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Published November 15, 1960 | public
Journal Article Open

Pion-nucleon scattering in the Mandelstam representation


Using the analytic properties of partial wave scattering amplitudes, as derived from Mandelstam's representation, we have studied the J=3/2, P state of the pion-nucleon system. The method used is covariant, it incorporates unitarity, and the effect of a possible pion-pion resonance has been investigated. Using the "single nucleon term" and the low-energy scattering properties of the "crossed states," we obtain a resonance in the J=3/2, T=3/2 pion-nucleon state without the aid of a cutoff. We have also investigated the scattering in the T=1/2 state. The pion-pion resonance appears to have only a very small effect in the T=3/2 state whereas in the T=1/2 state it increases the phase shift by a factor of 2. The resonance obtained in the T=3/2 state occurs at too low an energy. There are several factors which may account for this: We have not been able to include fully the contributions from crossed states, and we have not systematically included inelastic scattering.

Additional Information

©1960 The American Physical Society. Received 6 June 1960. We are indebted to G. F. Chew and S. Mandelstam for constant advice and encouragement. Some correspondence with W. Frazer was also helpful. Supported in part by the U.S. Air Force through the Air Force Office of Scientific Research. [S.C.F. was] [s]upported by National Science Foundation Grant. [J.D.W. was a] National Science Foundation Postdoctoral Fellow.


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