Game saturation of intersecting families

We consider the following combinatorial game: two players, Fast and Slow, claim $k$-element subsets of $[n]=\{1,2,...,n\}$ alternately, one at each turn, such that both players are allowed to pick sets that intersect all previously claimed subsets. The game ends when there does not exist any unclaimed $k$-subset that meets all already claimed sets. The score of the game is the number of sets claimed by the two players, the aim of Fast is to keep the score as low as possible, while the aim of Slow is to postpone the game's end as long as possible. The game saturation number is the score of the game when both players play according to an optimal strategy. To be precise we have to distinguish two cases depending on which player takes the first move. Let $gsat_F(\mathbb{I}_{n,k})$ and $gsat_S(\mathbb{I}_{n,k})$ denote the score of the saturation game when both players play according to an optimal strategy and the game starts with Fast's or Slow's move, respectively. We prove that $\Omega_k(n^{k/3-5}) \le gsat_F(\mathbb{I}_{n,k}),gsat_S(\mathbb{I}_{n,k}) \le O_k(n^{k-\sqrt{k}/2})$ holds

Advanced experimental applications for x-ray transmission gratings Spectroscopy using a novel grating fabrication method

A novel fabrication method for soft x-ray transmission grating and other optical elements is presented. The method uses Focused-Ion-Beam (FIB) technology to fabricate high-quality free standing grating bars on Transmission Electron Microscopy grids (TEM-grid). High quality transmission gratings are obtained with superb accuracy and versatility. Using these gratings and back-illuminated CCD camera, absolutely calibrated x-ray spectra can be acquired for soft x-ray source diagnostics in the 100-3000 eV spectral range. Double grating combinations of identical or different parameters are easily fabricated, allowing advanced one-shot application of transmission grating spectroscopy. These applications include spectroscopy with different spectral resolutions, bandwidths, dynamic ranges, and may serve for identification of high-order contribution, and spectral calibrations of various x-ray optical elements

Development of a triple GEM UV-photon detector operated in pure CF4 for the PHENIX experiment

Results obtained with a triple GEM detector operated in pure CF4 with and without a reflective CsI photocathode are presented. The detector operates in a stable mode at gains up to 10^4. A deviation from exponential growth starts to develop when the total charge exceeds ~ 4 10^6 e leading to gain saturation when the total charge is ~ 2 10^7 e and making the structure relatively robust against discharges. No aging effects are observed in the GEM foils after a total accumulated charge of ~ 10 mC/cm^2 at the anode. The ion back-flow current to the reflective photocathode is comparable to the electron current to the anode. However, no significant degradation of the CsI photocathode is observed for a total ion back-flow charge of ~ 7 mC/cm^2.Comment: 14 pages, 11 figures, Submitted to NIM

Construction and Expected Performance of the Hadron Blind Detector for the PHENIX Experiment at RHIC

A new Hadron Blind Detector (HBD) for electron identification in high density hadron environment has been installed in the PHENIX detector at RHIC in the fall of 2006. The HBD will identify low momentum electron-positron pairs to reduce the combinatorial background in the $e^{+}e^{-}$ mass spectrum, mainly in the low-mass region below 1 GeV/c$^{2}$. The HBD is a windowless proximity-focusing Cherenkov detector with a radiator length of 50 cm, a CsI photocathode and three layers of Gas Electron Multipliers (GEM). The HBD uses pure CF$_{4}$ as a radiator and a detector gas. Construction details and the expected performance of the detector are described.Comment: QM2006 proceedings, 4 pages 3 figure

Design, Construction, Operation and Performance of a Hadron Blind Detector for the PHENIX Experiment

A Hadron Blind Detector (HBD) has been developed, constructed and successfully operated within the PHENIX detector at RHIC. The HBD is a Cherenkov detector operated with pure CF4. It has a 50 cm long radiator directly coupled in a window- less configuration to a readout element consisting of a triple GEM stack, with a CsI photocathode evaporated on the top surface of the top GEM and pad readout at the bottom of the stack. This paper gives a comprehensive account of the construction, operation and in-beam performance of the detector.Comment: 51 pages, 39 Figures, submitted to Nuclear Instruments and Method

A Hadron Blind Detector for the PHENIX Experiment

A novel Hadron Blind Detector (HBD) has been developed for an upgrade of the PHENIX experiment at RHIC. The HBD will allow a precise measurement of electron-positron pairs from the decay of the light vector mesons and the low-mass pair continuum in heavy-ion collisions. The detector consists of a 50 cm long radiator filled with pure CF4 and directly coupled in a windowless configuration to a triple Gas Electron Multiplier (GEM) detector with a CsI photocathode evaporated on the top face of the first GEM foil.Comment: 4 pages, 3 figures, Quark Matter 2005 conference proceeding

Measurement of L-shell emission from mid-Z targets under non-LTE conditions using Transmission Grating Spectrometer and DANTE power diagnostics

Producción CientíficaIn this work, we present the measurement of L-band emission from buried Sc/V targets in experiments performed at the OMEGA laser facility. The goal of these experiments was to study non-local thermodynamic equilibrium plasmas and benchmark atomic physics codes. The L-band emission was measured simultaneously by the time resolved DANTE power diagnostic and the recently fielded time integrated Soreq-Transmission Grating Spectrometer (TGS) diagnostic. The TGS measurement was used to support the spectral reconstruction process needed for the unfolding of the DANTE data. The Soreq-TGS diagnostic allows for broadband spectral measurement in the 120 eV–2000 eV spectral band, covering L- and M-shell emission of mid- and high-Z elements, with spectral resolution λ/Δλ = 8–30 and accuracy better than 25%. The Soreq-TGS diagnostic is compatible with ten-inch-manipulator platforms and can be used for a wide variety of high energy density physics, laboratory astrophysics, and inertial confinement fusion experiments

Low-mass e+e- pair production in 158 A GeV Pb-Au collisions at the CERN SPS, its dependence on multiplicity and transverse momentum

We report a measurement of low-mass electron pairs observed in 158 GeV/nucleon Pb-Au collisions. The pair yield integrated over the range of invariant masses 0.2 < m < 2.0 GeV is enhanced by a factor of 3.5 +/- 0.4 (stat) +/- 0.9 (syst) over the expectation from neutral meson decays. As observed previously in S-Au collisions, the enhancement is most pronounced in the invariant-mass region 300-700 MeV. For Pb-Au we find evidence for a strong increase of the enhancement with centrality. In addition, we show that the enhancement covers a wide range in transverse momentum, but is largest at the lowest observed pt.Comment: 17 pages, 4 figures, submitted to Phys.Lett.