Cross sections for pi+-p elastic scattering have been measured to high precision, for beam momenta between 800 and 1240 MeV/c, by the EPECUR Collaboration, using the ITEP proton synchrotron. The data precision allows comparisons of the existing partial-wave analyses (PWA) on a level not possible previously. These comparisons imply that updated PWA are required.
Differential cross section of elastic $\pi^+$p-scattering at P= 800.25 MeV/c. Errors shown are statistical only.
Differential cross section of elastic $\pi^+$p-scattering at P= 803.75 MeV/c. Errors shown are statistical only.
Differential cross section of elastic $\pi^+$p-scattering at P= 807.25 MeV/c. Errors shown are statistical only.
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We report the results of the investigation of 18 500 frames of π+p interactions in the Brookhaven 20-in. bubble chamber at an incident energy of 900 MeV. It is found that single-pion production proceeds almost entirely through formation of the N33* isobar. The production mechanism of the N33* is analyzed in terms of its spin density matrix. Comparison is made with Stodolsky and Sakurai's ρ-exchange model and with the absorptive peripheral model.
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The Berkeley 15-in. hydrogen bubble chamber was used to investigate π+−p interactions at 600 MeV. There were 1738 good events, of which 71.9±0.8% were elastic. Partial waves up to at least D52 are required to fit the elastic angular distribution. The inelastic events were almost entirely single-pion production. The ratio (p+0)(n++) was found to be 5.5±0.8 which agrees well with 4.9 predicted by the (32, 32) pion-nucleon isobar model of Olsson and Yodh. It is also consistent with 6.5 predicted by Sternheimer and Lindenbaum. The pion momentum spectra and the π−π Q-value distributions also support the Olsson and Yodh model. Thus the (32, 32) pion-nucleon isobar is apparently the principal mechanism for single-pion production at 600 MeV. Angular distributions for the single-pion-production data are presented.
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The π + p cross section for elastic scattering from hydrogen was measured at seven incident energies ranging from 20.8 to 95.9 MeV for an angular range from 60° to 145°. The experimental set-up is discussed in detail as well as the method used for data analysis. A table of results and a set of phase shifts are provided.
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The differential cross section for π ± p elastic scattering below 2 GeV/ c has been measured at small forward pion angles by an electronics experiment. The interference effects observed between the Coulomb and the nuclear interaction have been used to determine the magnitude and sign of the real parts of the π ± p forward scattering amplitude. The latter are compared to the values predicted by the dispersion relations.
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Measurements of π±p elastic differential cross-sections have been performed in the forward direction, using a missing-mass spark chamber spectrometer. The films have been seanned by an automatic apparatus. A phase-shift analysis of the experimental data has been done, leading to three solutions. Various experiments are proposed in order to resolve the ambiguities.
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In this paper we present the π + p differential elastic scattering cross sections at five momenta between 0.6 and 0.8 GeV/ c . The data were collected in a bubble chamber exposure and consequently are susceptible to different systematic errors from counter experiments. Our results are generally in good agreement with those of counter experiments in the same momentum range and with the predictions of the various elastic partial wave analyses. The majority of partial wave analyses do not however yield parameters which fit our data in detail without modification.
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Differential cross sections for π + p and π − p elastic scattering have been measured with an accuracy of typically ±2% at 10 and 9 energies respectively in the range 88 to 292 MeV of lab kinetic energy.
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π±p elastic differential cross sections in the momentum range 1.72-2.80 GeV/c have been measured at the proton synchrotron "NIMROD" of the Rutherford High Energy Laboratory. The results are tabulated, and analyses of the differential cross sections employing optical models and Legendre polynomial expansions are advanced. A critical discussion of a recent interpretation of differential-cross-section structure in terms of interference between resonant and background amplitudes is presented.
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The differential cross section for π±−p elastic scattering at 180° was measured from 0.572 to 1.628 GeVc using a double-arm scintillation-counter spectrometer with an angular acceptance θ* in the center-of-mass system defined by −1.00≤cosθ*≤−0.9992. The π+−p cross section exhibits a large dip at 0.737 GeVc and a broad peak centered near 1.31 GeVc. The π−−p cross section exhibits peaks at 0.69, 0.97, and 1.43 GeVc.
