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An Analytical Approach to Resonant and Direct Fragmentation of Many-Body Coulomb Systems

  • J. Berakdar
Part of the Physics of Atoms and Molecules book series (PAMO)

Abstract

The description of the correlated motion of few Coulomb interacting particles is one of the fundamental unsolved problems in theoretical physics. At energies above the total fragmentation threshold the infinite-range of Coulomb forces leads to phase distortions of the plane-wave motion of the escaping particles [1, 2, 3, 4]. The determination of this correlated phase modifications leads to asymptotic scattering states of the many-body Coulomb systems [1, 2, 3, 4]. On the other hand evaluation of scattering amplitudes requires the knowledge of the many-body scattering state in the whole Hilbert space. In fact, the reaction zones most important for such amplitudes are often confined to a small region around the origin, the so-called condensation region, where all particles are close together. Therefore, a correct propagation of asymptotic states to finite ranges (in phase space) is crucial for the correct description of scattering reactions. Thus, we first discuss asymptotic scattering states of N interacting charged particles. Based on that we develop then a theoretical model for calculating scattering amplitudes of reactions leading to four-body Coulomb continuum systems. Subsequently, we introduce a method to incorporate the reaction dynamics at finite distances of three interacting charged particles whilst maintaining the requirement of correct asymptotic behaviour of scattering states.

