Exact and Approximate Methods of the Rigorous Coulomb Scattering Theory

  • Igor V. Farnakeev
  • Vladimir L. Shablov
  • Yuri V. Popov
Part of the Physics of Atoms and Molecules book series (PAMO)


Intensive experimental studies of (e,2e) and (e,3e) processes have caused a new wave of interest to the approximate methods of the rigorous many-body Coulomb scattering theory. The vast “market” of such methods was replenished recently by the convergent close-coupling method of Brayl, the hyperradial-adiabatic approach of Matveenko and Fukuda2, the parabolic — hyperspherical approach of Berakdar3, and many others.


Wave Operator Asymptotic Operator Renormalization Operator Reaction Amplitude Abel Limit 
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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  1. 1.
    I. Bray, Convergent close-coupling method for the calculation of electron scattering on hydrogenlike targets, Phys.Rev.A 49: 1066 (1994).ADSCrossRefGoogle Scholar
  2. 2.
    A. V. Matveenko, and H. Fukuda, Hyperradial-adiabatic approach to Coulomb three-body systems, J.Phys B: At.Mol.Opt.Phys 29: 1575 (1996).ADSCrossRefGoogle Scholar
  3. 3.
    J. Berakdar, Parabolic-hyperspherical approach to the fragmentation of three-particle Coulomb systems, Phys.Rev.A 54: 1480 (1996).ADSCrossRefGoogle Scholar
  4. 4.
    Y. Popov, Investigation of a three-charged-particle break-up scattering amplitude, J.Phys.B: At.Mol.Phys. 14: 2449 (1981).ADSCrossRefGoogle Scholar
  5. 5.
    A. M. Mukhamedzhanov, Integral equations for Coulomb scattering wave functions and Coulomb asymptotic states, Theor.Math.Phys. (Rus.) 62: 105 (1985).MathSciNetGoogle Scholar
  6. 6.
    J.D. Dollard, Asymptotic convergency and Coulomb interaction, J.Math.Phys 5: 729 (1964).MathSciNetADSCrossRefGoogle Scholar
  7. 7.
    D. Muhlerin, and I.I. Zinnes, Coulomb scattering. I. Single channel. J.Math.Phys. 11: 1402 (1970).ADSCrossRefGoogle Scholar
  8. 8.
    C. Chandler, and A. G. Gibson, Time-dependent Coulomb scattering theory, J.Math.Phys. 15: 291 (1974).MathSciNetADSCrossRefGoogle Scholar
  9. 9.
    C. Chandler, The Coulomb problem. A selective review, Nucl.Phys.A 353: 1290 (1981).CrossRefGoogle Scholar
  10. 10.
    S.P. Merkuriev, and L.D. Faddeev, Quantum Scattering Theory for the Systems of Few Particles, Nauka, Moscow (1985).Google Scholar
  11. 11.
    M. Reed, and B. Simon, Methods of Modern Mathematical Physics. V. Scattering Theory, Academic Press, New York (1979).Google Scholar
  12. 12.
    Y.V. Popov, V.L. Shablov, and Y.Y. Shitkov, The relation between time-dependent and time-independent scattering theories for the system of particles with Coulom interaction, Fundamental and Applied Math. (Rus.) 2: 925 (1996).MathSciNetzbMATHGoogle Scholar
  13. 13.
    E. Prugovecki, and J. Zorbas, Many-body modified Lippmann-Schwinger equation for Coulomb-like potentials, Nucl.Phys.A 213: 541 (1973).MathSciNetADSCrossRefGoogle Scholar
  14. 14.
    A.A. Kvitsinsky, V.V. Kostrykin, and S.P. Mercuriev, Scattering theory for quantum three-body systems at fixed total-angular momentum, J.Elem.Part. and Atom.Nucl. (Rus.) 21: 1301 (1986).Google Scholar
  15. 15.
    M. Brauner, J.S. Briggs, and H. Klar, Triply differential cross section for ionisation of hydrogen atoms by electrons and positrons, J.Phys.B: At.Mol.Opt.Phys. 22: 2265 (1989).ADSCrossRefGoogle Scholar
  16. 16.
    A.M. Veselova, The definition of the scattering amplitudes in the problems of two and three charged particles, Theor.Math.Phys. (Rus.) 35: 180 (1978).Google Scholar
  17. 17.
    V.V. Komarov, A.M. Popova, and V.L. Shablov, Scattering of Few Quantum Particles, Moscow University Press, Moscow (1993).Google Scholar

Copyright information

© Springer Science+Business Media New York 1997

Authors and Affiliations

  • Igor V. Farnakeev
    • 1
  • Vladimir L. Shablov
    • 1
  • Yuri V. Popov
    • 2
  1. 1.Obninsk Institute of Nuclear Power EngineeringObninskRussia
  2. 2.Institute of Nuclear PhysicsMoscow State UniversityMoscowRussia

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