Dynamic structure factors of a dense mixture

We compute the dynamic structure factors of a dense binary liquid mixture. These describe dynamics on molecular length scales, where structural relaxation is important. We find that the presence of a few large particles in a dense fluid of small particles slows down the dynamics considerably. We also observe a deep narrowing of the spectrum for a disordered mixture composed of a nearly equal packing of the two species. In contrast, a few small particles diffuse easily in the background of a dense fluid of large particles. We expect our results to describe neutron scattering from a dense mixture

Theorem on the Distribution of Short-Time Particle Displacements with Physical Applications

The distribution of the initial short-time displacements of particles is considered for a class of classical systems under rather general conditions on the dynamics and with Gaussian initial velocity distributions, while the positions could have an arbitrary distribution. This class of systems contains canonical equilibrium of a Hamiltonian system as a special case. We prove that for this class of systems the nth order cumulants of the initial short-time displacements behave as the 2n-th power of time for all n>2, rather than exhibiting an nth power scaling. This has direct applications to the initial short-time behavior of the Van Hove self-correlation function, to its non-equilibrium generalizations the Green's functions for mass transport, and to the non-Gaussian parameters used in supercooled liquids and glasses.Comment: A less ambiguous mathematical notation for cumulants was adopted and several passages were reformulated and clarified. 40 pages, 1 figure. Accepted by J. Stat. Phy

On a complex differential Riccati equation

We consider a nonlinear partial differential equation for complex-valued functions which is related to the two-dimensional stationary Schrodinger equation and enjoys many properties similar to those of the ordinary differential Riccati equation as, e.g., the famous Euler theorems, the Picard theorem and others. Besides these generalizations of the classical "one-dimensional" results we discuss new features of the considered equation like, e.g., an analogue of the Cauchy integral theorem

Fluctuating magnetic moments in liquid metals

We re-analyze literature data on neutron scattering by liquid metals to show that non-magnetic liquid metals possess a magnetic moment that fluctuates on a picosecond time scale. This time scale follows the motion of the cage-diffusion process in which an ion rattles around in the cage formed by its neighbors. We find that these fluctuating magnetic moments are present in liquid Hg, Al, Ga and Pb, and possibly also in the alkali metals.Comment: 17 pages, 5 figures, submitted to PR

Unified description of long-time tails and long-range correlation functions for sheared granular liquids

Unified description on the long-time tail of velocity autocorrelation function and the long-range correlation for the equal-time spatial correlation functions is developed based on the generalized fluctuating hydrodynamics. The cross-over of the long-time tail from $t^{-3/2}$ to $t^{-5/2}$ is predicted independent of the density, and the equal-time spatial density correlation function and the equal-time spatial velocity correlation function respectively satisfy $r^{-11/3}$ and $r^{-5/3}$ for large $r$ limit.Comment: 10 pages. to be published in Euro. Phys. J.

Short-wavelength collective modes in a binary hard-sphere mixture

We use hard-sphere generalized hydrodynamic equations to discuss the extended hydrodynamic modes of a binary mixture. The theory presented here is analytic and it provides us with a simple description of the collective excitations of a dense binary mixture at molecular length scales. The behavior we predict is in qualitative agreement with molecular-dynamics results for soft-sphere mixtures. This study provides some insight into the role of compositional disorder in forming glassy configurations.Comment: Published; withdrawn since already published. Ordering in the archive gives misleading impression of new publicatio

Decay-assisted collinear resonance ionization spectroscopy: Application to neutron-deficient francium

This paper reports on the hyperfine-structure and radioactive-decay studies of the neutron-deficient francium isotopes $^{202-206}$Fr performed with the Collinear Resonance Ionization Spectroscopy (CRIS) experiment at the ISOLDE facility, CERN. The high resolution innate to collinear laser spectroscopy is combined with the high efficiency of ion detection to provide a highly-sensitive technique to probe the hyperfine structure of exotic isotopes. The technique of decay-assisted laser spectroscopy is presented, whereby the isomeric ion beam is deflected to a decay spectroscopy station for alpha-decay tagging of the hyperfine components. Here, we present the first hyperfine-structure measurements of the neutron-deficient francium isotopes $^{202-206}$Fr, in addition to the identification of the low-lying states of $^{202,204}$Fr performed at the CRIS experiment.Comment: Accepted for publication with Physical Review

Laser spectroscopy of francium isotopes at the borders of the region of reflection asymmetry

The magnetic dipole moments and changes in mean-square charge radii of the neutron-rich $^{218m,219,229,231}\text{Fr}$ isotopes were measured with the newly-installed Collinear Resonance Ionization Spectroscopy (CRIS) beam line at ISOLDE, CERN, probing the $7s~^{2}S_{1/2}$ to $8p~^{2}P_{3/2}$ atomic transition. The $\delta\langle r^{2}\rangle^{A,221}$ values for $^{218m,219}\text{Fr}$ and $^{229,231}\text{Fr}$ follow the observed increasing slope of the charge radii beyond $N~=~126$. The charge radii odd-even staggering in this neutron-rich region is discussed, showing that $^{220}\text{Fr}$ has a weakly inverted odd-even staggering while $^{228}\text{Fr}$ has normal staggering. This suggests that both isotopes reside at the borders of a region of inverted staggering, which has been associated with reflection-asymmetric shapes. The $g(^{219}\text{Fr}) = +0.69(1)$ value supports a $\pi 1h_{9/2}$ shell model configuration for the ground state. The $g(^{229,231}\text{Fr})$ values support the tentative $I^{\pi}(^{229,231}\text{Fr}) = (1/2^{+})$ spin, and point to a $\pi s_{1/2}^{-1}$ intruder ground state configuration.Comment: Accepted for publication with Physical Review

The HERMES Dual-Radiator Ring Imaging Cerenkov Detector

The construction and use of a dual radiator Ring Imaging Cerenkov(RICH) detector is described. This instrument was developed for the HERMES experiment at DESY which emphasizes measurements of semi-inclusive deep-inelastic scattering. It provides particle identification for pions, kaons, and protons in the momentum range from 2 to 15 GeV, which is essential to these studies. The instrument uses two radiators, C4F10, a heavy fluorocarbon gas, and a wall of silica aerogel tiles. The use of aerogel in a RICH detector has only recently become possible with the development of clear, large homogeneous and hydrophobic aerogel. A lightweight mirror was constructed using a newly perfected technique to make resin-coated carbon-fiber surfaces of optical quality. The photon detector consists of 1934 photomultiplier tubes for each detector half, held in a soft steel matrix to provide shielding against the residual field of the main spectrometer magnet.Comment: 25 pages, 23 figure