Surface-Integral Approach to the Coulomb Few-Body Scattering Problem (original) (raw)

Abstract

We present main features of a surface-integral approach to the Coulomb few-body scattering problem. This approach is valid for both short-range and Coulombic longe-range interactions. We give new general definitions for the potential scattering amplitude. For the Coulombic potentials the generalized amplitude gives the physical on-shell amplitude without recourse to a renormalization procedure. New post and prior forms for the amplitudes of breakup, direct and rearrangement scattering in a Coulomb three-body system are also presented. The Green's functions and formal solutions of the Schrödinger equation in integral form are not used. Therefore, for the purpose of defining the scattering amplitudes the knowledge of a complicated analytic structure of the Green's function in the complex-energy plane is not required.

Loading...

Loading Preview

Sorry, preview is currently unavailable. You can download the paper by clicking the button above.

References (21)

  1. H. van Haeringen, Charged-particle Interactions (Coulomb Press Leyden, Leiden, 1985).
  2. L. D. Faddeev, Sov. Phys. -JETP 12, 1014 (1961).
  3. L. D. Faddeev, Mathematical Aspects of the Three- Body Problem in the Quantum Scattering (Israel Program for Scientific Translations, Jerusalem, 1965).
  4. E. O. Alt, W. Sandhas, and H. Ziegelmann, Phys. Rev. C 17, 1981 (1978).
  5. T. N. Rescigno, M. Baertschy, W. A. Isaacs, and C. W. McCurdy, Science 286, 2474 (1999).
  6. M. Baertschy, T. N. Rescigno, and C. W. Mc- Curdy, Phys. Rev. A 64, 022709 (2001).
  7. I. Bray and A. T. Stelbovics, Phys. Rev. Lett. 69, 53 (1992).
  8. A. S. Kadyrov, A. M. Mukhamedzhanov, A. T. Stelbovics, and I. Bray, Phys. Rev. Lett. 91, 253202 (2003).
  9. A. S. Kadyrov, A. M. Mukhamedzhanov, A. T. Stelbovics, and I. Bray, Phys. Rev. A 70, 062703 (2004).
  10. R. K. Peterkop, Opt. Spectrosc. 13, 87 (1962).
  11. A. S. Kadyrov, I. Bray, A. M. Mukhamedzhanov, and A. T. Stelbovics, Phys. Rev. Lett. 101, 230405 (2008).
  12. A. S. Kadyrov, I. Bray, A. M. Mukhamedzhanov, and A. T. Stelbovics, Ann. Phys. 324, 1516 (2009).
  13. A. Messiah, Quantum Mechanics, vol. 2 (North- Holland Publishing, Amsterdam, 1965).
  14. A. S. Kadyrov, I. Bray, A. M. Mukhamedzhanov, and A. T. Stelbovics, Phys. Rev. A 72, 032712 (2005).
  15. R. G. Newton, Ann. Phys. 74, 324 (1972).
  16. J. Schwinger, J. Math. Phys. 5, 1606 (1964).
  17. P. A. M. Dirac, in AIP Conf. Proc. 74, edited by D. W. Duke and J. F. Owens (AIP, New York, 1981), pp. 129-130.
  18. W. Pauli, Nobel Lectures, Physics 1942-1962 (El- sevier, Amsterdam, 1964), pp. 27-43.
  19. R. P. Feynman, QED, The Strange Theory of Light and Matter (Princeton University Press, Princeton, 1985), pp. 128-129.
  20. V. B. Berestetskii, E. M. Lifshitz, and L. P. Pitaevskii, Quantum electrodynamics (Pergamon press, 1982), pp. 3-4, 2nd ed.
  21. L. H. Ryder, Quantum Field Theory (Cambridge University Press, Cambridge, 1996), p. 390, 2nd ed.