Advertisement

Il Nuovo Cimento (1955-1965)

, Volume 4, Issue 2, pp 369–389 | Cite as

Meson NucleonS scattering and crossing theorem

  • A. Martin
Article

Summary

It is noticed that the low energyS wave calculations of meson nucleon scattering cannot be very satisfactory if they do not obey the « crossing theorem ». It may be interesting to modify the iteration treatments in order to satisfy the symmetry requirements. For this purpose the series of scattering processes considered is completed by a new series in which the initial meson and the final meson are exchanged. In this way, we generalize Lévy’s covariant treatment ofS wave scattering. The result of the calculation is deeply modified by the introduction of these new processes. It is not possible to get a quantitative agreement with experiment. The signs of the phase shifts, however, are correct near G2/4π = 15. The approximations used in solving the integral equations are discussed by comparison with other calculations.

Riassunto

Si nota che i calooli dell’ondaS di bassa energia dello scattering mesone-nucleone non possono dare risultati soddisfacenti se non rispettano il cosidetto « teorema di cancellazione ». Può essere opportuno modificare i procedimenti di iterazione per soddisfare alle condizioni di simmetria. A questa scopo si completa la serie dei processi di scattering considerati con una nuova serie nella quale i mesoni iniziale e finale sono scambiati. In tal modo si generalizza il trattamento covariante di Lévy dello scattering dell’ondaS. L’introduzione di questi nuovi procedimenti modifica profondamente il risultato del calcolo. Non è possibile ottenere un accordo quantitativo con l’esperienza. I segni degli spostamenti di fase sono, tuttavia, corretti in prossimità di G2/4π = 15. Si discutono le approssimazioni usate nella soluzione delle equazioni integrali confrontandole con altri calcoli.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. (1).
    F. J. Dyson, M. Ross, E. E. Salpeter, S. S. Schweber, M. K. Sundaresan, W. M. Visscher andH. A. Bethe:Phys. Rev.,95, 1644 (1954).ADSCrossRefMATHGoogle Scholar
  2. (2).
    M. H. Kalos andR. H. Dalitz:Phys. Rev.,100, 1515 (1955).ADSCrossRefMATHGoogle Scholar
  3. (3).
    G. F. Chew:Phys. Rev.,95, 1669 (1954).MathSciNetADSCrossRefGoogle Scholar
  4. (4).
    G. F. Chew:Proc. of the Pisa Conf. on Elementary Particles (to be published).Google Scholar
  5. (5).
    G. C. Wick:Rev. Mod. Phys.,27, 339 (1955).MathSciNetADSCrossRefMATHGoogle Scholar
  6. (6).
    M. Cini andS. Fubini:Nuovo Cimento,11, 142 (1954);L. Sartori andV. Wataghin:Nuovo Cimento,12, 260 (1954).MathSciNetCrossRefMATHGoogle Scholar
  7. (7).
    D. ItO andH. Tanaka:Proy. Theor. Phys.,12, 105 (1954).ADSCrossRefGoogle Scholar
  8. (8).
    M. M. Levy andE. E. Marshak:Nuovo Cimento,11, 366 (1954).CrossRefMATHGoogle Scholar
  9. (9).
    M. M. Lévy:Phys. Rev.,94, 460 (1954) (referred to as Λ in the present paper)ADSCrossRefMATHGoogle Scholar
  10. (10).
    M. M. Lévy:Phys. Rev.,98, 1470 (1955) (referred to asB in the present paper).MathSciNetADSCrossRefMATHGoogle Scholar
  11. (11).
    J. Orear:Phys. Rev.,100, 288 (1955).ADSCrossRefGoogle Scholar
  12. (12).
    M. Gell-Mann andM. L. Goldberger:Proc. of the Fourth Annual Rochester Gonf. on High Energy Nuclear Physics.Google Scholar
  13. (13).
    This property becomes evident if the matrix element for scattering is expressed in terms of Heisenberg operators (F. E. Low:Phys. Rev.,97, 1392 (1955)).MathSciNetADSCrossRefMATHGoogle Scholar
  14. (14).
    H. W. Wyld Jr.:Thesis, University of Chicago, 1955.Google Scholar
  15. (15).
    K. A. Brueckner, M. Gell-Mann andL. M. Goldberger:Phys. Rev.,90, 476 (1953).ADSCrossRefMATHGoogle Scholar
  16. (16).
    A calculation is made on this subject byG. Bonnevay at the University of Paris.Google Scholar

Copyright information

© Società Italiana di Fisica 1956

Authors and Affiliations

  • A. Martin
    • 1
  1. 1.École Normals SupérieureUniversité de ParisEngland

Personalised recommendations