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Partial wave dispersion relations for photon-nucleon scattering and nucleon-antinucleon production by photons

  • Published:
Il Nuovo Cimento (1955-1965)

Summary

Partial wave dispersion relations for the processes γ

→→γ+

and γ+γ→

+

to the ordere 2 are derived with the help of the Mandelstam representation. The angular momentum decomposition for both processes is carried out and the analytic properties of the partial wave amplitudes are determined. The absorptive parts of these amplitudes along part of the physical branch cuts are calculated by means of the unitarity condition. For γ+

→γ+

the resulting expressions involve amplitudes for single pion photoproduction; for γ+γ→

+

they involve theT=0s-wave pion-pion phase shift and the total cross-section for the process γ+π→π+π. The discontinuities along the unphysical branch cuts are calculated by means of crossing symmetry and of analytic continuation through Legendre polynomials. The limits of convergence of the Legendre expansions are discussed and reasons for the importance of the two-pion exchange contribution in photon-nucleon scattering are presented.

Riassunto

In base alla rappresentazione di Mandelstam si deducono le relazioni di dispersione dell’onda parziale per i processi γ+

→γ+

e γ+d→

+

fino all’ordinee 2. Si fa la scomposizione del momento angolare per entrambi i processi e si determinano le proprietà analitiche delle ampiezze dell’onda parziale. Per mezzo della condizione di unitarietà si calcolano, lungo una parte dei tagli del ramo fisico, le parti assorbenti di queste ampiezze. Per γ+

→γ+

le espressioni risultanti coinvolgono ampiezze per la fotoproduzione di singoli pioni; per γ+γ→

+

coinvolgono lo spostamento di fase pione-pione in ondas conT=0 e la sezione d’urto totale del processo γ+π→π+π. A mezzo della simmetria incrociata e della continuazione analitica ćon polinomi di Legendre si calcolano le discontinuità lungo i tagli del ramo non fisico. Si discutono i limiti di convergenza degli sviluppi di Legendre e si danno le ragioni dell’importanza del contributo dello scambio di due pioni nello scattering fotone-nucleone.

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Authors and Affiliations

  1. Laboratory of Nuclear Studies, Cornell University, Ithaca, N. Y.

    A. P. Contogouris

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  1. A. P. Contogouris
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Supported by the joint program of the Office of Naval Research and the U. S. Atomic Energy Commission.

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Contogouris, A.P. Partial wave dispersion relations for photon-nucleon scattering and nucleon-antinucleon production by photons. Nuovo Cim 25, 104–134 (1962). https://doi.org/10.1007/BF02733319

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  • DOI: https://doi.org/10.1007/BF02733319

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