Comparison of small-angle p and pp elastic scattering at 52.8 GeV center-of-mass energy at the CERN intersecting storage rings

Proton-antiproton and proton-proton elastic scattering have been measured in the four-momentum transfer range 0.001|t|0.06 GeV² 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 p and pp differential cross sections yields the p 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 p and pp. Our results show conclusively that the p total cross section is rising at ISR energies and lend support to conventional theories in which the difference between the p and pp total cross section vanishes at very high energy.     

Diffraction of light by superposed parallel supersonic waves,one being then-th harmonic of the other. Solution of the system of difference-differential equations for the amplitudes by a series expansion method

In the problem of the diffraction of light by two parallel supersonic waves, consisting of a fundamental tone and itsn-th harmonic, the solution of the system of difference-differential equations for the amplitudes has been reduced to the integration of a partial differential equation. The expressions for the amplitudes of the diffracted light waves are obtained as the coefficients of the Laurent expansion of the solution of this partial differential equation. The latter has been integrated for two approximations:

1. Forρ = 0, the results of Murty’s elementary theory are reestablished.
2. Forρ ≤ 1, a power series inρ, the terms of which are calculated as far as the third one, leads to a new expression for the intensities of the diffracted light waves, verifying the general symmetry properties obtained by Mertens.

     

Electronic structure of graphite

Semi-empirical calculations of the π-band structure of planar and three-dimensional graphite are described. Special attention is given to the significance of band parameters. The theoretical results are in good agreement with experiment.     

A theoretical study of special acoustic effects caused by the staircase of the El Castillo pyramid at the Maya ruins of Chichen-Itza in Mexico

It is known that a handclap in front of the stairs of the great pyramid of Chichen Itza produces a chirp echo which sounds more or less like the sound of a Quetzal bird. The present work describes precise diffraction simulations and attempts to answer the critical question what physical effects cause the formation of the chirp echo. Comparison is made with experimental results obtained from David Lubman. Numerical simulations show that the echo shows a strong dependence on the kind of incident sound. Simulations are performed for a (delta function like) pulse and also for a real handclap. The effect of reflections on the ground in front of the pyramid is also discussed. The present work also explains why an observer seated on the lowest step of the pyramid hears the sound of raindrops falling in a water filled bucket instead of footstep sounds when people, situated higher up the pyramid, climb the stairs.     

Extension of the mode method for viscoelastic media and focused ultrasonic beams

In the present study viscoelasticity is introduced in the mode model and the orthogonality condition is adapted for viscous media. The expansion of convergent acoustic Gaussian beams in terms of radiation modes for viscoelastic media is studied as well. The effects on the reflected and transmitted profiles of acoustic beams incident from an ideal liquid onto a viscoelastic plate are shown and physically explained. It is shown that focusing the incident beam can suppress divergence effects and gives the possibility to measure shear wave attenuation coefficients.     

Collinear acousto-optic diffraction using two nearby sound frequencies

Collinear acousto-optic spectrometers with sound consisting of one frequency have a spectral transfer function with many good characteristics, such as a narrow bandwidth, ... the side lobes, however, are rather high. To reduce these side lobes, one can try to apodize the sound in the acousto-optic cell by using a sound wave consisting out of two frequencies. At certain times, this produces a more smoothened sound field in the cell than in the one-frequency case. The resulting transfer function will contain lower side lobes. Also, the influence of all the sound field parameters--the amplitude, frequency difference, and time--on the transmission function is studied. Out of these results, better-performing collinear spectrometers can be designed.     

Action du methyltri(n-butyl)fluorophosphorane sur les halogenures et les sulfonates d'alkyle

Monofluorophosphoranes R₃MePF are used in exchange reactions to prepare monofluorinated organic compounds. Tri(n-butyl)methylfluorophosphorane (n-Bu₃MePF), easily available, is the most reactive. In solvents of low polarity or even in non-polar solvents, it reacts at ?70° with alkyl sulphonates and halides activated by ester, ketone, or ether functions. Thus, fluorinated epoxides can be obtained directly by exchange from their chlorinated or brominated homologues.