Higher Order Processes in Electromagnetic Production of Electron Positron Pairs in Relativistic Heavy Ion Collisions

We study higher-order effects in the electromagnetic production of electron-positron pairs in relativistic heavy ion collisions. Treating the field of the heavy ions as an external field and neglecting the interaction among electrons and positrons, we show that the $N$-pair creation amplitude is the antisymmetrised product of $N$ one-pair creation amplitudes and the vacuum amplitude. Neglecting contributions coming from exchange terms, we show that the total probability for $N$ pairs is approximately a Poisson distribution. We investigate further the structure of the reduced one-pair amplitude, concentrating especially on multiple-particle corrections. We calculate the first of these corrections in second order Magnus theory based on our previous result in second-order Born approximation for impact parameter $b$ zero. Explicit calculations show that the total probability is increased up to 10 \% by this correction for realistic collider parameters. The calculations can also be used to confirm the use of the Poisson distribution for the total probability.Comment: 29 pages RevTeX and 12 uuencoded figures (compressed postscript

On the Testing of Seismicity Models

Recently a likelihood-based methodology has been developed by the Collaboratory for the Study of Earthquake Predictability (CSEP) with a view to testing and ranking seismicity models. We analyze this approach from the standpoint of possible applications to hazard analysis. We arrive at the conclusion that model testing can be made more efficient by focusing on some integral characteristics of the seismicity distribution. This is achieved either in the likelihood framework but with economical and physically reasonable coarsening of the phase space or by choosing a suitable measure of closeness between empirical and model seismicity rate in this space.Comment: To appear at Acta Geophysic

Coulomb Effects on Electromagnetic Pair Production in Ultrarelativistic Heavy-Ion Collisions

We discuss the implications of the eikonal amplitude on the pair production probability in ultrarelativistic heavy-ion transits. In this context the Weizs\"acker-Williams method is shown to be exact in the ultrarelativistic limit, irrespective of the produced particles' mass. A new equivalent single-photon distribution is derived which correctly accounts for the Coulomb distortions. As an immediate application, consequences for unitarity violation in photo-dissociation processes in peripheral heavy-ion encounters are discussed.Comment: 13 pages, 4 .eps figure

Fate of biosolids trace metals in a dryland wheat agroecosystem

Biosolids land application for beneficial reuse applies varying amounts of trace metals to soils. Measuring plant-available or total soil metals is typically performed to ensure environmental protection, but these techniques do not quantify which soil phases play important roles in terms of metal release or attenuation. This study assessed the distribution of Cd, Cr, Cu, Mo, Ni, Pb, and Zn associated with soluble/exchangeable, specifically adsorbed/carbonate-bound, amorphous Mn hydroxyoxide-bound, amorphous Fe hydroxyoxide–bound, organically complexed, and residual inorganic phases. Biosolids were applied every 2 yr from 1982 to 2002 (except in 1998) at rates of 0, 6.7, 13.4, 26.8, and 40.3 dry Mg biosolids ha?1 to 3.6- by 17.1-m plots. In 2003, 0- to 20-cm and 20- to 60-cm soil depths were collected and subjected to 4 mol L?1 HNO3 digestion and sequential extraction. Trace metals were concentrated in the 0- to 20-cm depth, with no significant observable downward movement using 4 mol L?1 HNO3 or sequential extraction. The sequential extraction showed nearly all measurable Cd present in relatively mobile forms and Cr, Cu, Mo, Ni, Pb, and Zn present in more resistant phases. Biosolids application did not affect Cd or Cr fractionation but did increase relatively immobile Cu, Mo, and Zn phases and relatively mobile Cu, Ni, and Pb pools. The mobile phases have not contributed to significant downward metal movement. Long-term, repeated biosolids applications at rates considered several times greater than agronomic levels should not significantly contribute to downward metal transport and ground water contamination for soils under similar climatic conditions, agronomic practices, and histories