LARGE-ORDER PERTURBATION EXPANSIONS FOR THE CHARGED HARMONIC-OSCILLATOR

The charged oscillator, defined by the Hamiltonian H = -d2/dr2+ r2 + lambda/r in the domain [0, infinity], is a particular case of the family of spiked oscillators, which does not behave as a supersingular Hamiltonian. This problem is analysed around the three regions lambda --> infinity, lambda --> 0 and lambda --> -infinity by using Rayleigh-Ritz large-order perturbative expansions. A path is found to connect the large lambda regions with the small lambda region by means of the renormalization of the series expansions in lambda. Finally, the Riccati-Pade method is used to construct an implicit expansion around lambda --> 0 which extends to very large values of Absolute value of lambda.

Determination of the U-238 spontaneous fission decay constant without neutron irradiation

We have developed a methodology for measuring the decay constant of the spontaneous fission of U-238, lambda(f), using nuclear particle track detectors where thermal neutron irradiation is unnecessary. This methodology is based on the fact that the radiation damage caused by spontaneous fission of trans-uranium elements bearing a mass number close to 238 are similar to U-238 spontaneous-fission ones. Loading a thick source of uranium (thickness greater than the fission fragment range) with a small amount of a suitable trans-uranium element (for instance, Pu-242, which presents a spontaneous fission half-life of 6.75(.)10(10) y), it is possible to determine the observation efficiency of a particle-track detector for fission fragments. Procedures concerning our thick source manufacture and uniformity tests of the trans-uranium distribution are also presented. These results make it possible for the exposure of thick uranium sources (without trans-uranium element) to lead to a lambda(f) value.

D-n-forced symmetry breaking of O(2)-equivariant problems

We use singularity theory to classify forced symmetry-breaking bifurcation problemsf(z, lambda, mu) = f(1)(z, lambda) + muf(2)(z, lambda, mu) = 0,where f(1) is O(2)-equivariant and f(2) is D-n-equivariant with the orthogonal group actions on z is an element of R-2. Forced symmetry breaking occurs when the symmetry of the equation changes when parameters are varied. We explicitly apply our results to the branching of subharmonic solutions in a model periodic perturbation of an autonomous equation and sketch further applications.

Spectrophotometric determination of formaldehyde with chromotropic acid in phosphoric acid medium assisted by microwave oven

In the present study. a spectrophotometric method for the determination of formaldehyde by using chromotropic acid was devised. in which the use of potentially hazardous and corrosive concentrated sulfuric acid was eliminated and advantageously C replaced by a mixture of H, concentrated H3PO4 and H2O2. The reaction between formaldehyde and chromotropic acid (CA) in a cone phosphoric acid medium was accelerate by irradiating the mixture with microwave energy for 35 s (1100 W), producing a violetred compound (lambda(max)=570 nm). Beer's Law is obeyed in a concentration range of 0.8-4.8 mg 1(-1) of formaldehyde with a good correlation coefficient (r = 0.9968). The proposed method was applied in the analysis of formaldehyde in commercial disinfectants. Recoveries were within 98.0-100.4%, with standard deviations ranging from 0.03 to 0.13%. (C) 2003 Elsevier B.V All rights reserved.

Asymmetry parameter for nonmesonic hypernuclear decay

We give general expressions for the vector asymmetry in the angular distribution of protons in the nonmesonic weak decay of polarized hypernuclei. From these we derive an explicit expression for the calculation of the asymmetry parameter, a(Lambda), which is applicable to the specific cases of He-5(Lambda) and C-12(Lambda) described within the extreme shell model. In contrast to the approximate formula widely used in the literature, it includes the effects of three-body kinematics in the final states of the decay and correctly treats the contribution of transitions originating from single-proton states beyond the s-shell. This expression is then used for the corresponding numerical computation of a(Lambda) within several one-meson-exchange models. Besides the strictly local approximation usually adopted for the transition potential, we also consider the addition of the first-order nonlocality terms. We find values for a(Lambda) ranging from -0.62 to -0.24, in qualitative agreement with other theoretical estimates but in contradiction with some recent experimental determinations.

2-DIMENSIONAL QUANTUM GAS

Identical impenetrable particles in a 2-dimensional configuration space obey braid statistics, intermediate between bosons and fermions. This statistics, based on braid groups, is introduced as a generalization of the usual statistics founded on the symmetric groups. The main properties of an ideal gas of such particles are presented. They do interpolate the properties of bosons and fermions but include classical particles as a special case. Restriction to 2 dimensions precludes lambda points but originates a peculiar symmetry, responsible in particular for the identity of boson and fermion specific heats.

RELATING THE QCD POMERON TO AN EFFECTIVE GLUON MASS

We construct the Pomeron as an exchange of two nonperturbative gluons, where the nonperturbative gluon propagator is described by an approximate solution of the Schwinger-Dyson equation which contains a dynamically generated gluon mass. We compute the total and elastic differential (dsigma/dt) cross sections for pp scattering, obtaining agreement with the experimental data for a gluon mass m = 370 MeV for LAMBDA(QCD) = 300 MeV. In particular, the Pomeron effectively behaves like a photon-exchange diagram with a coupling determined by the glucon mass.

