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

Abstract

The cross section for the scattering of ${\ensuremath{\pi}}^{+}$ and ${\ensuremath{\pi}}^{\ensuremath{-}}$ 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 ${R}_{l}=\frac{{\ensuremath{\sigma}}_{l}(\mathrm{tot})}{{\ensuremath{\sigma}}_{l}(\mathrm{el})}$ 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, ${p}_{11}$, ${s}_{11}$, and ${d}_{13}$ waves all playing an important part. The width of the ${d}_{13}$ resonance is found to be considerably smaller than previous values from total cross-section measurements. The role of the (possibly resonant) amplitudes ${p}_{11}$ and ${s}_{11}$ is discussed.