- Physical Review Journals
All JournalsPhysics Magazine
All JournalsPhysics Magazine
Access Provided by Xinjiang University

Physical Review Journals Archive

Export citation

Export citation

Choose format for download:

Download Citation
  • Access by Xinjiang University

Watson-Sommerfeld Transformation for Many-Particle Scattering Amplitudes

James B. Hartle*

  • California Institute of Technology, Pasadena, California

  • *National Science Foundation Predoctoral Fellow.
PDF

Phys. Rev. 134, B612 – Published 11 May, 1964

DOI: https://doi.org/10.1103/PhysRev.134.B612

Abstract

The continuation of many-particle partial-wave scattering amplitude to complex values of the total angular momentum is discussed in the framework of potential scattering. We show that if there is a continuation for which a Watson-Sommerfeld transformation of the full scattering amplitude can be made, then it is unique and determines the behavior of the amplitude for large values of any single scattering angle. The continuation of the partial-wave Schrödinger equation to complex values of the angular momentum is discussed, and the results are generalized to the case when exchange forces are present. As a simple application of the results, we discuss a crude nuclear model to illustrate how sequences of rotational levels can be described by Regge trajectories.

View figure in article

References (17)

  1. A. Bottino, A. Longoni, and T. Regge, Nuovo Cimento 23, 954 (1962)
  2. J. Charap and E. Squires, Ann. Phys. (N.Y.) 20, 145 (1962) ibid.21, 8 (1963)
  3. L. Favella and M. Reineri, Nuovo Cimento 23, 616 (1962)
  4. A. Jaffe and Y. Kim, Phys. Rev. 127, 2261 (1962)
  5. A. Edmonds, Angular Momentum in Quantum Mechanics (Princeton University Press, Princeton, New Jersey, 1957)
  6. [J. B. Hartle, Phys. Rev. 134, B620 (1964)] G. Derrick and J. Blatt, Nucl. Phys. 8, 310 (1958)
  7. [5], p. 63
  8. M. Gell-Mann, Proceedings of the 1962 Annual International Conference on High-Energy Physics at CERN, edited by J. Prentki (CERN, Geneva, 1962) [2]
  9. [5], p. 60
  10. E. Squires, Nuovo Cimento 24, 242 (1962)
  11. R. Boas, Entire Functions (Academic Press, Inc., New York, 1954), p. 153
  12. V. Gribov and I. Ya. Pomeranchuk, Phys. Rev. Letters 8, 343 (1962)
  13. A. Bohr and B. Mottelson, Kgl. Danske Videnskab. Selskab, Mat. Fys. Medd. 27, No. 16 (1953)
  14. E. Kazes, Nuovo Cimento 27, 995 (1963)
  15. [5]
  16. J. Gunson (to be published) E. Beltrametti and G. Luzzato, Nuovo Cimento 29, 1003 (1963)
  17. A. Erdelyi et al., Higher Transcendental Functions (McGraw-Hill Book Company, Inc., New York, 1953), p. 168

Outline

Information

Phys. Rev. 134, B612– Published 11 May, 1964
  • Received 30 September 1963

© 1964 American Physical Society

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation