Contribution of multiple scattering to the dielectric constant of a randomly inhomogeneous medium

Within the statistical theory of multiple scattering of light in random media, the dielectric constant of a suspension is represented as a diagram series in scattering orders and concentration of particles. The contributions of double and triple scattering events are determined. The extinction length and the transport mean free path in highly concentrated suspensions calculated with the use of the optical theorem are in good agreement with the available data. It is shown that the two-particle Born approximation, combined with the Mie form factor and the Percus-Yevick structure factor, is not adequate for systems with a high concentration of scatterers. A contribution to the optical parameters is found that is missing in the above approximation.     

Permittivity of suspensions

The permittivity of a suspension treated as a system of hard spheres is calculated in the Born approximation. The structure of the suspension is described by the Percus-Yevick correlation function. The permittivity of the system under consideration is expressed through a nonlocal susceptibility whose spatial extension is determined by the form factor of suspension particles and the characteristic value of the structure factor. It is shown that the permittivity of the suspension mixture is characterized by a spatial dispersion that manifests itself already in the first order of the perturbation theory. It is demonstrated that the concentration dependences of the extinction length and the transport length calculated from the obtained data on the permittivity tensor exhibit substantially nonlinear behavior. Within the range of applicability of the theory, the results obtained are in agreement with available experimental data.     

The state space of short-range Ising spin glasses: the density of states

The correlations between the segments of a semidilute polymer solution are found to induce correlations in the positions of small particles added to the solution. Small means a diameter much less than the polymer's correlation length. In the presence of polymer the particles behave as if they attracted each other. It is shown how the polymer's correlation length may be determined from a scattering experiment performed on the spheres. Received: 7 July 1997 / Received in final form: 12 November 1997 / Accepted: 19 November 1997     

The multiple scattering model analysis of high energy multiparticle production on emulsion nuclei

Data on multiparticle production on emulsion nuclei in the range 50–400 GeV/c have been analyzed in the framework of multiple scattering model developed by Capella and Krzywicki. It is shown that under some reasonable assumptions multiple scattering type models qualitatively reproduce multiplicity distributions of relativistic charged particles, one-particle spectra and two-particle inclusive correlations. When considering one-particle distributions a particular attention was given to the regions of small and large pseudorapidities. In the first region we found an apparent evidence for low-energy cascading, contribution and main features of which have been discussed. It is also discussed how strongly the behaviour of one-particle spectra at large rapidities would depend on the internal structure of a projectile particle.     

Ward identities for interacting electronic systems

A Ward-Takahashi identity, as a consequence of gauge invariance and in a form that relates self-energy to the two-particle Bethe-Salpeter scattering kernel, was first derived by Vollhardt and Wölfle for a system of independent particles moving in a random medium. This is generalized to a class of interacting electronic systems in materials with or without random impurities, following a procedure previously used for classical wave transport in disordered media. This class of systems also possesses other symmetry properties such as invariance under time translations and local spin rotations, which imply local conservation laws for energy and spin current. They imply additional Vollhardt-Wölfle type identities. We present non-perturbative derivations of these identities, and consider the constraints they impose on the relationship between the self-energy and the two-particle scattering kernel.     

Optical properties of a suspension of hard spheres

The optical properties of suspensions are studied in a wide range of concentrations. An expression for the polarization operator is obtained taking into account the contributions of two-and three-particle correlations. The extinction length l and the transport length l* are calculated in terms of a model of hard spheres. A detailed comparison of the results of calculations with experimental data is performed. In calculations, the structure factor is determined in the Percus-Yevick approximation, while the form factor is taken into account in the Rayleigh-Gans approximation and in terms of the Mie theory. It is shown that taking into account the contribution of three-particle correlations improves the agreement of the theory with experiment. It is found that, in the range of high suspension concentrations, the optical parameters are more sensitive to the choice of the model for the structure factor than for the form factor.     

