Finiteness of Total Cross-Sections

  • A. Martin
Conference paper
Part of the Acta Physica Austriaca book series (FEWBODY, volume 23/1981)


We derive an optimal condition for the finiteness of total cross-sections in potential scattering at any given energy, and by copying Froissart’s trick for elementary particles, explicit bounds on amplitudes and cross-sections in the spherically symmetric case. We also study the coupling constant dependence of the cross-sections for potentials of a given sign by using analyticity properties with respect to this coupling constant. This paper contains several new unpublished results.


Partial Wave Hard Core Incident Direction Potential Scattering Partial Wave Amplitude 
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.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    W.O. Amrein and D.C. Pearson, J. Phys. A12 (1979) 1469MathSciNetADSGoogle Scholar
  2. W. O. Amrein, D. C. Pearson and K. B. Sinha, Scattering Theory in Quantum Mechanics, Reading, Benjamin (1977).MATHGoogle Scholar
  3. This paper contains references to previous work.Google Scholar
  4. 2.
    V. Enss and B. Simon, Phys. Rev. Letters 44 (1980) 319 and 764MathSciNetADSCrossRefGoogle Scholar
  5. V. Enss and B. Simon, to appear in Comm. Math. Phys.Google Scholar
  6. V. Enss and B. Simon, preprint to appear in Classical, Semi-Classical and Quantum Mechanical Problems in Mathematics, Chemistry and Physics, editors K. Gustafson and W. P. Reinhardt, Plenum (1980/81).Google Scholar
  7. 3.
    J.M. Combes and M. Guez, private communication, to be published.Google Scholar
  8. 4.
    M. Froissart, Phys. Rev. 123 (1961) 1053ADSCrossRefGoogle Scholar
  9. 5.
    A. Martin, Nuovo Cimento 42 (1966) 930.ADSMATHCrossRefGoogle Scholar
  10. 6.
    A. Martin, Lectures at the University of Washington, Seattle (1964), unpublished.Google Scholar
  11. See also A. Martin, Nuovo Cimento 23 (1962) 641MATHCrossRefGoogle Scholar
  12. A. Martin, Nuovo Cimento 31 (1964) 1229.MATHCrossRefGoogle Scholar
  13. 7.
    K. Chadan and A. Martin, appendix of Comm. Math. Phys. 70 (1979) 1.MathSciNetADSCrossRefGoogle Scholar
  14. 8.
    A. Martin, Comm. Math. Phys. 69 (1979) 89;MathSciNetADSCrossRefGoogle Scholar
  15. Notice that in the present lectures we give an improved version in which the total cross-section is bounded by I3/2 for large I, Instead of I2 Google Scholar
  16. 9.
    A. Martin, Comm. Math. Phys. 73(1980) 79.MathSciNetADSCrossRefGoogle Scholar
  17. 10.
    J.A. Shohat and J.D. Tamarkin, “The Problem of Moments”, American Mathematical Society, New York (1943).MATHGoogle Scholar
  18. 11.
    See for instance, A. Martin, Nuovo Cimento 39 (1965) 704CrossRefGoogle Scholar

Copyright information

© Springer-Verlag 1981

Authors and Affiliations

  • A. Martin
    • 1
  1. 1.CERNGenevaSwitzerland

Personalised recommendations