Dusty Plasma Correlation Function Experiment

Dust particles immersed within a plasma environment, such as those in protostellar clouds, planetary rings or cometary environments, will acquire an electric charge. If the ratio of the inter-particle potential energy to the average kinetic energy is high enough the particles will form either a "liquid" structure with short-range ordering or a crystalline structure with long range ordering. Many experiments have been conducted over the past several years on such colloidal plasmas to discover the nature of the crystals formed, but more work is needed to fully understand these complex colloidal systems. Most previous experiments have employed monodisperse spheres to form Coulomb crystals. However, in nature (as well as in most plasma processing environments) the distribution of particle sizes is more randomized and disperse. This paper reports experiments which were carried out in a GEC rf reference cell modified for use as a dusty plasma system, using varying sizes of particles to determine the manner in which the correlation function depends upon the overall dust grain size distribution. (The correlation function determines the overall crystalline structure of the lattice.) Two dimensional plasma crystals were formed of assorted glass spheres with specific size distributions in an argon plasma. Using various optical techniques, the pair correlation function was determined and compared to those calculated numerically.Comment: 6 pages, Presented at COSPAR '0

Determining Ω\Omega from cluster correlation function

It is shown how data on the cluster correlation function can be used in order to reconstruct the density of the pregalactic density field on the cluster mass scale. The method is applied to the data on the cluster correlation amplitude -- richness dependence. The spectrum of the recovered density field has the same shape as the density field derived from data on the galaxy correlation function which is measured as function of linear scales. Matching the two amplitudes relates the mass to the comoving scale it contains and thereby leads to a direct determination of $\Omega$. The resultant density parameter turns out to be $\Omega$=0.25.Comment: to appear in Physics Reports, "Dark Matter 98", vol.30

Sum rule of the correlation function

We discuss a sum rule satisfied by the correlation function of two particles with small relative momenta. The sum rule, which results from the completeness condition of the quantum states of the two particles, is first derived and then we check how it works in practice. The sum rule is shown to be trivially satisfied by free particle pair, and then there are considered three different systems of interacting particles. We discuss a pair of neutron and proton in the s-wave approximation and the case of the so-called hard spheres with the phase shifts taken into account up to l=4. Finally, the Coulomb system of two charged particles is analyzed.Comment: 18 pages, 18 figures, revised, to appear in Phys. Rev.

Correlation function of dyonic strings

We investigate the two- and three-point correlation functions of the dyonic magnon and spike, which correspond to the solitonic string moving in the Poincare AdS and three-dimensional sphere. We show that the coupling between two dyonic magnons or spikes together with a marginal scalar operator in the string theory is exactly the same as one obtained by the RG analysis in the gauge theory.Comment: 15 pages, no figur

Evolution of the Cluster Correlation Function

We study the evolution of the cluster correlation function and its richness-dependence from z = 0 to z = 3 using large-scale cosmological simulations. A standard flat LCDM model with \Omega_m = 0.3 and, for comparison, a tilted \Omega_m = 1 model, TSCDM, are used. The evolutionary predictions are presented in a format suitable for direct comparisons with observations. We find that the cluster correlation strength increases with redshift: high redshift clusters are clustered more strongly (in comoving scale) than low redshift clusters of the same mass. The increased correlations with redshift, in spite of the decreasing mass correlation strength, is caused by the strong increase in cluster bias with redshift: clusters represent higher density peaks of the mass distribution as the redshift increases. The richness-dependent cluster correlation function, presented as the correlation-scale versus cluster mean separation relation, R_0 - d, is found to be, remarkably, independent of redshift to z <~ 2 for LCDM and z <~ 1 for TCDM (for a fixed correlation function slope and cluster mass within a fixed comoving radius). The non-evolving R_0 - d relation implies that both the comoving clustering scale and the cluster mean separation increase with redshift for the same mass clusters so that the R_0 - d relation remains essentially unchanged. The evolution of the R_0 - d relation from z ~ 0 to z ~ 3 provides an important new tool in cosmology; it can be used to break degeneracies that exist at z ~ 0 and provide precise determination of cosmological parameters.Comment: AASTeX, 15 pages, including 5 figures, accepted version for publication in ApJ, vol.603, March 200

Two-proton correlation function: a gentle introduction

The recent COSY-11 collaboration measurement of the two-proton correlation function in the pp -> ppeta reaction, reported at this meeting [1], arouse some interest in a simple theoretical description of the correlation function. In these notes we present a pedagogical introduction to the practical methods that can be used for calculating the correlation function.Comment: Prepared for the proceedings of the Symposium on Meson Physics at COSY-11 and WASA-at-COSY, Krakow, Poland, 17-22 June 200