MODEL INDEPENDENCE OF SCATTERING OF 3 IDENTICAL BOSONS IN 2 DIMENSIONS

Within the framework of scattering integral equations in momentum space, we present numerical results of scattering of three identical bosons at low energies in two dimensions for short-range separable potentials. An analysis of the present numerical results reveals the three-particle scattering observables to be independent of potential shape provided the low-energy two-particle binding energy and scattering length are held fixed throughout the investigation. We think that the present conclusion of model independence will be valid for any potential, local or nonlocal, whose range is much smaller than the size of the two-particle bound state.

Fluorescence and confocal laser scanning microscopy imaging of elastic fibers in hematoxylin-eosin stained sections

We have studied the possibility of associating fluorescence microscopy and hematoxylin-eosin staining for the identification of elastic fibers in elastin-rich tissues. Elastic fibers and elastic laminae were consistently identified by the proposed procedure, which revealed itself to be easy and useful for the determination of such structures and their distribution. The fluorescence properties of stained elastic fibers are due to eosin staining as revealed by fluorescence analysis of the dye in solution, with no or only minor contribution by the elastin autofluorescence. The main advantage of this technique resides in the possibility of studying the distribution of elastic fibers in file material without further sectioning and staining. The use of the confocal laser scanning microscope greatly improved the resolution and selectivity of imaging elastic fibers in different tissues. The determination of the three-dimensional distribution and structure of elastic fiber and laminae using the confocal laser scanning microscope was evaluated and also produced excellent results.

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).

Hardness and elastic modulus of carbon-germanium alloys

This work reports on the mechanical properties of germanium-rich amorphous carbon-germanium alloys prepared by RF sputtering of a germanium/graphite target under an argon/hydrogen atmosphere. Nano-hardness, elastic modulus and stress were investigated as a function of the carbon content. The stress, which is reduced by the incorporation of carbon, was related to the film structure and to the difference in the Ge-Ge and Ge-C bond length. Contrary to what was expected, the hardness and elastic modulus of the alloys are lower than the corresponding values for pure amorphous hydrogenated germanium film, which in turn has both properties also smaller than those of crystalline germanium. These properties are analyzed in terms of the structural properties of the films. (C) 2001 Elsevier B.V. B.V All rights reserved.

ITERATIVE NUMERICAL-SOLUTION OF SCATTERING PROBLEMS

An iterative Neumann series method, employing a real auxiliary scattering integral equation, is used to calculate scattering lengths and phase shifts for the atomic Yukawa and exponential potentials. For these potentials the original Neumann series diverges. The present iterative method yields results that are far better, in convergence, stability and precision, than other momentum space methods. Accurate result is obtained in both cases with an estimated error of about 1 in 10(10) after some 8-10 iterations.

Small angle X-ray scattering and IR spectroscopy study of metal carbonyl complexes immobilized on a silica gel surface chemically modified with piperazine

The carbonyl complexes [WCl(CO)(3)(bipy) (HgCl)] (1), [Fe(CO)(4)(HgCl)(2)] (2) and W(CO)(6)] (3) were immobilized on a silica gel surface organofunctionalized with piperazine groups. The products obtained were studied by IR spectroscopy and small angle X-ray scattering (SAXS) techniques. The IR data show that the immobilization of heterobimetallic compounds 1 and 2, on the functionalized surface, occurred through the mercury atom, while for 3 the displacement of one CO group by the nitrogen of a piperazine molecule was observed. The data obtained from SAXS indicate that particles have a uniform size and reveal suitable modifications on the functionalized surface after immobilization of metal carbonyl complexes. The average intermolecular distance (l(ij)) for piperazine ligands on support is 8.7 Angstrom, for the metal carbonyl complex 1 it is 18.8 Angstrom, for complex 2 it is 16.2 Angstrom and for complex 3 it is 15.3 Angstrom. Copyright (C) 1996 Elsevier B.V. Ltd

On a regular convex solver potential for an elastic-damage constitutive model: a theoretical analysis

This work is related with the proposition of a so-called regular or convex solver potential to be used in numerical simulations involving a certain class of constitutive elastic-damage models. All the mathematical aspects involved are based on convex analysis, which is employed aiming a consistent variational formulation of the potential and its conjugate one. It is shown that the constitutive relations for the class of damage models here considered can be derived from the solver potentials by means of sub-differentials sets. The optimality conditions of the resulting minimisation problem represent in particular a linear complementarity problem. Finally, a simple example is present in order to illustrate the possible integration errors that can be generated when finite step analysis is performed. (C) 2003 Elsevier Ltd. All rights reserved.

Band-edge states of the zero(th)-order gap in quasi-periodic photonic superlattices

The photonic modes of Thue-Morse and Fibonacci lattices with generating layers A and B, of positive and negative indices of refraction, are calculated by the transfer-matrix technique. For Thue-Morse lattices, as well for periodic lattices with AB unit cell, the constructive interference of reflected waves, corresponding to the zero(th)-order gap, takes place when the optical paths in single layers A and B are commensurate. In contrast, for Fibonacci lattices of high order, the same phenomenon occurs when the ratio of those optical paths is close to the golden ratio. In the long wavelength limit, analytical expressions defining the edge frequencies of the zero(th) order gap are obtained for both quasi-periodic lattices. Furthermore, analytical expressions that define the gap edges around the zero(th) order gap are shown to correspond to the = 0 and = 0 conditions.

Small-angle X-ray scattering study of the smart thermo-optical behavior of zirconyl aqueous colloids

The smart thermo-optical systems studied here are based on the unusual thermoreversible sol-gel transition of zirconyl chloride aqueous solution modified by sulfuric acid in the molar ratio Zr/SO4:3/1. The transparency to the visible light changes during heating due to light scattering. This feature is related to the aggregates growth that occurs during gelation. These reversible changes can be controlled by the amount of chloride ions in solution. The thermoreversible sol-gel transition temperature increases from 323 to 343 K by decreasing the molar ratio Cl/Zr from 7.0 to 1.3. In this work the effect of the concentration of chloride ions on the structural characteristics of the system has been analyzed by in situ SAXS measurements during the sol-gel transition carried out at 323 and 333 K. The experimental SAXS curves of sols exhibit three regions at small, medium and high scattering vectors characteristics of Guinier, fractal and Porod regimes, respectively. The radius of primary particles, obtained from the crossover between the fractal and Porod regimes, remains almost invariable with the chloride concentration, and the value (4 Angstrom) is consistent with the size of the molecular precursor. During the sol-gel transition the aggregates grow with a fractal structure and the fractal dimensionality decreases from 2.4 to 1.8. This last value is characteristic of a cluster-cluster aggregation controlled by a diffusion process. Furthermore, the time exponent of aggregate growth presents values of 0.33 and 1, typical of diffusional and hydrodynamic motions. A crossover between these two regimes is observed.

Metal-Organic Semiconductor Nanostructures for Surface-Enhanced Raman Scattering

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)