Single- and Double-Pion Production by One-Pion Exchange and a Comparison with Experimental Data between 1.6 and20 GeVc

A detailed comparison has been made between predictions of elementary one-pion exchange (OPE) and existing experimental data. The Benecke-Dürr (BD) parametrization was used to describe the vertex functions. The BD parametrization has one free parameter $R$ for each vertex. The momentum transfer ($t$) distributions as measured between 1.6 and $10 \frac{\mathrm{GeV}}{c}$ for the reactions $\overline{p}p\to {\overline{\Delta }}^{--}{\Delta }^{++}\left[\Delta \equiv \Delta \mathrm{}\right(1236\left)\right]$, $\mathrm{pp}\to {\Delta }^{++}n$, ${\pi }^{+}p\to {\Delta }^{++}{\rho }^0$, and ${\pi }^{-}p\to n{\rho }^0$ were used to fit the parameters $R_{\Delta N\pi }$, $R_{\mathrm{NN}\pi }$, and $R_{\rho \pi \pi }$ which describe the $\mathrm{NN}\pi$, $\Delta N\pi$, and $\rho \pi \pi$ vertices. With the three-parameter fit an excellent description of the data is achieved for $\mathrm{}\left|t\right|<1\mathrm{}$ Ge${\mathrm{V}}^2$ at all energies, a result which independently of any model demonstrates that the energy dependence of these reactions is that of elementary OPE. From the $R$ parameters, values for various pionic rms radii were deduced: $〈{{r_{\mathrm{NN}\pi }}^2〉}^{\frac{1}{2}}=1.06\mathrm{}\pm 0.04$ F, $〈{{r_{\Delta N\pi }}^2〉}^{\frac{1}{2}}=0.86\mathrm{}\pm 0.02$ F, and $〈{{r_{\rho \pi \pi }}^2〉}^{\frac{1}{2}}=0.65\mathrm{}\pm 0.05$ F. The $\mathrm{NN}\pi$ and $\Delta N\pi$ values agree with results from $\pi N$ and $\mathrm{ep}$ scattering. As a further consistency check, the BD parametrization was used to describe the ($\frac{3}{2},\frac{3}{2}$) pion nucleon phase shift ${\delta }_{33}$ in the neighborhood of the $\Delta$. A good fit to the