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Il Nuovo Cimento (1955-1965)

, Volume 4, Issue 6, pp 1316–1328 | Cite as

Causality and dispersion relations for the scattering of mesons by fixed nucleons

  • E. Oehme
Article

Summary

The derivation of dispersion relations for meson-nucleon scattering is reexamined. So far, all proofs given require the assumption that the Fourier representation of the scattering amplitude exists in the unphysical energy region. In this note it is shown that in the limit of fixed nucleons the causality condition and the properties of the spectrum are already sufficient to derive dispersion formulae for the forward scattering amplitudes. With the same assumptions one can also derive dispersion relations for the derivative amplitudes. The complete relativistic case is discussed briefly in the appendix.

Riassunto

Si riesamina la derivazione delle relazioni di dispersione per lo scattering mesonenucleone. Finora. tutte le prove fornite richiedono l’ipotesi che la rappresentazione di Fourier dell’ampiezza di scattering esista nella regione non fisica. In questa nota si mostra come al limite dei nucleoni fissi la condizione di causalità e le proprietà della spettro sono già sufficienti per derivare delle formule di dispersione per le ampiezze di scattering in avanti. Con la stessa ipotesi si possono anche ottenere relazioni di dispersione per le ampiezze di derivazione. Il caso relativistico complete si discute brevemente in appendice.

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Copyright information

© Società Italiana di Fisica 1956

Authors and Affiliations

  • E. Oehme
    • 1
  1. 1.Enrico Fermi Institute for Nuclear StudiesUniversity of ChicagoChicago

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