Backwardπ+pElastic Scattering from 2.18 to5.25 GeVc

Differential cross sections are presented for pion-proton elastic scattering in the angular range $-0.6\mathrm{}\gtrsim cos{\theta }_{\mathrm{c}.\mathrm{m}.\mathrm{}}\gtrsim -0.98\mathrm{}$ at 15 incident ${\pi }^{+}$ momenta from $2.18-5.25 \frac{\mathrm{GeV}}{c}$. The angular distributions rise steeply near 180° at all momenta. For laboratory momenta $\gtrsim 2.75 \frac{\mathrm{GeV}}{c}$ they show a minimum at $u\approx -0.17\mathrm{} {\left(\frac{\mathrm{GeV}}{c}\right)}^2$ and a broad maximum near $u\approx -0.6\mathrm{} {\left(\frac{\mathrm{GeV}}{c}\right)}^2$. When the data are plotted versus $s$, for fixed $u$, a strong signal from the $\Delta \mathrm{}\left(2420\right)\mathrm{}$ resonance is observed. The data are compared with a direct-channel resonance model and with a Regge model which considers the exchange of the $N_{\alpha }$, $N_{\gamma }$, and ${\Delta }_{\delta }$ Regge trajectories. The qualitative success of both the direct-channel resonance model and the Regge model lends support to the concept of duality.