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 differential cross section of K − p and K + p elastic scattering has been measured at 4.2, 7 and 10 GeV/ c in the very forward region of scattering angles. The measurements have been made at the CERN PS by means of multiwire proportional chambers and counters. The region of momentum transfers t is 0.001 ⩽ | t | ⩽ 0.10 GeV 2 at the highest momentum and 0.001 ⩽ | t | ⩽ 0.03 GeV 2 at the lowest. Over these regions the Coulomb and the nuclear amplitudes reach their maximum interference. We have used a parametrisation of the above amplitudes to determine the value of the real part of the nuclear forward scattering amplitude. A dispersion relation fit has then been performed using these and earlier measurements; the asymptotic behaviour of the K ± p real parts has been examined in the light of this fit.
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Proton-antiproton and proton-proton elastic scattering have been measured in the four-momentum transfer range 0.001⩽| t |⩽0.06 GeV 2 for center-of-mass energy 52.8 GeV at the CERN Intersecting Storage Rings (ISR). Using the known pp total cross section, a simultaneous fit to the pp̄ and pp differential cross sections yields the pp̄ total cross section; in addition, we obtain the ratio of the real-to-imaginary part of the forward nuclear-scattering amplitude and the nuclear-slope parameter for both pp̄ and pp. Our results show conclusively that the pp̄ total cross section is rising at ISR energies and lend support to conventional theories in which the difference between the pp̄ and pp total cross section vanishes at very high energy.
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Antiproton-proton and proton-proton small-angle elastic scattering was measured for centre-of-mass energies s =30.6, 52.8 and 62.3 GeV at the CERN Intersectung Storage Rings. In addition, proton-proton elastic scattering was measured at s =23.5 GeV . Using the optical theorem, total cross sections are obtained with an accuracy of about 0.5% for proton-proton scattering and about 1% for antiproton-proton scattering. The measurement of the interference of the Coulomb scattering and the hadronic scattering permits a determination of the ratio of the real-to-imaginary part of the forward hadronic scattering amplitude. Also presented are measurements of the hadronic slope parameter.
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Antiproton-proton and proton-proton small-angle elastic scattering have been measured for centre-of-mass energies √ s = 30.7 and 62.5 GeV at the CERN Intersecting Storage Rings (ISR). Antiproton-proton and proton-proton total cross sections are obtained using the optical theorem. The measurement of the Coulomb scattering and its interference with the nuclear scattering allows a determination of the ratio of the real-to-imaginary part of the forward nuclear scattering amplitude. Also presented are measurements for the nuclear slope parameter at √ s = 62.5 GeV. Our new results reinforce the conclusions drawn recently from our measurements at √ s = 52.8 GeV. In particular, the pp̄ total cross section is rising at ISR energies and should continue to rise well beyond these energies.
DATA REQUESTED FROM AUTHORS.
RESULTS OF FITS.
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Differential cross sections have been measured in the region of small forward angles (between 0 and ∼40 mrad) for the elastic scattering reactions pp → pp at 4.2, 7.0 and 10.0 GeV /c and p p → p p at 4.2, 6.0, 8.0 and 10.0 GeV /c . The maximum momentum transfer is ∼0.025 GeV 2 at the lowest and ∼0.10 GeV/c at the highest incident momentum. Values of the slope and the real part of the forward scattering amplitude of the above reactions have been derived; the values obtained are in good agreement with dispersion relations.
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TABLE ALSO GIVES SIG, SLOPE AND T-RANGE USED IN FIT.
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