Separation ofNandΔExchanges inπNScattering and Deduction of Amplitude Zeros

Linear combinations of $\pi N$ differential cross sections and polarizations are used to isolate the $I_u=\frac{1}{2}$ and $I_u=\frac{3}{2}$ exchange amplitudes directly from data. For $I_u=\frac{1}{2}$ exchange the cross section has a zero at $u=-0.15\mathrm{}$ ${(\mathrm{G}\mathrm{e}\mathrm{V}/\mathit{c})}^2$ and the polarization becomes large and negative for $\mathrm{}\left|u\right|>0.25\mathrm{}$ ${(\mathrm{G}\mathrm{e}\mathrm{V}/\mathit{c})}^2$. Our phenomenological analysis indicates that in the dip region the $I_u=\frac{1}{2}$ amplitude is inconsistent with appreciable secondary trajectories or absorptive corrections. For $I_u=\frac{3}{2}$ exchange we infer that the imaginary $s$-channel helicity-flip amplitude has a zero near $u=-0.15\mathrm{}$ ${(\mathrm{G}\mathrm{e}\mathrm{V}/\mathit{c})}^2$, consistent with peripherality for $\Delta$ exchange. We also derive a sum rule relating the $\pi N$ differential cross sections at 180° to the Regge-trajectory difference ${\alpha }_{\Delta }-{\alpha }_N$.