LOW-ENERGY BEHAVIOR OF FEW-PARTICLE SCATTERING-AMPLITUDES IN 2 DIMENSIONS

A study of the analytic behavior of different few-particle scattering amplitudes at low energies in two space dimensions is presented. Such a study is of use in modeling and understanding different few-particle processes at low energies. A detailed discussion of the energy and the momentum dependence of the partial-wave on-the-energy-shell and off-the-energy-shell two-particle t matrices is given. These t-matrix elements tend to zero as the energy and momentum variables tend to zero. The multiple-scattering series is used to show that the connected three-to-three amplitudes diverge in the low-energy-momentum limit. Unitarity relations are used to show that the connected two-to-three and one-to-three amplitudes have specific logarithmic singularities at the m-particle breakup threshold. The subenergy singularity in the two-to-three amplitudes is also studied, and comments are made on some applications of the present study in different problems of ph cal interest.

RELATIVISTIC 3-PARTICLE SCATTERING EQUATIONS

We derive a set of relativistic three-particle scattering equations in the three-particle c.m. frame employing a relativistic three-particle propagator suggested long ago by Ahmadzadeh and Tjon in the c.m. frame of a two-particle subsystem. We make the coordinate transformation of this propagator from the c.m. frame of the two-particle subsystem to the three-particle c.m. frame. We also point out that some numerical applications of the Ahmadzadeh and Tjon propagator to the three-nucleon problem use unnecessary nonrelativistic approximations which do not simplify the computational task, but violate constraints of relativistic unitarity and/or covariance.

NEAR-RESONANT SCATTERING FROM NONSYMMETRIC DIMERS - APPLICATIONS TO SUBSTITUTED POLYANILINES

In this work we show that, beyond the prediction of the random dimer model [Wu and Phillips, Phys. Rev. Lett. 66, 1366 (1991)], it is possible to have near resonant scattering from nonsymmetric dimers. It is shown by direct density of states calculations as well as by a procedure similar to the random dimer model that protonated chains of alkyl-substituted polyanilines support extended electronic states at the Fermi energy when a disordered distribution of symmetric or asymmetric bipolarons is present. An extension of the random dimer model to include resonant scattering by nonsymmetric dimers is proposed.

Interactions between the non-ionic surfactant C(12)E(5) and poly(ethylene oxide) studied using dynamic light scattering and fluorescence quenching

Dynamic light scattering measurements have been made to elucidate changes in the coil conformation of a high molecular weight poly(ethylene oxide) (PEG) fraction when the non-ionic surfactant C(12)E(5) is present in dilute solutions. The measurements were made at 20 degrees C as functions of(a) the C(12)E(5) concentration at constant PEO concentration, (b) the PEO concentration at constant C(12)E(5) concentration, and (c) the C(12)E(5)/PEO concentration ratio. The influence of temperature on the interactions in terms of the relaxation time distributions was also examined up to the cloud point. It was found that when the C(12)E(5)/PEO weight ratio was >2 and when the temperature was >14 degrees C, the correlation functions became bimodal with well-separated components. The fast mode derives fi om individual surfactant micelles which are present in the solution at high number density. The appearance of the slow mode, which dominates the scattering, is interpreted as resulting from the formation of micellar clusters due to an excluded-volume effect when the high molar mass (M = 6 x 10(5)) PEO is added to the surfactant solution. It is shown that the micellar clusters form within the PEO coils and lead to a progressive swelling of the latter for steric reasons. The dimensions of the PEO/C(12)E(5) complex increase with increasing surfactant concentration to a value of R(H) approximate to 94 nm (R(g) approximate to 208 nm) at C-C12E5 = 3.5%. Fluorescence quenching measurements show that the average aggregation number of C(12)E(5) increases significantly on addition of the high molar mass PEG. With increasing temperature toward the cloud point the clusters increase in number density and/or become larger. The cloud point is substantially lower than that for C12E5 in water solution and is strongly dependent on the PEO concentration.

Positronium scattering from ions, atoms and molecules

Elastic and inelastic scattering of positronium (Ps) by H, He, He(+) and H(2) have been studied using coupled-channel calculations with a regularised nonlocal model exchange potential. Suitability and reliability of the theoretical scheme have been demonstrated by studying scattering cross-sections in various systems and also by addressing critical dynamic features like binding and resonances of Ps to open-shell-atoms. Results are found to be in good agreement with Variational predictions and experimental observations. (C) 2000 Elsevier B.V. Ltd. All rights reserved.

Small-angle X-ray scattering and X-ray absorption near-edge structure study of iron-doped siloxane-polyoxyethylene nanocomposites

The local and medium-range structures of siloxane-POE hybrids doped with Fe(III) ions and prepared by the sol-gel process were investigated by X-ray absorption near-edge structure (XANES)/extended X-ray absorption fine structure (EXAFS) and small-angle X-ray scattering (SAXS), respectively. The experimental results show that the structure of these composites depends on the doping level. EXAFS data reveal that, for low doping levels ([O]/[Fe] > 40, oxygens being of the ether-type of the POE chains), Fe(III) ions are surrounded essentially by a shell of chlorine atoms, suggesting the formation of FeCl4- anions. At high doping levels ([O]/[Fe] < 20), Fe(III) ions interacts mainly with oxygen atoms and form FeOx species. The relative proportion of FeOx species increases with iron concentration, this result being consistent with the results of SAXS measurements showing that increasing iron doping induces the formation of iron-rich nanodomains embedded in the polymer matrix.

