Summary
It is shown that two types of Fourier-Bessel representation for the helicity amplitude, which are valid for arbitrary physical energies and scattering angles, can be derived from the Jacob-Wick expansion. Provided certain conditions are satisfied, the spectral functions are expressed as Neumann series over the partial-wave amplitudes; and conversely, the latter are expressed as integrals over the former. High-energy unitarity conditions on the spectral functions are derived for the case of πN scattering; and an illustration of the use of such unitarity conditions is briefly discussed.
Riassunto
Si dimostra che due tipi di rappresentazioni di Fourier-Bessel, valide per ogni valore fisico dell’energia e dell’angolo di diffusione, possono essere ottenute a partire dallo sviluppo di Jacob-Wick. A patto che certe condizioni matematiche siano soddisfatte, le funzioni spettrali sono espresse come serie di Neumann delle ampiezze d’onda parziale e, viceversa, queste ultime sono date da integrali delle funzioni spettrali. Le condizioni di unitarietà ad alte energie per le funzioni spettrali sono dedotte per lo scattering pione-nucleone ed un esempio di tali condizioni d’unitarietà è brevemente discusso.
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Luming, M., Predazzi, E. On the fourier-bessel representation for helicity amplitudes. Nuovo Cimento A (1965-1970) 42, 878–893 (1966). https://doi.org/10.1007/BF02720564
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DOI: https://doi.org/10.1007/BF02720564