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Il Nuovo Cimento (1955-1965)

, Volume 13, Issue 2, pp 381–393 | Cite as

The inelastic scattering of elementary particles

  • P. T. Matthews
  • A. Salam
Article

Summary

The requirements of unitarity and causality are used to obtain a convenient set of real constant parameters for the phenomenological description of low energy elementary particle scattering. It is assumed that an arbitrary number of channels are open but that there are just two particles in each channel. This discussion is a direct generalization of effective range theory. We also derive from this point of view the Breit-Wigner and Chew-Low formulas. Unitarity is then used to relate the parameters, below threshold for one or more of the channels, to the larger number of parameters required when all channels are open. Finally these considerations are applied to the K-nucleon system.

Riassunto

Si utilizzano le esigenze di unitarietà e causalità per ottenere una opportuna serie di parametri costanti per la descrizione fenomenologica dello scattering delle particelle elementari di bassa energia. Si assume che un numero arbitrario di canali sia aperto ma che in ogni canale si trovino solo due particelle. Questa discussione è una generalizzazione diretta della teoria del range effettivo. Da questo punto di vista deriviamo pure le formule di Breit-Wigner e di Chew-Low. Si utilizza poi l’unitarietà per mettere in relazione i parametri, sotto la soglia, per uno o più canali al maggior numero di parametri richiesto quando tutti i canali sono aperti. Finalmente si applicano queste considerazioni al sistema K-nucleone.

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References

  1. (1).
    A well known example is photo-pion production where thes-wave electric dipole scattering is ordinary scattering, while thep-wave magnetic dipole proceeds through the (3/2, 3/2) resonance.G. F. Chew andF. Low:Phys. Rev. 101, 1579 (1956).MathSciNetADSCrossRefzbMATHGoogle Scholar
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    These parameters are alternatives to the eigen-phase shifts and mixing parameters and avoid the necessity of transforming the physical states to a mixed representation which is awkward when different momenta are associated with different channels. See for exampleBlatt andBiedenharn:Rev. Mod. Phys.,24, 258 (1952).Y. Yamaguchi:Prog. Theor. Phys. (to be published).ADSCrossRefzbMATHGoogle Scholar
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    R. H. Capps andW. G. Holladay:Phys. Rev.,99, 931 (1955);R. K. Adair:Phys. Rev.,111, 632 (1958);A. Baz andN. O’Kun:Journ. Exp. Theor. Phys.,35, 526 (1959).ADSCrossRefzbMATHGoogle Scholar
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    See report byM. F. Kaplon:Intern. Conf. on High Energy Physics, CERN (Geneva, 1958), p. 171.Google Scholar
  8. (14).
    P. T. Matthew andA. Salam:Phys. Rev. Lett.,2, 226 (1959).ADSCrossRefGoogle Scholar

Copyright information

© Società Italiana di Fisica 1959

Authors and Affiliations

  • P. T. Matthews
    • 1
  • A. Salam
    • 1
  1. 1.Imperial CollegeLondon

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