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We have measured the differential cross section for π−p elastic scattering at 180° in steps of 0.10 GeV/c or less in the region P0=1.6 to 5.3 GeV/c. We detected elastic scattering events, from protons in a liquid H2 target, with a double spectrometer consisting of magnets and scintillation counters in coincidence. The incident π− beam was counted by scintillation counters. The cross section was found to have considerable structure. This may be interpreted as interference between the resonant amplitudes and the nonresonant or background amplitude. Very strong destructive interference occurs around P0=2.15 GeV/c, where the cross section drops almost two orders of magnitude in passing through the N*(2190). Another interesting feature of the data is a large narrow peak in the cross section at P0=5.12 GeV/c, providing firm evidence for the existence of a nucleon resonance with a mass of 3245±10 MeV. This N*(3245) has a full width of less than 35 MeV, which is about 1% of its mass. From this experiment we were able to determine the parity and the quantity χ(J+12) for each N* resonance, where χ is the elasticity and J is the spin of the resonance.
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We present a series of numerical and statistical techniques for interpolating and combining ("amalgamating") data from meson-nucleon scattering experiments. These techniques have been extensively applied to πp elastic and charge-exchange differential-cross-section and polarization data in the resonance region. The amalgamation is done by fitting a momentum- and angle-dependent interpolating surface to the data over a moderately narrow momentum range, typically ∼150 MeV/c, using the interpolating surface to shift data in a narrower central momentum region into fixed angular bins at a predetermined central momentum, and then statistically combining the data in each bin. The fitting procedure takes into account normalization errors, momentum calibration errors, momentum resolution, electromagnetic corrections, threshold structure, and inconsistencies among the data. The full covariance matrix of the amalgamated data is calculated, including contributions of statistical error, systematic error, and interpolation error. Techniques are presented for extracting from the covariance matrix information on the collective statistical fluctuations which correlate the errors of the amalgamated data. These fluctuations are described in terms of "correlation vectors" which facilitate the use of the amalgamated data as input for resonance-region phenomenology.
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