π−+p→π0+nCharge Exchange Cross Sections at 20.7 and 31.0 Mev

A measurement has been made of the differential and total cross sections at 31.0 Mev and the total cross section at 20.7 Mev for the reaction ${\pi }^{-}+p\to {\pi }^0+n$. A thin-walled liquid hydrogen target was used. The gamma telescopes used a Čerenkov counter to identify the conversion electrons and a thin-lead converter to avoid complications from cascade processes. The angular distribution in mb/sr at 31.0 Mev is: $\frac{d\sigma }{d\Omega }=(1.00\mathrm{}\pm 0.02)\left[\right(0.51\pm 0.04)-(0.61\pm 0.11\left)P_1\right(cos\theta )+(0.12\mathrm{}\pm 0.36\left)P_2\right(cos\theta \left)\right]$. The total cross sections at 31.0 and 20.7 Mev are 6.5±0.5 and 5.4±0.4 mb, respectively. The data are also analyzed in terms of the phase shifts ${\alpha }_{\mathrm{ij}}$. Assuming that the $S$-wave phase shifts extrapolate to zero pion energy as ${\alpha }_i=a_i\eta$, where $\eta$ is the pion momentum in the c.m. system in units of $m_{\pi }c$, the quantity $(a_1-a_3)=0.27\mathrm{}\pm 0.02$. This agrees with Hamilton and Woolcock's prediction from photoproduction and the Panofsky ratio $(a_1-a_3)=0.245\mathrm{}\pm 0.01$. There are theoretical and experimental grounds for a nonlinear behavior of ${\alpha }_3$ and ${\alpha }_1$, which should improve the agreement.