Scattering of 217-Mev Positive Pions on Hydrogen

The total and differential cross section for the scattering of 217-Mev positive pions on hydrogen has been measured in nuclear emulsions. The total cross section, excepting Coulomb scattering, was found to be (151.0±18.2) mb. The angular distribution in the center of mass was fitted by $\frac{d\sigma }{d\Omega }=(5.22\mathrm{}\pm 1.42)+(7.53\pm 2.57)cos\chi +(20.36\mathrm{}\pm 4.61){cos}^2\chi$ mb/steradian, assuming $S$ and $P$ waves only. A phase shift analysis was carried out using the method of maximum likelihood. The phase-shift solution in agreement with the requirements of causality and corresponding to the preferred solution of de Hoffman et al. was ${\alpha }_3=-22.5\mathrm{}°\pm 5.8°$, ${\alpha }_{33}=114.0\mathrm{}°\pm 7.4°$, and ${\alpha }_{31}=-11.6\mathrm{}°\pm 9.7°$. The angular distribution showed strong forward scattering and a perference for positive Coulomb interference, in agreement with the hypothesis of a resonance in the state with angular momentum $\frac{3}{2}$ and isotopic spin $\frac{3}{2}$.