π+pbackward elastic scattering from 2 to 6 GeV/c

The backward angular distributions obtained in an experiment at the Zero Gradient Synchrotron of Argonne National Laboratory were used to systematically study the energy dependence of the 180° differential cross section for ${\pi }^{+}p$ elastic scattering in the center-of-mass energy region from 2159 to 3487 MeV. At each of 38 incident pion momenta between 2.0 and 6.0 GeV/c, a focusing spectrometer and scintillation counter hodoscopes were used to obtain differential cross sections for typically five pion scattering angles from 141° to 173° in the laboratory. Values for $\frac{d\sigma }{d\Omega }$ at 180° were then obtained by extrapolation. A resonance model and an interference model were used to perform fits to the energy dependence of $\frac{d\sigma }{d\Omega }$ (180°). Both models led to good fits to our data and yielded values for the masses, widths, parities, and the product of spin and elasticity for the $\Delta \mathrm{}\left(2200\right)\mathrm{}$, $\Delta \mathrm{}\left(2420\right)\mathrm{}$, $\Delta \mathrm{}\left(2850\right)\mathrm{}$, and $\Delta \mathrm{}\left(3230\right)\mathrm{}$ resonances. Our data confirm the existence of the $\Delta \mathrm{}\left(3230\right)\mathrm{}$ and require the negative-parity $\Delta \mathrm{}\left(2200\right)\mathrm{}$.