Extended Derivative Dispersion Relations

It is shown that, for a wide class of functions with physical interest as forward scattering amplitudes, integral dispersion relations can be replaced by derivative forms without any high-energy approximation. The applicability of these extended derivative relations, in the investigation of forward proton-proton and antiproton-proton elastic scattering, is exemplified by means of a Pomeron-Reggeon model with totally nondegenerate trajectories.Comment: 7 pages, 1 figure, contribution to "Sense of Beauty in Physics", Miniconference in Honor of Adriano Di Giacomo on his 70th Birthday, Pisa, Italy, Jan. 26-27, 200

Derivative dispersion relations above the physical threshold

We discuss some formal and practical aspects related to the replacement of Integral Dispersion Relations (IDR) by derivative forms, without high-energy approximations. We first demonstrate that, for a class of functions with physical interest as forward scattering amplitudes, this replacement can be analytically performed, leading to novel Extended Derivative Dispersion Relations (EDDR), which, in principle, are valid for any energy above the physical threshold. We then verify the equivalence between the IDR and EDDR by means of a popular parametrization for total cross sections from proton-proton and antiproton-proton scattering and compare the results with those obtained through other representations for the derivative relations. Critical aspects on the limitations of the whole analysis, from both formal and practical points of view, are also discussed in some detail.Comment: Final version, published in Brazilian Journal of Physics, V. 37, 358 (2007

Optical turbulence vertical distribution with standard and high resolution at Mt. Graham

A characterization of the optical turbulence vertical distribution (Cn2 profiles) and all the main integrated astroclimatic parameters derived from the Cn2 and the wind speed profiles above the site of the Large Binocular Telescope (Mt. Graham, Arizona, US) is presented. The statistic includes measurements related to 43 nights done with a Generalized Scidar (GS) used in standard configuration with a vertical resolution Delta(H)~1 km on the whole 20 km and with the new technique (HVR-GS) in the first kilometer. The latter achieves a resolution Delta(H)~20-30 m in this region of the atmosphere. Measurements done in different periods of the year permit us to provide a seasonal variation analysis of the Cn2. A discretized distribution of Cn2 useful for the Ground Layer Adaptive Optics (GLAO) simulations is provided and a specific analysis for the LBT Laser Guide Star system ARGOS (running in GLAO configuration) case is done including the calculation of the 'gray zones' for J, H and K bands. Mt. Graham confirms to be an excellent site with median values of the seeing without dome contribution epsilon = 0.72", the isoplanatic angle theta0 = 2.5" and the wavefront coherence time tau0= 4.8 msec. We find that the optical turbulence vertical distribution decreases in a much sharper way than what has been believed so far in proximity of the ground above astronomical sites. We find that 50% of the whole turbulence develops in the first 80+/-15 m from the ground. We finally prove that the error in the normalization of the scintillation that has been recently put in evidence in the principle of the GS technique, affects these measurements with an absolutely negligible quantity (0.04").Comment: 11 figures. MNRAS, accepte