Keywords

SchrOdinger Equation Double Ionization Coulomb System Continuum Particle Product Charge 
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]
    L. Rosenberg, Phys. Rev. D 8, 1833 (1973).Google Scholar
  2. [2]
    M. Brauner, J. S. Briggs and H. Klar, J. Phys. B 22, 2265 (1989).ADSCrossRefGoogle Scholar
  3. [3]
    E. O. Alt and A. M. Mukhamedzhanov, Phys. Rev. A 47, 2004 (1993).Google Scholar
  4. [4]
    J. Berakdar Phys. Rev. A 53, 2314 (1996); ibid 54, 1480 (1996).Google Scholar
  5. [5]
    J. Berakdar Phys. Rev. A (1997) in pressGoogle Scholar
  6. [6]
    G. Garibotti and J. E. Miraglia, Phys. Rev. A 21, 572 (1980).ADSCrossRefGoogle Scholar
  7. [7]
    A. Lahmam-Bennani, C. Dupre and A. Duguet, Phys. Rev. Lett. 63, 1582 (1989).ADSCrossRefGoogle Scholar
  8. [8]
    A. Lahmam-Bennani, A. Duguet, A. M. Grisogono and M. Lecas, J. Phys. B 25, 2873 (1992).ADSCrossRefGoogle Scholar
  9. [9]
    R. Dörner, V. Mergel, L. Spielberger, O. Jagutzki, S. Nuttgens, M. Unverzagt, H. SchmidtBöcking, J. Ullrich, R. E. Olson, K. Tokesi, W. E. Meyerhof, W. Wu and C. L. Cocke, Nuclear Instr. & Meth. B 99, 111 (1995).Google Scholar
  10. [10]
    B. El Marji, A. Duguet, A. Lahmam-Bennani, M. Lecas and H. E Wellenstein, J. Phys. B 26, L733 (1995).CrossRefGoogle Scholar
  11. [11]
    O. Jagutzki, L. Spielberger, R. Dörner, S. Nuttgens, V. Mergel, H. Schmidt-Böcking, J. Ullrich, R. E. Olson and U. Buck, Z. Phys. D 36, 5 (1996).ADSCrossRefGoogle Scholar
  12. [12]
    L. Avaldi, P. Belotti, P. Bolognesi, R. Camilloni and G. Stefani, Phys. Rev. Lett 75, 1915 (1995).ADSCrossRefGoogle Scholar
  13. [13]
    M. J. Ford, J. H. Moore, M. A. Coplan, J. W. Cooper and J. P. Doering, Phys. Rev. Lett. 77, 2650 (1996).ADSCrossRefGoogle Scholar
  14. [14]
    B. Joulakian, C. Dal Cappello and M. Brauner, J. Phys. B 25, 2863 (1992).ADSCrossRefGoogle Scholar
  15. [15]
    B. Joulakian and C. Dal Cappello, Phys. Rev. A 47, 3788 (1993).ADSCrossRefGoogle Scholar
  16. [16]
    C. Dal Cappello and H. Le Rouzo, Phys. Rev. A 43, 1395 (1991).ADSCrossRefGoogle Scholar
  17. [17]
    R. J. Tweed, J. Phys. B 6, 270 (1973).ADSCrossRefGoogle Scholar
  18. [18]
    Yu. F. Smirnov, A. V. Pavlitchenkov, V. G. Levin and G. Neudatchin, J. Phys. B 11, 20 (1978).CrossRefGoogle Scholar
  19. [19]
    J. Berakdar and H. Klar, J. Phys. B 26, 4219 (1993).ADSCrossRefGoogle Scholar
  20. [20]
    J. Berakdar, J. Phys. (France) IV 3, C6–135 (1993).Google Scholar
  21. [21]
    J. Berakdar, Phys. Rev. A 53, 2281 (1996).Google Scholar
  22. [22]
    R. K. Peterkop, Theory of Ionization of Atoms by the Electron Impact ( Colorado Associated University Press, Boulder, 1977 ).Google Scholar
  23. [23]
    S. Jetzke and E H. M. Faisal, J. Phys. B 25, 1543 (1992).ADSCrossRefGoogle Scholar
  24. [24]
    M.R.H. Rudge and M.J. Seaton Proc.Roy.Soc. A, 283, 262 (1965).Google Scholar
  25. [25]
    G. Wannier, Phys. Rev. 90, 817 (1953).ADSzbMATHCrossRefGoogle Scholar
  26. [26]
    H. Klar and W. Schlecht, J. Phys. B 9, 1699 (1976).ADSCrossRefGoogle Scholar
  27. [27]
    J. Berakdar Phys. Lett. A 220, 237 (1996).ADSCrossRefGoogle Scholar
  28. [28]
    A. R. P. Rau, Phys. Rev. A 4, 207 (1971)Google Scholar
  29. A. R. P. Rau, Phys. Rep. 110, 369 (1984).ADSCrossRefGoogle Scholar
  30. [29]
    H. A. Bethe and E. E. Salpeter, Quantum mechanics of one-and two-electron atoms ( Springer, Berlin, 1957 ).zbMATHGoogle Scholar
  31. [30]
    J. Berakdar, unpublished.Google Scholar
  32. [31]
    J. Berakdar and J.S. Briggs, Phys. Rev. Lett. 72, 3799 (1994)ADSCrossRefGoogle Scholar
  33. J. Berakdar and J.S. Briggs, J. Phys. B. 27, 4271 (1994)ADSCrossRefGoogle Scholar
  34. J. Berakdar and J.S. Briggs, ibid 29, 2289 (1996).Google Scholar
  35. [32]
    J. Berakdar, J. Räder, J. S. Briggs and H. Ehrhardt J. Phys. B. in press (1996).Google Scholar
  36. [33]
    K. A. Berrington, P. G. Burke, K. Butler, M. J. Seaton, P. J. Storey, K. T. Taylor and Yu Yan, J. Phys. B. 20, 6379 (1987).ADSCrossRefGoogle Scholar
  37. [34]
    T. Kato, Commun. Pure Appl. Math. 10, 151 (1957).zbMATHGoogle Scholar
  38. [35]
    J. W. Cooper, U. Fano and F. Prats Phys. Rev. Lett. 10, 538 (1963).Google Scholar
  39. [36]
    E. Maulbetsch, M. Pont, J. S. Briggs and R. Shakeshaft, J. Phys. B. 28, L341 (1995).ADSCrossRefGoogle Scholar
  40. [37]
    F. Maulbetsch, Ph.D. thesis, Freiburg University (1995).Google Scholar
  41. [38]
    J. Röder private communication, see also M. Brauner, J. S. Briggs, H. Klar, J. T. Broad, T. Rosel, K. Jung and H. Ehrhardt, J. Phys. B 24, 657 (1991).Google Scholar
  42. [39]
    A. Huetz, L. Andric, A. Jean, P. lablanquie, P. Selles and J. Mazeau, private communication and Proceedings of XIX ICPEAC, Whistler, edited by L. Dube’ et al ( AlP Press, New York, 1995 ).Google Scholar

Copyright information

© Springer Science+Business Media New York 1997

Authors and Affiliations

  • J. Berakdar
    • 1
  1. 1.Atomic and Molecular Physics Laboratories, Research School of Physical Sciences and Engineering, Institute of Advanced StudiesAustralian National UniversityCanberraAustralia

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