Pion-Proton Scattering below 150 Mev. I

Positive-pion proton differential cross sections have been measured at 41.5 Mev for six angles. The angles in the center-of-mass system are 53°, 69.1°, 100.4°, 128°, 141.7°, and 163.5° and the corresponding cross sections in mb/sterad in the center-of-mass system are 0.252±0.020, 0.354±0.025, 0.777±0.038, 1.145±0.067, 1.495±0.084, and 1.750±0.110. Negative pion elastic cross sections have been measured for the first five of the above angles and are, respectively, in mb/sterad in the c.m. system: 0.338±0.047, 0.281±0.038, 0.148±0.029, 0.112±0.042, and 0.085±0.25. Phase-shift analyses of these data and those of other authors lead to the following expressions for the low-energy behavior of the $T=\frac{3}{2}$ phases: ${{\alpha }_{31}}^N=-(0.0418\mathrm{}\pm 0.004){\eta }^3$, ${{\alpha }_3}^N=-(0.1145\mathrm{}\pm 0.0026)\eta$, and $cot{{\alpha }_{33}}^N=\frac{\frac{4}{3}{\eta }^3(0.0877\mathrm{}\pm 0.0014)}{\left[{\omega }^{*}\right(1-\frac{{\omega }^{*}}{2.17}\left)\right]}$.