Elastic Scattering of Positive Pions by Protons in the Energy Range 500-1600 MeV

Differential cross sections for the elastic scattering of positive pi mesons by protons were measured at the Berkeley Bevatron at pion laboratory kinetic energies between 500 and 1600 MeV. Fifty scintillation counters and a matrix coincidence system were used to identify incoming pions and detect the recoil proton and pion companions. Results were fitted with a power series in the cosine of the center-of-mass scattering angle, and total elastic cross sections were obtained by integrating under the fitted curves. The coefficients of the cosine series are displayed, plotted versus the laboratory kinetic energy of the pion. The most striking features of these curves are the large positive value of the coefficient of ${{cos}^6\theta }^{*}$, and the large negative value of the coefficient of ${{cos}^4\theta }^{*}$, both of which maximize in the vicinity of the 1350-MeV peak in the total cross section. These results indicate that the most predominant state contributing to the scattering at the 1350-MeV peak has total angular momentum $J=\frac{7}{2}$, since the coefficients for terms above ${{cos}^6\theta }^{*}$ are negligible at this energy. One possible explanation is that the 1350-MeV peak is the result of an $F_{\frac{7}{2}}$ resonance lying on the same Regge-pole trajectory as the ($\frac{3}{2}, \frac{3}{2}$) resonance near 195 MeV.