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The energy dependence of backward π+p elastic scattering has been measured for incident π momenta 2.0-6.0 GeV/c in steps of typically 100 MeV/c. Values are presented for both the differential cross section extrapolated to 180° and the slope of the backward peak as a function of momentum. In the s channel we see the effects of the established Δ++ resonances and evidence for the Δ(3230). Also, the data show the existence of a negative-parity Δ resonance with mass ∼2200 MeV/c2.
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The contradiction of the σ term of pion-nucleon scattering as deduced from the Karlsruhe-Helsinki phase shifts with the smaller value calculated by the chiral perturbation theory of QCD is well known. In an effort to clarify the discrepancy we have determined the real part of the isospin-even forward-scattering amplitude of pion-nucleon scattering at a pion energy Tπ=54.3 MeV by measurement of the elastic scattering of positive and negative pions on protons in the Coulomb-nuclear interference region. The deduced value is in agreement with the prediction of the Karlsruhe-Helsinki phase-shift analysis for that energy. The resulting large value of the σ term may be interpreted as being due to the influence of s¯s sea pairs even at large distances (small Q2) as previously suggested by the European Muon Collaboration measurement of deep-inelastic scattering of polarized muons on polarized protons.
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Differential cross sections are presented for pion-proton elastic scattering in the angular range −0.6≳cosθc.m.≳−0.98 at 15 incident π+ momenta from 2.18−5.25 GeVc. The angular distributions rise steeply near 180° at all momenta. For laboratory momenta ≳2.75 GeVc they show a minimum at u≈−0.17 (GeVc)2 and a broad maximum near u≈−0.6 (GeVc)2. When the data are plotted versus s, for fixed u, a strong signal from the Δ(2420) resonance is observed. The data are compared with a direct-channel resonance model and with a Regge model which considers the exchange of the Nα, Nγ, and Δδ Regge trajectories. The qualitative success of both the direct-channel resonance model and the Regge model lends support to the concept of duality.
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The real part of the isospin-even forward-scattering amplitude of pion-nucleon scattering has been determined at a pion energy of Tπ=55 MeV by measurement of the elastic scattering of positive and negative pions on protons within the Coulomb-nuclear interference region. The value confirms the prediction of the Karlsruhe-Helsinki phase-shift analysis for that energy. These phases have been used to determine the σ term of pion-nucleon scattering by means of dispersion relations, resulting in a value for σ which is in contradiction with chiral perturbation theory of QCD.
PI- P cross sections normalised to the Coulomb cross section taken from the Karlesruhe-Helsinki phase shift analysis (R. Koch, E. Pietarinen (NP A336(80)331).
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Results of a spark chamber experiment on elastic scattering of pions on protons are presented and analyzed. The processes studied were π+p at 2.92 GeV/c, and π−p at 3.15, 4.13, and 4.95 GeV/c. The data are fitted to an exponential function of the four-momentum transfer, t, in several different ways in attempts to explore systematic energy and angular dependences. No shrinkage of the diffraction peak is seen in comparing the coefficients of a linear exponential fit for |t|<0.4 (GeV/c)2; at larger |t|, however, the cross section falls off with increasing energy. The large-angle differential cross section is examined for structure and is compared with all other large angle scattering data. The results are compared with proton-proton scattering data over the same energy range and substantial differences between the two processes are evident.
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As part of a program of measurements of the πp system we have measured the backward differential cross section for π+p elastic scattering at 16 momenta from 1.25 to 2.0 GeV/c inclusive. The angular region covered is -0.46 to -0.97 in cosθc.m.. The high resolution in u of 0.03 to 0.04 (GeV/c)2, together with good statistics, enables a detailed examination of the momentum and angular dependence of structure in this channel. The data are compared with distributions from other experiments and with the most recent phaseshift fit.
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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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A simple, large-solid-angle apparatus, specially suited for the measurement of backward elastic scattering of medium-energy pions on protons and deuterons, is described. The method of analysis which reduces background and determines elastic events from a data sample of 185 MeV negative pions incident on a D 2 O target is discussed. Results for 141 MeV π + p and 185 MeV π − p backward cross-sections are also presented and compared with cross-sections calculated from known phase shifts.
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Differential cross sections for pi- p and pi+ p elastic scattering were measured at five energies between 19.9 and 43.3 MeV. The use of the CHAOS magnetic spectrometer at TRIUMF, supplemented by a range telescope for muon background suppression, provided simultaneous coverage of a large part of the full angular range, thus allowing very precise relative cross section measurements. The absolute normalisation was determined with a typical accuracy of 5 %. This was verified in a simultaneous measurement of muon proton elastic scattering. The measured cross sections show some deviations from phase shift analysis predictions, in particular at large angles and low energies. From the new data we determine the real part of the isospin forward scattering amplitude.