Three-body treatment of Coulomb effects in the problem of long-range effective interactions

The problem of Coulomb scattering of a charged particle by a two-particle bound system, consisting of a charged and a neutral particle, is investigated in the integral-equation approach of rigorous three-body theory. The bound state of the two particles is provided by a short-range interaction chosen in the simplest form using anS-wave separable potential. The integral equation defining the effective potential of the interaction of the charged particle with the two-particle bound system is formulated. It is shown that the multiple Coulomb scattering of the involved charged particles generates a sequence of long-range terms in the effective potential. It turns out that the long-range effects of Coulomb scattering are partly cancelled. As a result the polarization potential does not contain the longest-ranged terms which decrease at large distances as ^–2 and ^–3.     

Light scattering by composite particles comparable with wavelength and their approximation by systems of spheres

Scattering properties of an ensemble of independent, randomly-oriented systems consisting of two contacting wavelength-sized dielectric particles of spherical and random shapes are studied. The optical properties of such ensembles are shown to be determined, to a considerable degree, by the properties of individual components of the system; the role of collective effects is insignificant. For large scattering angles, systems consisting of two spheres form the negative branch of the degree of linear polarization when an individual sphere also forms it, and when systems composed of equivalent particles of random shape do not exhibit the negative branch. The conclusion is made that the modeling of the scattering properties of aspherical and aggregate particles by using systems of spheres of size of the order of the optical wavelength is inadequate.     

Influence of correlated impurities on the onset of cooper pairing

Effect of two-particle correlations between impurities on the temperature of transition of a Fermi liquid in the superfluid or superconducting state is analyzed. It is shown, that correlations with a radius, exceeding correlation length of the superconductor can have a pronounced effect on the transition temperature. The equation for the transition temperature is corrected for correlations of the impurities. Possible applications of the new equation are discussed.     

快度间隔分析与逐事件快度关联

本文推导了逐事件快度间隔的起伏与逐事件快度关联的关系. 分析表明：快度间隔分析中新的和有意义的部分是推广的两粒子快度关联矩. 对于一些特殊的两粒子和矩阶数这些矩有明确的物理意义.     

Coherent Transmission and Reflection by a monolayer of discrete scatterers

Coherent transmission and reflection of a plane wave through a monolayer of discrete particles are considered on the basis of simple and physically transparent formulae for the single scattering approximation (SSA) corrected by introducing a multiple scattering permittivity factor. This factor allows for multiple scattering of Waves between monolayer particles, opposite to the SSA. The multiple scattering permittivity factor is considered on the basis of the quasi-crystalline approximation (QCA) via ? matrix formalism. The multiple scattering permittivity factor and parameters for obtaining coherent transmission and reflection coefficients (the effective extinction coefficient and the transmission and reflection coefficients due to rescattering) are calculated within the scope of QCA and plotted for comparison with SSA results. The expressions for these values are simplified for small Rayleigh particles to simple analytical formulae.     

On the extension of the Boltzmann equation to include pair correlations

The derivation of kinetic equations, including the effects of pair correlations, for a gas of particles interacting via purely repulsive forces is reported. An additional assumption on the form of the two-particle distribution function yields the Enskog equation for a dense hard-sphere gas. However, the true two-particle distribution function is not of this form.     

Unstable states produced in multiparticle reactions

Normalized wavefunctions for unstable-particle states are constructed to meet the following physically plausible specifications. The wavefunctions of such states should enter into the theoretical production cross section in the same manner as the boundstate wavefunctions of stable particles. The cross section for the production of an unstable particle should be equal to the breakup cross section integrated over the resonance minus the background. For this purpose the multiparticle reaction cross section is brought into a form such that final-state resonances and interference corrections can be exhibited explicitly. The present theory is limited to unstable particles that decay into one or several two-body channels. For heuristic purposes, rearrangement and breakup scattering for three simple particles is treated numerically. For two particles interacting via a local potential, the wavefunction of the unstable state and the scattering phase shifts are computed with a simple algebraic technique. In order to treat complex multiparticle systems, we extend the resonance theory of simple two-particle systems to resonances in multiparticle two-body channels.     

