Elastic Scattering of Negative Pions on Protons in the Energy Range 500-1000 MeV

Differential cross sections for the elastic scattering of negative pi mesons on protons (${\pi }^{-}-p\to {\pi }^{-}-p$) were measured at the Berkeley Bevatron at five laboratory kinetic energies of the pion between 500 and 1000 MeV. The results were least-squares fitted with a power series in the cosine of the center-of-mass scattering angle, and total elastic cross sections for ${\pi }^{-}-p\to {\pi }^{-}-p$ were obtained by integrating under the fitted curves. The coefficients of the cosine series are shown plotted versus the incident pion laboratory kinetic energy. These curves display as a striking feature a large value of the coefficient of ${{cos}^5\theta }^{*}$ peaking in the vicinity of the 900-MeV resonance. This implies that a superposition of $F_{\frac{5}{2}}$ and $D_{\frac{5}{2}}$ partial waves is prominent in the scattering at this energy, since the coefficients for terms above ${{cos}^5\theta }^{*}$ are negligible. One possible explanation is that the $F_{\frac{5}{2}}$ enhancement comes from an elastic resonance in the isotopic spin $T=\frac{1}{2}$ state, consistent with Regge-pole formalism, and the $D_{\frac{5}{2}}$ partial-wave state may be enhanced by inelastic processes. At 600 MeV the values of the coefficients do not seem to demand the prominence of any single partial-wave state, although the results are compatible with an enhancement in the $J=\frac{3}{2}$ amplitude. A table listing quantum numbers plausibly associated with the various peaks and "shoulders" seen in the ${\pi }^{\pm }-p$ total cross-section curves is presented.