Elastic PI- P cross section for incident kinetic energy 43.3 MeV for the rotated target data. Errors shown are statistical only.
Elastic PI- P cross section for incident kinetic energy 43.3 MeV. Errors shown are statistical only.
Elastic PI- P cross section for incident kinetic energy 37.1 MeV. Errors shown are statistical only.
We present results on $\pi^+$-p interactions at 500 MeV from an experiment performed with the Saclay 35 cm hydrogen bubble chamber. A total of 1840 events have been observed. The branching ratio for elastic events is equal to 0.883$\pm$0.008. Eight events are unambiguously attributed to the reaction $\pi^+p\to\pi^+p\gamma$. Cross sections for the various reactions are given. The elastic angular distribution has been determined up to cos$\theta$ = +0.975 and shows evidence for S, P, D waves in good agreement with the results obtained in other experiments. For the one-pion production reactions, the ratio of $\pi^0$ production to $\pi^+$ production is found equal to 4.1$\pm$0.8. This result and the corresponding distributions for momentum and angle of the secondaries are compared with the predictions of the isobaric models.
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The energy dependence of the differential cross section for $\pi^+ p$ elastic scattering at a c.m. angle near 174 ° has been measured. The momentum range of incident $\pi^+$ was 2.06-4.70 GeV/c. On this energy dependence one can see a structure, i.e. maxima corresponding to the baryon resonances $\Delta(2420)$ and $\Delta(2840)$. The structure is used for determination of the parities of these resonances.
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A precision measurement of absolute pi+p and pi-p elastic differential cross sections at incident pion laboratory kinetic energies from T_pi= 141.15 to 267.3 MeV is described. Data were obtained detecting the scattered pion and recoil proton in coincidence at 12 laboratory pion angles from 55 to 155 degrees for pi+p, and six angles from 60 to 155 degrees for pi-p. Single arm measurements were also obtained for pi+p energies up to 218.1 MeV, with the scattered pi+ detected at six angles from 20 to 70 degrees. A flat-walled, super-cooled liquid hydrogen target as well as solid CH2 targets were used. The data are characterized by small uncertainties, ~1-2% statistical and ~1-1.5% normalization. The reliability of the cross section results was ensured by carrying out the measurements under a variety of experimental conditions to identify and quantify the sources of instrumental uncertainty. Our lowest and highest energy data are consistent with overlapping results from TRIUMF and LAMPF. In general, the Virginia Polytechnic Institute SM95 partial wave analysis solution describes our data well, but the older Karlsruhe-Helsinki PWA solution KH80 does not.
Centre of mass absolute differential cross sections at pion kinetic energy 141.15 MeV using the liquid H2 target and single arm pion detection. There is an additional systematic error of 1.1 PCT for PI+ beams which is not included in the errors shown in the table.
Centre of mass absolute differential cross sections at pion kinetic energy 141.15 MeV using the liquid H2 target and two arm pion detection. There is an additional systematic error of 1.3 PCT for PI+ beams which is not included in the errors shown in the table.
Centre of mass absolute differential cross sections at pion kinetic energy 141.15 MeV using the liquid H2 target and two arm pion detection. There is an additional systematic error of 1.3 PCT (1.6 PCT) for PI+ (PI-) beams which is not included in the errors shown in the table.
Experimental results are presented on $\pi^+ p$ interactions at 850 MeV/c incident momentum. Cross sections for the various reactions are given. The elastic differential cross section has been fitted to a polynomial in, cos$\theta$ and the resulting coefficients are compared to results at neighbouring incident momenta. For the one-pion-production reactions, the (N$\pi$) effective mass distributions and the ratio of $\pi^0$ to $\pi^+$ production have been compared to the predictions of several theoretical models.
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Differential cross sections for π + p elastic scattering were measured for seven incident energies from 65 to 140 MeV at laboratory scattering angles between 93° and 165°. The results are compared with previous results of Bertin et al. and the phase-shift analysis of Arndt and Roper. Agreement between the phase-shift analysis and the data is good.
ABSOLUTE NORMALIZATION UNCERTAINTY = 2.4 PCT.
