Lattice discretization in quantum scattering

The utility of lattice discretization technique is demonstrated for solving nonrelativistic quantum scattering problems and specially for the treatment of ultraviolet divergences in these problems with some potentials singular at the origin in two- and three-space dimensions. This shows that the lattice discretization technique could be a useful tool for the numerical solution of scattering problems in general. The approach is illustrated in the case of the Dirac delta function potential.

Small-angle X-ray scattering study of gelation and aging of Eu3+-doped sol-gel-derived siloxane-poly(oxyethylene) nanocomposites

The aggregation, gelation, and aging of urea-cross-linked siloxane-poly(oxyethylene) nanohybrids [(U600)-n] containing two different amounts of europium triflate initially dissolved in an ethanol-water mixture were investigated by in situ small-angle X-ray scattering (SAXS). For both low (n = [O]/[Eu] = 80) and high (n = 25) europium contents, the SAXS intensity was attributed to the formation of siloxane clusters of about 8-11 Angstrom in size. Siloxane cluster formation and growth is a rapid process in hybrids with low Eu contents and slow in Eu-rich hybrids. An additional contribution to the scattering intensity at very low angles was attributed to the formation of a coarse structure level. At this secondary level, the structure can be described as a set of dense domains containing siloxane clusters embedded in a depleted matrix composed of unfolded polymer chains and solvent. By fitting a theoretical function for this model to the experimental SAXS curves, relevant structural parameters were determined as functions of time during the sol-gel transition and gel aging. For hybrids with low europium contents (n = 80), the size of the siloxane clusters remains essentially invariant, whereas the dense segregation domains progressively grow. In hybrids with high doping contents (n = 25), the preponderant structure variation during the first stages of the sol-gel transformation is the slow growth of siloxane clusters. For these hybrids, the segregation of siloxane clusters forming dense domains occurs only during advanced stages of the process.

New higher-derivative R-4 theorems for graviton scattering

The nonminimal pure spinor formalism for the superstring is used to prove two new multiloop theorems which are related to recent higher-derivative R-4 conjectures of Green, Russo, and Vanhove. The first theorem states that when 0 < n < 12, partial derivative R-n(4) terms in the Type II effective action do not receive perturbative contributions above n/2 loops. The second theorem states that when n <= 8, perturbative contributions to partial derivative R-n(4) terms in the IIA and IIB effective actions coincide. As shown by Green, Russo, and Vanhove, these results suggest that d=4 N=8 supergravity is ultraviolet finite up to eight loops.

Electron scattering and effects of sources of light on photoconductivity of SnO2 coatings prepared by sol-gel

Electro-optical properties of sol-gel derived 2 mol% antimony or niobium doped tin dioxide films have been measured. The electron density has been calculated considering all the relevant scattering mechanisms and experimental conductivity data measured in the range -197 to 25 degrees C. The results support the hypothesis that both ionised impurity scattering and grain boundary scattering have comparable effects in the resistivity of coatings, for free electron density congruent to 5 x 10(18) cm(-3). We have measured variation of photoconductivity excitation with wavelength using xenon and deuterium lamp as light sources. Results show that the main band in the photoconductivity spectrum is dependent on the spectral light source emission, the excitation peak reaching 5 eV (deuterium lamp). This band is due to the recombination process involving oxygen species and photogenerated electron-hole pairs. (C) 1999 Elsevier B.V. B.V. All rights reserved.

Small angle X-ray scattering study of surface modified tin oxide nanoparticles prepared by sol-gel route

The surface properties of SnO2 nanoparticles were modified by grafting ionic (Tiron (R). (OH)(2)C6H2(SO3Na)(2)(H2O)-H-.) or non-ionic (Catechol (R). C6H4-1,2-(OH)(2)) capping Molecules during aqueous sol-gel processing to improve the redispersibility of powdered xerogel. The effect of the amount of grafted organic molecules on the redispersibility of powders in aqueous solution at several basic pH values was Studied. The nanostructural features of the colloidal suspensions were analyzed by small angle X-ray scattering (SAXS) measurements. Irrespective of the nature and amount of grafted molecules, complete redispersion was obtained in aqueous solution at pH = 13. The redispersion at pH = 11 results in a mixture of dispersed primary particles and aggregates. The proportion of well dispersed nanoparticles and aggregates (and their average size) can be tuned by the quantity of grafted ionic molecules.

On the scattering of comets by a planet

In this paper, numerical simulations are made, using the three-dimensional restricted three-body problem as the mathematical model, to calculate the effects of a swing-by with the planet Saturn in the orbit of a comet. To show the results, the orbit of the comet is classified in four groups: elliptic direct, elliptic retrograde, hyperbolic direct and hyperbolic retrograde. Then, the modification in the orbit of the comet due to the close approach is shown in plots that specify from which group the comet's orbit is coming and to which group it is going. Several families of orbits are found and shown in detail. An analysis about the trends as parameters (position and velocity at the periapse) vary is performed and the influence of each of them is shown and explained. The result is a collection of maps that describe the evolution of the trajectory of the comet due to the close approach. Those maps can be used to estimate the probability of some events, like the capture or escape of a comet. An example of this technique is shown in the paper. (C) 2005 COSPAR. Published by Elsevier Ltd. All rights reserved.

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.