Measurements of the polarization in pp elastic scattering have been made at 5.15 GeV/c over the range −t=0.2 to 1.8 (GeV/c)2. The data are compared with a Regge-pole model, and with the diffraction model of Durand and Lipes in which the absorptive part of the pp interaction is derived from the electromagnetic form factor of the proton. The latter model reproduces the t dependence of the experimental data in a qualitative way.
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Elastic differential cross sections were measured at 6 energies between 2.3 and 6 BeVc for π++p and π−+p. The behavior of the secondary peak as a function of energy and charge is shown. Evidence for considerable resonance structure is seen in the angular distributions.
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Protons of the internal circulating beam of the Bevatron were scattered in a polyethylene target. Both scattered and recoil protons were detected by scintillation counters at angles which define elastic proton-proton events. An internal counter was located within a few inches of the beam to permit measurements at laboratory scattering angles as low as 2°. Absolute values are based on the calibration of the induction electrode that monitors the circulating beam. Total elastic cross sections obtained by integrating the differential spectra are 17, 10, and 8 mb at 2.24, 4.40, and 6.15 Bev, respectively. The experimental angular distributions are consistent with the prediction of a simple optical model with a complex index of refraction at short range.
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Interactions initiated by 3-Bev protons of the Brookhaven Cosmotron were studied by photoemulsion technique. With appropriate criteria, 115 events are attributed to interactions of the incident beam protons with hydrogen nuclei (∼55%) and with bound protons of other nuclei (∼45%). A detailed analysis allowed the subdivision of the 115 events in categories, according to the number of π mesons (N>~0) produced in the collision. The ratio of elastic scattering to the total number of events was estimated to be σelσtotal=0.20−0.07+0.04. The observed cross section for pure elastic scattering is σel=8.9±1.0 mb. The percentages of single, double, triple, and quadruple π-meson production are respectively: 34−20+22; 35.6−23+20; 9.6−4+6; ∼1.0+3.5. Among the 20 most probable cases of single π-meson production—the estimated ratio of π+ to π0 is σπ+σπ0=5.3−1.4+0.3. The experimental results are not in agreement with the Fermi statistical-model theory (in particular the lower limit for the experimental ratio of triple to single production is given by σ3σ1>∼110 in contrast with the predicted ratio σ3σ1=167) but are not inconsistent with the Peaslee excited-state-model theory.
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A bubble chamber investigation of π−+p elastic scattering at 1 200 MeV (K.E.) is reported. The total and differential cross-sections are determined. By extrapolation of the angular distribution, the 0° cross-section is derived and compared with the results obtained with the help of the dispersion relations and the optical theorem. The forward peak is investigated in terms of diffraction scattering and a value for the optical radius is derived.
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The interactions of 775 MeV (kinetic energy) π−-mesons in a hydrogen bubble chamber have been studied. Total and partial crosssections have been determined with the following results: σ (total) = (39.0±1.6) mb, σ (elastic)=(14.8±0.7) mb, σ (π− + p → all neutrals) = (9.0 ± 0.5) mb, σ (π− + p = π− + π+ + n) = (9.8 ± 0.5) mb, and σ (π− + p = π− + p + π0) = (4.8 ± 0.3) mb. The elastic-scattering angular distribution has been fitted with a Legendre polynomial series terminated at the fifth order. Various angular and effective-mass distributions of single-π production are presented and discussed in terms of the Olsson-Yodh and O.P.E. models.
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Interactions of 683-MeV/c negative pions with protons were investigated using the BNL 14-in. hydrogen bubble chamber in a 17-kG field. Two thousand elastic scatterings were analyzed, yielding a cross section of 18.9±1.0 mb. No evidence for powers of cosθ higher than the second was observed in the elastic angular distribution. The angular distribution obtained was dσdω=(0.384±0.026)+(1.70±0.06)cosθ+(3.36±0.11)cos2θ mb/sr. The single-pion production reactions π−+p→π−+π0+p and π−+p→π−+π++n were studied in detail. A total of 441 π0 productions and 833 π+ productions were analyzed giving cross sections of 3.99±0.50 and 7.50±0.80 mb, respectively. The differential distributions for these inelastic processes are presented and compared with the predictions of the model of Olsson and Yodh. The distribution of events on the Dalitz plots for π0 production is accounted for by the model. However, for the π+ reaction, the model (so far developed) does not describe adequately the distribution of events on the Dalitz plot. In particular, the model fails to account for the enhancement at high (π+π−) effective masses in ππ mass distribution. The center-of-mass angular distributions for π0 and π+ production reactions are presented and compared with the model.
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We discuss how the spatial intermittency of energy dissipation in 3D fully developed turbulence affects the small-scale statistics of passive scalars. We relate the passive-scalar behaviour to the diffusion properties of particle pairs in turbulent fluids. We thus find the intermittency correction to the -5/3 Obukhov-Corrsin law for the power spectrum of a passive scalar at wavenumber k where molecular diffusion and viscosity play a negligible role (inertial convective subrange). This correction is positive at difference with the negative correction to the -5/3 Kolmogorov law for the energy spectrum. We finally show that the structure functions of passive scalars have scaling exponents linear in the moment order, even in the framework of multifractal models.
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The c.m. angular distribution of π+p elastic scattering at 1.6 GeV/c shows a strong forward diffraction peak decreasing exponentially with a slopeA + = (6.9±0.5) GeV−2 comparable to thatA − = (7.2±0.5) GeV−2 observed in a previous experiment for π-p elastic scattering at the same incident momentum. The behaviour of the π+ and the π− angular distributions is quite different beyond the diffraction peak. The π+p total elastic cross-section is found to be Σ01 = (16.70±0.45) mb.
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