Superposition Formulas for Darboux Integrable Exterior Differential Systems

In this paper we present a far-reaching generalization of E. Vessiot's analysis of the Darboux integrable partial differential equations in one dependent and two independent variables. Our approach provides new insights into this classical method, uncovers the fundamental geometric invariants of Darboux integrable systems, and provides for systematic, algorithmic integration of such systems. This work is formulated within the general framework of Pfaffian exterior differential systems and, as such, has applications well beyond those currently found in the literature. In particular, our integration method is applicable to systems of hyperbolic PDE such as the Toda lattice equations, 2 dimensional wave maps and systems of overdetermined PDE.Comment: 80 page report. Updated version with some new sections, and major improvements to other

Transition Radiation Spectra of Electrons from 1 to 10 GeV/c in Regular and Irregular Radiators

We present measurements of the spectral distribution of transition radiation generated by electrons of momentum 1 to 10 GeV/c in different radiator types. We investigate periodic foil radiators and irregular foam and fiber materials. The transition radiation photons are detected by prototypes of the drift chambers to be used in the Transition Radiation Detector (TRD) of the ALICE experiment at CERN, which are filled with a Xe, CO2 (15 %) mixture. The measurements are compared to simulations in order to enhance the quantitative understanding of transition radiation production, in particular the momentum dependence of the transition radiation yield.Comment: 18 pages, 15 figures, submitted to Nucl. Instr. Meth. Phys. Res.

Production of deuterium, tritium, and 3^3He in central Pb+Pb collisions at 20A, 30A, 40A, 80A, and 158A GeV at the CERN SPS

Production of $d$, $t$, and $^3$He nuclei in central Pb+Pb interactions was studied at five collision energies ($\sqrt{s_{NN}}=$ 6.3, 7.6, 8.8, 12.3, and 17.3 GeV) with the NA49 detector at the CERN SPS. Transverse momentum spectra, rapidity distributions, and particle ratios were measured. Yields are compared to predictions of statistical models. Phase-space distributions of light nuclei are discussed and compared to those of protons in the context of a coalescence approach. The coalescence parameters $B_2$ and $B_3$, as well as coalescence radii for $d$ and $^3$He were determined as a function of transverse mass at all energies.Comment: 22 pages, 29 figures, 8 tables, for submission to Phys. Rev.

NA49 results on hadron production: indications of the onset of deconfinement ?

The NA49 experiment at the CERN SPS measured the energy and system size dependence of particle production in A+A collisions. A change of the energy dependence of several hadron production properties at low SPS energies is observed which suggests a scenario requiring the onset of deconfinement.Comment: XXXV International Symposium on Multiparticle Dynamics 200

Energy dependence of particle ratio fluctuations in central Pb+Pb collisions from sNN=\sqrt{s_{_{NN}}} =~6.3 to 17.3 GeV

We present measurements of the energy dependence of event-by-event fluctuations in the K/pi and (p + \bar{p})/pi multiplicity ratios in heavy ion collisions at the CERN SPS. The particle ratio fluctuations were obtained for central Pb+Pb collisions at five collision energies, \sqrt{s_{_{NN}}}, between 6.3 and 17.3 GeV. After accounting for the effects of finite-number statistics and detector resolution, we extract the strength of non-statistical fluctuations at each energy. For the K/pi ratio, larger fluctuations than expected for independent particle production are found at all collision energies. The fluctuations in the (p + \bar{p})/pi ratio are smaller than expectations from independent particle production, indicating correlated pion and proton production from resonance decays. For both ratios, the deviation from purely statistical fluctuations shows an increase towards lower collision energies. The results are compared to transport model calculations, which fail to describe the energy dependence of the K/pi ratio fluctuations.Comment: 11 pages, 10 figures, update to published versio