Pion-Nucleon Scattering Amplitudes in the Range 300-700 MeV

The cross section for the scattering of π⁺ and π^- by nucleons in the energy range 300-700 MeV has been analyzed in terms of energy-independent parameters. The parameterization is based on a dispersion relation satisfied by the partial-wave amplitudes, by replacing the left cut by a superposition of poles and the inelasticity function Rₗ=σₗ(tot)σₗ(el) by a ratio of polynomials in the momentum. Detailed results are presented for the real and imaginary parts of the phase shifts with $l<~3$. The structure of the "second resonance" is more complicated than has heretofore been thought, p₁₁, s₁₁, and d₁₃ waves all playing an important part. The width of the d₁₃ resonance is found to be considerably smaller than previous values from total cross-section measurements. The role of the (possibly resonant) amplitudes p₁₁ and s₁₁ is discussed.