Measurement of γp→K + Λ and γp→K + Σ 0 at photon energies up to 1.47 GeV

The reactions pK ⁺ and pK ^{+ 0} have been measured with the multiparticle detector system SAPHIR at ELSA in Bonn. Besides the differential cross sections the polarization and, for the first time, the ⁰ polarization have been determined in a photon induced reaction. All data are presented as functions of the photon energy (from threshold up to 1.47 GeV) and of the kaon production angle (0°–180°). The polarization of both and ⁰ is substantial at all energies and varies strongly with the production angle.This work is supported by the Bundesminister für Forschung und Technologie (BMFT), FK 06 BN 621 I     

MC-simulation of the 3D,q=3 Potts model

We consider theq=3 Potts model in three dimensions by Monte Carlo simulations. The microcanonical density of states is calculated as a function of the internal energy of the system. We extrapolate the data for the simulated finite systems to the thermo-dynamic limit and find a discontinuous phase transition. This method is checked in the two-dimensional case, where exact results are known.     

Production of relativistic antihydrogen atoms by pair production with positron capture and measurement of the Lamb shift

A beam of relativistic antihydrogen atoms — the bound state ( e⁺) — can be created by circulating the beam of an antiproton storage ring through an internal gas target. An antiproton which passes through the Coulomb field of a nucleus will create e⁺e⁻ pairs, and antihydrogen will form when a positron is created in a bound instead of continuum state about the antiproton. The cross section for this process is roughly 3Z ² pb for antiproton momenta about 6 GeV/c. A sample of 600 antihydrogen atoms in a low-emittance, neutral beam will be made in 1995 as an accidental byproduct of Fermilab experiment E760. We describe a simple experiment, Fermilab Proposal P862, which can detect this beam, and outline how a sample of a few-10⁴ atoms can be used to measure the antihydrogen Lamb shift to 1 %. Work supported in part by Department of Energy contract DE-AC03-76SF00515 (SLAC). Work supported by Fondo Nacional de Investigación Científica y Tecnológica, Chile.     

Northcott's theorem on heights I. A general estimate

Given a pointP=(a _o:...:a _n) of projective space ⁿ = ⁿ (A) whereA is the field of algebraic numbers, letd(P) be its degree andH(P) its absolute multiplicative height. Northcott's Theorem says that givend, n andX, there are only finitely many pointsP ⁿ withd(P)d andH(P)X. We will show that there are at mostc(d, n)X ^d(d+n) such points.Supported in part by NSF grant DMS-9108581.