Optical recording in Se(Te)/As2S3 multilayers

The development of Te containing nanoscaled, compositionally modulated Te/As2S3 multilayer structures enables the realisation of optical recording in real time with a CW He-Ne laser illumination (lambda=633 nm) with improved recording parameters in comparison with known Se/As2S3 structures. It is established that the efficiency of the recording process depends on the light stimulated interdiffusion and thickness of sub-layers.

THE VACUUM ENERGY OF QED WITH 4-FERMION INTERACTION

We consider quantum electrodynamics in the quenched approximation including a four-fermion interaction with coupling constant g. The effective potential at stationary points is computed as a function of the coupling constants alpha and g and an ultraviolet cutoff LAMBDA, showing a minimum of energy in the (alpha, g) plane for alpha = alpha(c) = pi/3 and g = infinity. When we go to the continuum limit (LAMBDA --> infinity), keeping finite the dynamical mass, the minimum of energy moves to (alpha = 0, g = 1), which correspond to a point where the theory is trivial.

Colorimetric determination of sulfur dioxide in air using a droplet collector of malachite green solution

The measurement of sulfur dioxide in air at the parts-per-billion level is described. The experimental arrangement consists of two optical fibers placed on opposite sides of a liquid droplet of malachite green solution. After light has been passed through the droplet, the transmitted light is measured by a referenced photodetection arrangement. The light used in this absorption process is from a monochromatic source (lambda(max) 625 nm). This arrangement permits the variation of color in the droplet to be measured. The sulfur dioxide in the sample is collected by the droplet; it reacts with malachite green resulting in a colorless dye. The decoloration of the solution is proportional to the concentration of sulfur dioxide sampled. The signal depends on the sample flow rate. The present technique is simple, inexpensive, and permits a fast and near real time measurement while consuming very little reagent, (C) 1999 Academic Press.

VARIATIONAL SPIKED OSCILLATOR

A variational analysis of the spiked harmonic oscillator Hamiltonian -d2/dr2 + r2 + lambda/r5/2, lambda > 0, is reported. A trial function automatically satisfying both the Dirichlet boundary condition at the origin and the boundary condition at infinity is introduced. The results are excellent for a very large range of values of the coupling parameter lambda, suggesting that the present variational function is appropriate for the treatment of the spiked oscillator in all its regimes (strong, moderate, and weak interactions).

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.

Chain sequences and symmetric generalized orthogonal polynomials

in this paper, we derive an explicit expression for the parameter sequences of a chain sequence in terms of the corresponding orthogonal polynomials and their associated polynomials. We use this to study the orthogonal polynomials K-n((lambda.,M,k)) associated with the probability measure dphi(lambda,M,k;x), which is the Gegenbauer measure of parameter lambda + 1 with two additional mass points at +/-k. When k = 1 we obtain information on the polynomials K-n((lambda.,M)) which are the symmetric Koornwinder polynomials. Monotonicity properties of the zeros of K-n((lambda,M,k)) in relation to M and k are also given. (C) 2002 Elsevier B.V. B.V. All rights reserved.

Application of standard and modified Judd-Ofelt theories to thulium doped fluoroindate glass

Fluoroindate glasses of the following compositions: (40-x)InF3-20ZnF(2)-16BaF(2)-20SrF(2)-2GdF(3)-2NaF-xTmF(3) with x = 1,3 mol% were prepared in a dry box under an argon atmosphere. The absorption spectra at room temperature in the spectral range 350-2200 nm were obtained. The spectra obtained for each sample had similar absorption and only the amplitude of the different bands changed as the concentration of Tm3+. The experimental oscillator strengths were determined from the areas under the absorption bands. Using the standard and modified Judd-Ofelt theory, intensity parameters Ohm(lambda) (lambda = 2,4,6) and (lambda = 2,3,4,5,6), respectively for f-f transitions of Tm3+ ions as well as transition probabilities, branching ratios and radiative lifetimes for each band were determined. The results are compared with those of other glasses described in the literature. (C) 1999 Elsevier B.V. B.V. All rights reserved.

GROUND-STATE-ENERGY OF SINGULAR POTENTIALS

It is shown that for singular potentials of the form lambda/r(alpha),the asymptotic form of the wave function both at r --> infinity and r --> 0 plays an important role. Using a wave function having the correct asymptotic behavior for the potential lambda/r(4), it is, shown that it gives the exact ground-state energy for this potential when lambda --> 0, as given earlier by Harrell [Ann. Phys. (NY) 105, 379 (1977)]. For other values of the coupling parameter X, a trial basis;set of wave functions which also satisfy the correct boundary conditions at r --> infinity and r --> 0 are used to find the ground-state energy of the singular potential lambda/r(4) It is shown that the obtained eigenvalues are in excellent agreement with their exact ones for a very large range of lambda values.