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Il Nuovo Cimento (1955-1965)

, Volume 23, Issue 6, pp 954–1004 | Cite as

Potential scattering for complex energy and angular momentum

  • A. Bottino
  • A. M. Longoni
  • T. Regge
Article

Summary

The analytic properties of the partial wave scattering amplitude for potential scattering in the pair of variablesk (wave number) andλ=l+1/2 have been derived when both variables are complex. Several results on the location of the poles of theS-matrix follow from a procedure of analytic completion. The scattering process is then considered as described by the variablesλ andk, instead ofs andt, as in Mandelstam work. The set of properties ofS(λ,k)=exp [2(λ,k)] here derived is exactly equivalent to the double dispersion formulas for energy and momentum transfer.

Riassunto

Vengono ricavate le proprietà analitiche dell’ampiezza di diffusione in onde parziali, per diffusione da potenziale, quando le variabilik (numero d’onda) eλ=l+1/2 sono simultaneamente complesse. Alcuni risultati sulla posizione dei poli della matriceS derivano da un procedimento di completamento analitico. Le proprietà qui derivate della matriceS sono esattamente equivalenti alle formule di dispersione doppie dell’ampiezza di diffusione nell’energia e nel momento trasferito.

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References

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  15. (*).
    We are indebted to Prof.R. Ascoli for very interesting discussions on this matter and to Prof.V. Glaser for his kind permission to use his results in this paper.Google Scholar
  16. (*).
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  24. (**).
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Copyright information

© Società Italiana di Fisica 1962

Authors and Affiliations

  • A. Bottino
    • 1
    • 2
  • A. M. Longoni
    • 1
    • 2
  • T. Regge
    • 1
    • 2
  1. 1.Istituto di Fisica dell’UniversitàTorino
  2. 2.Istituto Nazionale di Fisica NucleareSezione di TorinoItaly

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