A Walsh-Fourier approach to the circulant Hadamard conjecture

We describe an approach to the circulant Hadamard conjecture based on Walsh-Fourier analysis. We show that the existence of a circulant Hadamard matrix of order $n$ is equivalent to the existence of a non-trivial solution of a certain homogenous linear system of equations. Based on this system, a possible way of proving the conjecture is proposed.Comment: 8 page

Defect-induced condensation and central peak at elastic phase transitions

Static and dynamical properties of elastic phase transitions under the influence of short--range defects, which locally increase the transition temperature, are investigated. Our approach is based on a Ginzburg--Landau theory for three--dimensional crystals with one--, two-- or three--dimensional soft sectors, respectively. Systems with a finite concentration $n_{\rm D}$ of quenched, randomly placed defects display a phase transition at a temperature $T_c(n_{\rm D})$, which can be considerably above the transition temperature $T_c^0$ of the pure system. The phonon correlation function is calculated in single--site approximation. For $T>T_c(n_{\rm D})$ a dynamical central peak appears; upon approaching $T_c(n_{\rm D})$, its height diverges and its width vanishes. Using an appropriate self--consistent method, we calculate the spatially inhomogeneous order parameter, the free energy and the specific heat, as well as the dynamical correlation function in the ordered phase. The dynamical central peak disappears again as the temperatur is lowered below $T_c(n_{\rm D})$. The inhomogeneous order parameter causes a static central peak in the scattering cross section, with a finite $k$ width depending on the orientation of the external wave vector ${\bf k}$ relative to the soft sector. The jump in the specific heat at the transition temperatur of the pure system is smeared out by the influence of the defects, leading to a distinct maximum instead. In addition, there emerges a tiny discontinuity of the specific heat at $T_c(n_{\rm D})$. We also discuss the range of validity of the mean--field approach, and provide a more realistic estimate for the transition temperature.Comment: 11 pages, 11 ps-figures, to appear in PR

Transient effects in fission evidenced from new experimental signatures

A new experimental approach is introduced to investigate the relaxation of the nuclear deformation degrees of freedom. Highly excited fissioning systems with compact shapes and low angular momenta are produced in peripheral relativistic heavy-ion collisions. Both fission fragments are identified in atomic number. Fission cross sections and fission-fragment element distributions are determined as a function of the fissioning element. From the comparison of these new observables with a nuclear-reaction code a value for the transient time is deduced.Comment: 6 pages, 2 figures, background information at http://www-w2k.gsi.de/kschmidt

Ultracold-neutron infrastructure for the gravitational spectrometer GRANIT

The gravitational spectrometer GRANIT will be set up at the Institut Laue Langevin. It will profit from the high ultracold neutron density produced by a dedicated source. A monochromator made of crystals from graphite intercalated with potassium will provide a neutron beam with 0.89 nm incident on the source. The source employs superthermal conversion of cold neutrons in superfluid helium, in a vessel made from BeO ceramics with Be windows. A special extraction technique has been tested which feeds the spectrometer only with neutrons with a vertical velocity component v < 20 cm/s, thus keeping the density in the source high. This new source is expected to provide a density of up to 800 1/cm3 for the spectrometer.Comment: accepted for publication in Proceedings International Workshop on Particle Physics with Slow Neutron

Azimuthal Correlations in the Target Fragmentation Region of High Energy Nuclear Collisions

Results on the target mass dependence of proton and pion pseudorapidity distributions and of their azimuthal correlations in the target rapidity range $-1.73 \le \eta \le 1.32$ are presented. The data have been taken with the Plastic-Ball detector set-up for 4.9 GeV p + Au collisions at the Berkeley BEVALAC and for 200 $A\cdot$GeV/$c$ p-, O-, and S-induced reactions on different nuclei at the CERN-SPS. The yield of protons at backward rapidities is found to be proportional to the target mass. Although protons show a typical ``back-to-back'' correlations, a ``side-by-side'' correlation is observed for positive pions, which increases both with target mass and with impact parameter of a collision. The data can consistently be described by assuming strong rescattering phenomena including pion absorption effects in the entire excited target nucleus.Comment: 7 pages, figures included, complete postscript available at ftp://qgp.uni-muenster.de/pub/paper/azi-correlations.ps submitted to Phys. Lett.