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Polarization parameters for the π − p → π 0 n charge exchange scattering have been measured at eight beam momenta between 1965 and 4220 MeV/ c using two different experimental set-ups. The angular range covered is −0.90 < cos θ π ∗ < 0.95 at the five momenta of 1965, 2168, 2360, 2566 and 2960 MeV/ c , where θ π ∗ is the emission angle of the π 0 meson in the c.m.s.. For three momenta of 2770, 3490 and 4220 MeV/ c , the measurements cover the forward angles of 0.1 < cos θ π ∗ < 1.0 . The results are compared with the predictions of π N partial wave analyses.
Polarisation measurements from SETUP1. Errors are statistical only.
Polarisation measurements from SETUP2. Errors are statistical only.
Legendre polynomial coefficients for fit to differential cross section data.
This paper presents the results of a study of the dominant neutral final states from π−p interactions. The data were obtained in an experiment performed at the Brookhaven National Laboratory Alternating Gradient Synchrotron, using a set of steel-plate optical spark chambers surrounding a liquid-hydrogen target. We present differential and total cross sections for the reactions (1) π−p→n+π0 and (2) π−p→n+η0(η0→2γ) and total cross sections for the reactions (3) π−p→n+kπ0 (k=2, 3, 4, and 5) and (4) π−p→all neutrals for eighteen values of beam momentum in the interval 1.3 to 4.0 GeV/c. The angular distributions for (1) and (2) have been analyzed in terms of expansions in Legendre polynomials, the coefficients for which are also given.
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SIG = 4*PI*LEG(L=0).
FORWARD DIFFERENTIAL CROSS SECTION CALCULATED FROM LEGENDRE POLYNOMIAL COEFFICIENTS AND ERROR MATRICES.
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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Large-angle π±p elastic-scattering cross sections, measured between 2 and 9 GeV/c in fine intervals of incident momentum and scattering angle, are used to search for cross-section fluctuations occurring for small changes in the center-of-mass energy as suggested by Ericson and Mayer-Kuckuck and by Frautschi. Significant fluctuations are observed.
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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 π+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 dσdΩ at 180° were then obtained by extrapolation. A resonance model and an interference model were used to perform fits to the energy dependence of dσdΩ (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 Δ(2200), Δ(2420), Δ(2850), and Δ(3230) resonances. Our data confirm the existence of the Δ(3230) and require the negative-parity Δ(2200).
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The π−+p→π0+n differential cross section at 180° has been measured for 52 values of π− momentum from 1.8 to 6.0 GeV/c using a constant-geometry detection system. The average statistical uncertainty is ∼5% and the systematic uncertainty is ∼10%. The details of the experiment and the data analysis are discussed. The data are compared with those of other experiments with which they are generally in agreement. One set of data disagrees with those presented here and a possible reason for this is discussed. A five-parameter fit of the predictions of a dual-resonance model to our data gave excellent agreement. The differential cross sections at 180° for π±p elastic scattering have been compiled and the moduli and relative phase of the T=12 and T=32 pion-nucleon s- and u-channel amplitudes (|A12|, |A32|, and cosδ) have a minimum at u=0.4 GeV/c and, in the s channel, a corresponding minimum at s=2.2 GeV/c.
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Small-angle differential cross sections are presented here for π−+p→π0+n charge-exchange scattering between 2.4 and 3.8 GeV/c. The differential cross section near t=0 displays two minima and one maximum in this momentum interval, reflecting the presence of the N32*(2420), N32*(2850), and N12*(2650) resonances; at larger t values, the cross sections fall off exponentially as a function of t, just as has been previously observed for charge-exchange scattering above 6 GeV/c. The pion-charge-exchange data reported here at 6 and 10 GeV/c extend out to large angles, showing a maximum near t=0, followed by an exponential falloff as e10t, a minimum near −t=0.6 (GeV/c)2, and then a second maximum near −t=1.0 (GeV/c)2. The π−+p→η0+n differential cross section shows a maximum near t=0, followed by an exponential falloff as e4t, much less steep than the π0 slope. These data are compared to our previously published data and to those of the Saclay-Orsay group.
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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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