THE EFFECT OF POSITRONIUM FORMATION IN POSITRON ALKALI-ATOM SCATTERING

We study e+-Na, e+-K, and e+-Rb scattering using the close coupling approach in the static and coupled static expansion schemes. We calculate partial wave elastic scattering phase shifts and total elastic and Ps formation cross sections up to an incident positron energy of 100 eV. The effect of the positronium formation channel on the elastic channel is found to be strong in all cases up to an incident positron energy of 10 eV. We also make an estimate of the total cross section which exhibits a minimum as a function of energy at low energies.

Ps-H scattering using the three-state positronium close-coupling approximation

Positronium scattering off a hydrogen target has been studied employing a three-state positronium model close-coupling approximation (CCA) with and without electron exchange. Elastic, excitation and quenching cross sections are reported at low and medium energies. The effect of electron exchange is found to be significant at low energies. The ratio of quenching to the total cross section (the conversion ratio) approaches the value of 0.25 with increase of energy, as expected.

Raman scattering, differential scanning calorimetry and Nd3+ spectroscopy in alkali niobium tellurite glasses

Alkali niobium tellurite glasses have been prepared and some of their properties measured by differential scanning calorimetry and Raman scattering. The vitreous domain was established in the pseudo ternary phases diagram for the system TeO2-Nb2O5-(0.5K(2)O-0.5Li(2)O). Raman scattering shows that for samples in the TeO2 rich part of the phase diagram the vitreous structure is composed essentially of (TeO4) units connected by the vertices, as in the alpha-TeO2 crystal. The addition of alkali and niobium oxides causes depolymerization to occur with structures composed essentially of (TeO3) and (NbO6) units. Samples with the composition (mol%) 80TeO(2)-10Nb(2)O(5)-5K(2)O-5Li(2)O, stable against crystallization, were prepared containing up to 10% mol Nd3+. The addition of this oxide increases the rigidity of the vitreous network shifting characteristic temperatures to higher temperatures. For the 10% Nd3+ sample amorphous phase separation is assumed to exist from the observation of two glass transition temperatures. Spectroscopic properties such as Judd-Ofelt Omega(lambda) intensity parameters, radiative emission probabilities, and induced emission cross sections were calculated. From these results and also from the emission quenching observed as a function of Nd3+ concentration, we suggest that these glasses could be utilized in optical amplifying devices. (C) 1999 Elsevier B.V. B.V. All rights reserved.

Interaction between poly(ethylene glycol) and C12E8 investigated by dynamic light scattering, time-resolved fluorescence quenching, and calorimetry

Dynamic light scattering (DLS), time-resolved fluorescence quenching (TRFQ), and isothermal titration microcalorimetry have been used to show that, in dilute solution, low molecular weight poly(ethylene glycol) (PEG, M-w = 12 kDa) interacts with the nonionic surfactant octaethylene glycol n-dodecyl monoether, C12E8, to form a complex. Whereas the relaxation time distributions for the binary C12E8/water and PEG/water systems are unimodal, in the ternary mixtures they may be either uni- or bimodal depending on the relative concentrations of the components. At low concentrations of PEG or surfactant, the components of the relaxation time distribution are unresolvable, but the distribution becomes bimodal at higher concentrations of either polymer or surfactant. For the ternary system in excess surfactant, we ascribe, on the basis of the changes in apparent hydrodynamic radii and the scattered intensities, the fast mode to a single micelle, the surface of which is associated with the polymer and the slow mode to a similar complex but containing two or three micelles per PEG chain. Titration microcalorimetry results show that the interaction between C12E8, and PEG is exothermic and about 1 kJ mol(-1) at concentrations higher than the CMC of C12E8. The aggregation number, obtained by TRFQ, is roughly constant when either the PEG or the C12E8 concentration is increased at a given concentration of the second component, owing to the increasing amount of surfactant micelles inside the complex.

Surface-enhanced resonance Raman scattering as an analytical tool for single molecule detection

A perylene derivative, n-(n-butyl)-n'-(4-aminobutyl) perylene-3,4,9,10-tetracarboxylic acid diimide (simplified as nBu-PTCD-(CH2)(4)-NH2) has been chosen as the target molecule for studies involving single molecule detection (SMD) using Raman scattering. The enhancement of the Raman signal is the result of the multiplicative effects of two phenomena, resonance Raman scattering (RRS) and surface-enhanced Raman scattering (SERS), which leads to the resulting surface-enhanced resonance Raman scattering (SERRS) process. The SERRS spectra from a single molecule have been collected using both silver and gold colloids. The SMD detection of the fundamental vibrational frequencies characteristic of nBu-PTCD-(CH2)(4)-NH2 is complemented with the detection of some overtones and combinations from ring stretching modes at the single molecule level. The background characterization of the ensemble vibrational spectroscopy of the target perylene and its SERRS is also presented, which includes the UV-vis absorption, experimental and calculated Raman scattering and infrared absorption, and molecular organization using reflection-absorption infrared spectroscopy (RAIRS).