Electromagnetic structure of the proton within the CP-violation hypothesis

The so-called non-Rosenbluth behavior of the proton electromagnetic form factors can be explained within the hypothesis of CP violation in electromagnetic processes involving composite systems of strongly interacting particles. It is shown that this hypothesis leads to the appearance of an additional, anapole, form factor of the proton. The proton electromagnetic form factors, including the anapole form factor, are estimated on the basis of experimental data on elastic electron-proton scattering.     

Computer simulations for multiple scattering of light rays in systems of opaque particles

A new computer model for multiple light scattering in arbitrary systems of opaque diffusely scattering particles is considered. For ray tracing and scattering in such systems, the geometric optics approximation is used. Semi-infinite media and clusters with spherical and irregular shaped particles are investigated. The irregular particles are approximated with a discrete set of small triangular facets attached to each other. The particle surface is supposed to scatter by the Lambertian indicatrix. Scattering of the first six orders is considered, but the model can be effectively used for calculations of higher orders too. Phase-angle curves of scattering for media and clusters with different packing density are calculated. It is shown that the contributions of scattering orders rapidly diminish as the order grows even for non-absorbing particulate surfaces. Only the first scattering order shows the opposition effect and is rather sensitive to packing density. Higher orders do not show any features near zero phase angle. The contributions of high orders increase slightly, when the packing density increases. The form of particles is important mostly for the second scattering order. For clusters of particles both packing density and number of particles are important for phase function behavior. Clusters consisting of 100 particles show weak phase-angle dependences of high orders of scattering. These dependences become more prominent with increase of number of particles. Phase curves for spherical and cubic clusters are compared. It turns out that the influence of cluster shape is only a minor factor.     

Photon production in a dense medium

On the basis of diagram formalism for two-particle Green functions, the bremsstrahlung of charged particles interacting in a dense medium is investigated. In the case of production of soft photons, exact expressions for two-particle Green functions corresponding to the process of particle bremsstrahlung in the substance are obtained. The Green functions found are fully determined by the set of closed irreducible diagrams. It is shown that, in the case of radiation in a sufficiently dense medium in a far long-wave region of the spectrum, the coherent multiple particle scattering results in an additional (as compared that reported earlier in [1–13]) suppression of the bremsstrahlung photon yield.     

Two-particle scattering matrix of two interacting mesoscopic conductors

We consider two quantum coherent conductors interacting weakly via long range Coulomb forces. We describe the interaction in terms of two-particle collisions described by a two-particle scattering matrix. As an example we determine the transmission probability and correlations in a two-particle scattering experiment and find that the results can be expressed in terms of the density-of-states matrices of the noninteracting scatterers.     

Quantum kinetic equation for nonequilibrium dense systems

Using the density matrix method in the form developed by Zubarev, equations of motion for nonequilibrium quantum systems with continuous short range interactions are derived which describe kinetic and hydrodynamic processes in a consistent way. The T-matrix as well as the two-particle density matrix determining the nonequilibrium collision integral are obtained in the ladder approximation including the Hartree-Fock corrections and the Pauli blocking for intermediate states. It is shown that in this approximation the total energy is conserved. The developed approach to the kinetic theory of dense quantum systems is able to reproduce the virial corrections consistent with the generalized Beth-Uhlenbeck approximation in equilibrium. The contribution of many-particle correlations to the drift term in the quantum kinetic equation for dense systems is discussed.     

The gravitational dynamics of galaxies

The broad area of galactic dynamics is presented for a physics audience, with the requisite astronomy background in outline, and focusing on gravitational effects. The basic underlying model is a large number of particles (which could be stars or dark matter) moving in their self-consistent gravitational potential. The effects of two-particle correlations/scattering, although weak, can be cumulative and hence important for a class of systems such as star clusters which are hence termed collisional. On the larger scale of galaxies, we have collisionless behaviour which is different and in some ways richer. The basic ideas and applications in both these regimes are described, and some issues highlighted in conclusion.