle Scholar
  302. 302.
    J.A.R. Samson, W.C. Stolte, J. Electr. Spectros. Related Phenomena 123, 265 (2002)Google Scholar
  303. 303.
    A.L. Landers, F. Robicheaux, T. Jahnke, M. Schoffler, T. Osipov, J. Titze, S.Y. Lee, H. Adaniya, M. Hertlein, P. Ranitovic, I. Bocharova, D. Akoury, A. Bhandary, Th. Weber, M.H. Prior, C.L. Cocke, R. Dörner, A. Belkacem, Phys. Rev. Lett. 102, 223001 (2009)ADSGoogle Scholar
  304. 304.
    N. Sisourat, H. Sann, N.V. Kryzhevoi, P. Kolorenč, T. Havermeier, F. Sturm, T. Jahnke, H.-K. Kim, R. Dörner, L.S. Cederbaum, Phys. Rev. Lett. 105, 173401 (2010)ADSGoogle Scholar
  305. 305.
    E.B. Saloman, C.J. Sansonetti, J. Phys. Chem. Ref. Data 33, 1113 (2004)ADSGoogle Scholar
  306. 306.
    O.E. Alon, A.I. Streltsov, L.S. Cederbaum, Phys. Lett. A 362, 453 (2007)ADSGoogle Scholar
  307. 307.
    A.I. Streltsov, O.E. Alon, L.S. Cederbaum, Phys. Rev. Lett. 99, 030402 (2007)ADSGoogle Scholar
  308. 308.
    K. Sakmann, Exact quantum dynamics of a bosonic Josephson junction, Many-Body Schrödinger Dynamics of Bose-Einstein Condensates (Springer, 2011), p. 65Google Scholar
  309. 309.
    A.I. Streltsov, O.E. Alon, L.S. Cederbaum, Phys. Rev. Lett. 100, 130401 (2008)ADSGoogle Scholar
  310. 310.
    L. Cao, S. Kronke, O. Vendrell, P. Schmelcher, J. Chem. Phys. 139, 134103 (2013)ADSGoogle Scholar
  311. 311.
    M. Heimsoth, D. Hochstuhl, C.E. Creffield, L.D. Carr, F. Sols, New J. Phys. 15, 103006 (2013)ADSGoogle Scholar
  312. 312.
    T. Schoof, M. Bonitz, A. Filinov, D. Hochstuhl, J.W. Dufty, Contrib. Plasma Phys. 51, 687 (2011)ADSGoogle Scholar
  313. 313.
    A. Filinov, Yu.E. Lozovik, M. Bonitz, Physica Status Solidi (b) 221, 231 (2000)ADSGoogle Scholar
  314. 314.
    A. Filinov, M. Bonitz, Yu.E. Lozovik, Phys. Rev. Lett. 86, 3851 (2001)ADSGoogle Scholar
  315. 315.
    K. Balzer, M. Bonitz, J. Phys. A: Math. Theor. 42, 214020 (2009)ADSGoogle Scholar
  316. 316.
    L.M. Robledo, Phys. Rev. C 81, 044312 (2010)ADSGoogle Scholar
  317. 317.
    J. Jaklic, P. Prelovsek, Phys. Rev. B 49, 5065 (1994)ADSGoogle Scholar
  318. 318.
    U. Manthe, F. Matzkies, Chem. Phys. Lett. 252, 71 (1996)ADSGoogle Scholar
  319. 319.
    S.P. Webb, T. Iordanov, S. Hammes-Schiffer, J. Chem. Phys. 117, 4106 (2002)ADSGoogle Scholar
  320. 320.
    O.E. Alon, A.I. Streltsov, L.S. Cederbaum, Phys. Rev. A. 76, 062501 (2007)ADSGoogle Scholar
  321. 321.
    J Böning, A. Filinov, M. Bonitz, Phys. Rev. B 84, 075130 (2011)ADSGoogle Scholar
  322. 322.
    J. Schleede, A. Filinov, M. Bonitz, H. Fehske, Contrib. Plasma Phys. 52, 819 (2012)ADSGoogle Scholar
  323. 323.
    C. Buth, R. Santra, Phys. Rev. A. 75, 033412 (2007)ADSGoogle Scholar
  324. 324.
    A. Steinhoff, P. Gartner, M. Florian, F. Jahnke, Phys. Rev. B 85, 205144 (2012)ADSGoogle Scholar
  325. 325.
    U. Manthe, J. Chem. Phys. 128, 164116 (2008)ADSGoogle Scholar
  326. 326.
    J. Zanghellini, M. Kitzler, T. Brabec, A. Scrinzi, J. Phys. B: Atom Molec. Optical Phys. 37, 763 (2004)ADSGoogle Scholar
  327. 327.
    S. Bauch, K. Balzer, C. Henning, M. Bonitz, Phys. Rev. B 80, 054515 (2009)ADSGoogle Scholar
  328. 328.
    R. Schmitz, S. Krönke, L. Cao, P. Schmelcher, Phys. Rev. A 88, 043601 (2013)ADSGoogle Scholar
  329. 329.
    J.M. García de la Vega, B. Miguel, L.A. Montero, L.A. Díaz, R. Bader, Introduction to advanced topics of computational chemistry (Facultad de Química, Universidad de La Habana, 2003)Google Scholar
  330. 330.
    N. Vence, R. Harrison, P. Krstić, Phys. Rev. A 85, 033403 (2012)ADSGoogle Scholar
  331. 331.
    A.S. Dickinson, P.R. Certain, J. Chem. Phys. 49, 4209 (1968)MathSciNetADSGoogle Scholar
  332. 332.
    D.O. Harris, G.G. Engerholm, W.D. Gwinn, J. Chem. Phys. 43, 1515 (1965)ADSGoogle Scholar
  333. 333.
    T.N. Rescigno, C.W. McCurdy, Phys. Rev. A 62, 032706 (2000)ADSGoogle Scholar
  334. 334.
    B.I. Schneider, L.A. Collins, S.X. Hu, Phys. Rev. E 73, 036708 (2006)ADSGoogle Scholar
  335. 335.
    K. Balzer, S. Bauch, M. Bonitz, Phys. Rev. A 81, 022510 (2010)ADSGoogle Scholar
  336. 336.
    K. Balzer, S. Bauch, M. Bonitz, Phys. Rev. A 82, 033427 (2010)ADSGoogle Scholar
  337. 337.
    J. Rasch, A. Yu, SIAM J. Scientific Comput. 25, 1416 (2004)MathSciNetGoogle Scholar
  338. 338.
    J.H. Luscombe, M. Luban, Phys. Rev. E 57, 7274 (1998)ADSGoogle Scholar

Copyright information

© EDP Sciences and Springer 2014

Authors and Affiliations

  1. 1.Institut für Theoretische Physik und Astrophysik, Universität KielKielGermany

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