Dispersion Relations for Pion-Nucleon Scattering. 1. The Spin-Flip Amplitude
Dec 1, 19559 pages
Published in:
- Phys.Rev. 100 (1955) 1503-1512
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Abstract: (APS)
Dispersion relations are derived for the derivative with respect to sinϑ, taken at zero angle, of the spin-flip amplitude for pion-nucleon scattering. The derivation of these relations is based on general field-theoretical concepts. It is shown that the condition of microscopic causality is sufficient and essentially also necessary for the existence of these equations. The special form of the dispersion relations depends on the assumptions about the high-frequency behavior of the spin-flip amplitude.
The exact dispersion formulas, which are derived under the more stringent boundedness condition for the amplitude, can be reduced to the spin-flip part of Low's equations for P-wave scattering. This reduction involves approximations which correspond to those underlying the direct derivation of Low's equations.
Under certain conditions the dispersion relations may hold approximately at low energies even if the causality condition is not valid in small but finite regions. This possibility is discussed briefly.References(13)
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