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Communications in Mathematical Physics

, Volume 72, Issue 1, pp 1–13 | Cite as

Continuation of partial-wave two-cluster atomic scattering amplitudes

  • J. Nuttall
  • S. R. Singh
Article

Abstract

It is shown, with some restrictions, that on-shell two-cluster partial-wave scattering amplitudes for atomic systems whose particles interact via two-body Coulomb potentials have analytic continuations in the complex energy plane below the physical part of the real axis. The result is proved only for energies lower than any three (or more) cluster threshold. Poles of the amplitudes can occur only at discrete eigenvalues of the rotated Hamiltonian which may be reached by continuation along the same path. The method of proof uses analyticity related to a generalized scaling transformation and the boost transformation.

Keywords

Real Axis Quantum Computing Analytic Continuation Coulomb Potential Atomic System 
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.
    Nuttall, J., Singh, S. R.: Can. J. Phys.57, 449–456 (1979)Google Scholar
  2. 2.
    Combes, J. M.: In: Atomic scattering theory, p. 25, (ed. J. Nuttall). University of Western Ontario, 1978Google Scholar
  3. 3.
    Tip. A.: In: Atomic scattering theory, p. 195, (ed. J. Nuttall) University of Western Ontario, 1978Google Scholar
  4. 4.
    Hagedorn, G.: A link between scattering resonances and dilation analytic resonances in few body quantum mechanics. Preprint, Rockefeller University (1978)Google Scholar
  5. 5.
    Nuttall, J.: J. Math. Phys.8, 873–877 (1967)Google Scholar
  6. 6.
    Nuttall, J.: Comput. Phys. Commun.6, 331–335 (1974)Google Scholar
  7. 7.
    Singh, S. R., Nuttall, J.: In: Atomic scattering theory, p. 185, (ed. J. Nuttall) University of Western Ontario, 1978Google Scholar
  8. 8.
    See for example Int. J. Quantum Chem. Vol. 14, (1978)Google Scholar
  9. 9.
    Combes, J. M., Thomas, L.: Commun. Math. Phys.34, 251–270 (1973)Google Scholar

Copyright information

© Springer-Verlag 1980

Authors and Affiliations

  • J. Nuttall
    • 1
  • S. R. Singh
    • 1
  1. 1.Department of PhysicsUniversity of Western OntarioLondonCanada

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