ABSOLUTE NORMALIZATION UNCERTAINTY = 2.0 PCT.
ABSOLUTE NORMALIZATION UNCERTAINTY = 1.4 PCT.
Differential cross sections for π ± p→ π ± p have been measured at P π between 378 and 687 MeV / c at 9 angles in the range −0.8⩽cos θ c.m. ⩽0.6. Scattered pions and recoil protons were detected in coincidence using scintillation counter hodoscopes. For almost all of the data the statistical and normalization uncertainties are each less than 2%. Our measurements are compared with existing data and the results of recent partial wave analyses.
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Photographic plates were used to study the angular distribotion of 360 plus or minus 10 Mev pi /sup +/ mesons elastically scattered by protons. The differential cross sections derived from 218 scattering events for SP analysis and for SPD analysis are given. The phase shifts which correspond to these distributions are also given.
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The angular distribution π+-p at 1.0 GeV was determined on the basis of l032 events measured in a propane bubble chamber. Comparison is made with data of 820 and 900 MeV and with angular distributions π−+p at similar energies.
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The differential cross-section for π - -p elastic scattering over the angular range 125° to 178° center of mass has been measured between 1.28 and 3.0 GeV/ c . Considerable structure is found and is discussed in terms of direct channel resonances.
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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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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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Measurements have been made of the asymmetry in the scattering of π− mesons by a polarized proton target. Scattered π mesons and recoil protons were detected in arrays of scintillation counters; data were obtained at 16 scattering angles at each of 8 beam momenta between 875 and 1578 MeV/c. Analysis of these data together with earlier differential-cross-section measurements shows that there must exist at least three resonances in this energy region: (i) mass 1920 MeV/c2, Γ=170 MeV/c2, I=32, F72; (ii) mass 1682 MeV/c2, Γ=100 MeV/c2, I=12, F52; and (iii) mass 1674 MeV/c2, Γ=100 MeV/c2, I=12, D52.
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New high-statistics measurements of π + p elastic scattering differential cross sections are presented at 30 momentum points between 1.282 and 2.472 GeV/ c , covering most of the angular distribution outside the forward diffractive peak. These data show significant disagreements at some momenta with previous high-statistics experiments and with current partial wave analyses.
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Polarization and differential cross-section data for elastic scattering of positive pions on protons between 0.82 and 2.74 GeV/ c are presented. A dip in the polarization, at constant u ≈ −0.65 GeV 2 , is observed. The data are compared with published phase-shift analyses.
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The polarization and the differential cross section in π−p elastic scattering have been measured at incident pion laboratory momenta of 1.70, 1.88, 2.07, 2.27, and 2.50 GeV/c. The experiment was carried out at the Argonne zero-gradient synchrotron with a polarized proton target. Details of the apparatus and data analysis are presented here together with the final results. A partial-wave analysis of the data has verified the JP=72+ assignment for the Δ(1950) and established a JP=72− assignment for the N(2190). It does not support a JP=112+ assignment for the Δ(2460), nor does it give support for some of the possible resonances found in the CERN phase-shift analysis. Apart from the resonance behavior, the partial-wave analysis reveals several new features. We find a striking correlation among the various partial-wave amplitudes at the highest energy, which is different for J=l+12 and J=l−12. In addition, several fixed-(−t) features of high-energy scattering emerge in the energy region of this analysis.
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We have measured differential cross sections for both π+p and π−p elastic scattering at incident-pion kinetic energies of 30, 50, 70, and 90 MeV in the center-of-mass angular range between 50° and 150°. The experiment detected pions scattered from a liquid-hydrogen target with multiwire proportional chambers and scintillation-counter range telescopes. The relative accuracy of each angular distribution is better than 5%, while the absolute cross sections have uncertainties of 4% to 25%. Our results for the absolute cross section for π+p scattering at 30 and 90 MeV are inconsistent with previous measurements. Our π−p measurements comprise the first extensive set of precision differential cross sections below 90 MeV.
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The most recent total-cross-section data are used to calculate real parts of the forward elastic π±p scattering amplitudes from threshold to 240 GeV/c. Using statistical and systematic uncertainties of the total cross sections and their momenta, along with uncertainties of the subtraction and coupling constants, unphysical cuts, and cross-section extrapolations, we calculate the uncertainties of the real amplitudes. Our results are compared to experimental and other theoretical determinations of the π±p forward real amplitudes.
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