Scattering of 65-Mev Pions in Hydrogen

A measurement has been made at approximately 65 Mev of the differential cross sections in the processes ${\pi }^{+}+p\to {\pi }^{+}+p$, ${\pi }^{-}+p\to {\pi }^{-}+p$ and ${\pi }^{-}+p\to {\pi }^0+n$ using a liquid hydrogen target and scintillation counter detectors. The measured cross sections in the center-of-mass system are $\frac{d\sigma }{d\Omega }({\pi }^{-}\to {\pi }^0)=\left[0.96\pm 0.03-(1.38\pm 0.09)cos\theta +(0.14\mathrm{}\pm 0.24)\frac{3{cos}^2\theta -1\mathrm{}}{2}\right](1\mathrm{}\pm 0.10) \left(\mathrm{at} 65 \mathrm{Mev}\right).\mathrm{}$ Because of Coulomb interference effects, the experiment, affords the opportunity of determining the signs as well as the magnitudes of the phase shifts in an analysis including only $s$ and $p$ waves. It is found that two very markedly different sets of phase shifts fit the data. Each of these sets includes subsets of the Fermi and Yang type. The results of this experiment, in conjunction with those of similar experiments, favor a set characterized by a strong attractive $p$ wave interaction in the $T=\frac{3}{2}$ isotopic spin state.