Scattering of Positive Pions by Hydrogen at 189 Mev

The differential and total cross section of pions on hydrogen has been measured for 189 Mev positive pions. Liquid hydrogen was used as the scatterer; the incident and scattered pions were detected with scintillation counters. The angular distribution was fitted by: $\sigma =(7.24\mathrm{}\pm 0.76)+(3.1\pm 1.3)cos\chi +(25.6\mathrm{}\pm 2.6){cos}^2\chi$ millibarns per sterad. The total cross section measured by transmission was 194.1±5.2 millibarns. A phase shift analysis was made using these results in conjunction with data obtained previously on the scattering of negative pions. The analysis was restricted to $S$ and $P$ waves and assumed conservation of isotopic spin. Four solutions were obtained. The one which is consistent with the requirements of causality and which corresponds to the preferred solution of de Hoffmann et al. is ${\alpha }_1=-2.8\mathrm{}°\pm 4.5°$, ${\alpha }_3=-11.3\mathrm{}°\pm 3.2°$, ${\alpha }_{11}=-2.6\mathrm{}°\pm 7.5°$, ${\alpha }_{13}=-2.1\mathrm{}°\pm 3.8°$, ${\alpha }_{31}=-11.6\mathrm{}°\pm 5.1°$, ${\alpha }_{33}=98.8\mathrm{}°\pm 3.6°$.