Energy spectra of small bosonic clusters having a large two-body scattering length

In this work we investigate small clusters of bosons using the hyperspherical harmonic basis. We consider systems with $A=2,3,4,5,6$ particles interacting through a soft inter-particle potential. In order to make contact with a real system, we use an attractive gaussian potential that reproduces the values of the dimer binding energy and the atom-atom scattering length obtained with one of the most widely used $^4$He-$^4$He interactions, the LM2M2 potential. The intensity of the potential is varied in order to explore the clusters' spectra in different regions with large positive and large negative values of the two-body scattering length. In addition, we include a repulsive three-body force to reproduce the trimer binding energy. With this model, consisting in the sum of a two- and three-body potential, we have calculated the spectrum of the four, five and six particle systems. In all the region explored, we have found that these systems present two bound states, one deep and one shallow close to the $A-1$ threshold. Some universal relations between the energy levels are extracted; in particular, we have estimated the universal ratios between thresholds of the three-, four-, and five-particle continuum using the two-body gaussia

Bethe-Salpeter bound-state structure in Minkowski space

The quantitative investigation of the scalar Bethe-Salpeter equation in Minkowski space, within the ladder-approximation framework, is extended to include the excited states. This study has been carried out for an interacting system composed by two massive bosons exchanging a massive scalar, by adopting (i) the Nakanishi integral representation of the Bethe-Salpeter amplitude, and (ii) the formally exact projection onto the null plane. Our analysis, on one hand, confirms the reliability of the method already applied to the ground state and, on the other one, extends the investigation from the valence distribution in momentum space to the corresponding quantity in the impact-parameter space, pointing out some relevant features, like (i) the equivalence between Minkowski and Euclidean transverse-momentum amplitudes, and (ii) the leading exponential fall-off of the valence wave function in the impact-parameter space.Comment: 15 pages, 7 figure

Restricted infinitesimal deformations of restricted simple Lie algebras

We compute the restricted infinitesimal deformations of the restricted simple Lie algebras over an algebraically closed field of characteristic different from 2 and 3.Comment: 15 pages; final version, to appear in Journal of Algebra and Its Application

Sequential biological and photocatalysis based treatments for shipboard slop purification: A pilot plant investigation

This study investigated the treatment of a shipboard slop containing commercial gasoline in a pilot plant scale consisting of a membrane biological reactor (MBR) and photocatalytic reactor (PCR) acting in series. The MBR contributed for approximately 70% to the overall slop purification. More precisely, the biological process was able to remove approximately 40%, on average, of the organic pollution in the slop. Nevertheless, the membrane was capable to retain a large amount of organic molecules within the system, amounting for a further 30% of the influent total organic content removal. However, this affected the membrane fouling, thus resulting in the increase of the pore blocking mechanism that accounted for approximately 20% to the total resistance to filtration (2.85∙10 13 m −1 ), even if a significant restoration of the original membrane permeability was obtained after chemical cleanings. On the other hand, the biological treatment produced a clear solution for the photocatalytic system, thereby optimizing the light penetration and generation of highly oxidizing active oxygen species that enabled the degradation of bio-recalcitrant compounds. Indeed, low total organic carbon (TOC) values (<10 mg L −1 ) were achieved in the output of the photocatalytic reactor by means of only 60 Einstein (E) of cumulative impinging energy after the addition of K 2 S 2 O 8 . Overall, coupling the two processes enabled very high TOC removal (ca. 95%)

Calculation of the Alpha--Particle Ground State within the Hyperspherical Harmonic Basis

The problem of calculating the four--nucleon bound state properties for the case of realistic two- and three-body nuclear potentials is studied using the hyperspherical harmonic (HH) approach. A careful analysis of the convergence of different classes of HH functions has been performed. A restricted basis is chosen to allow for accurate estimates of the binding energy and other properties of the 4He ground state. Results for various modern two-nucleon and two- plus three-nucleon interactions are presented. The 4He asymptotic normalization constants for separation in 2+2 and 1+3 clusters are also computed.Comment: 29 pages, 4 figures, 11 tables, revtex

A formação inicial de professores de química e os saberes docentes : um processo de construção e reflexão

Este trabalho apresenta uma análise das concepções dos licenciandos do curso de Licenciatura e Bacharelado em Química da Universidade Federal de Uberlândia, Brasil, sobre ‘o que é ser um bom professor de química’ durante o processo de formação inicial. As concepções foram agrupadas em três categorias de saberes docentes: o ‘saber’, que compreende os saberes conceituais e teóricos; o ‘saber fazer’, relacionados com os conhecimentos pedagógicos e o ‘saber ser’, que engloba os saberes e competências relativos a ação do professor em sala de aula. Os resultados das análises mostram que estes saberes são necessários para uma sólida formação docente, tendo em vista a integração entre teoria e prática para que os licenciados possam compreender que ‘ser professor’ não é apenas saber o conteúdo específico da disciplina, mas envolve outras habilidades e competências

The Ay Problem for p-3He Elastic Scattering

We present evidence that numerically accurate quantum calculations employing modern internucleon forces do not reproduce the proton analyzing power, A_y, for p-3He elastic scattering at low energies. These calculations underpredict new measured analyzing powers by approximately 30% at E_{c.m.} = 1.20 MeV and by 40% at E_{c.m.} = 1.69 MeV, an effect analogous to a well-known problem in p-d and n-d scattering. The calculations are performed using the complex Kohn variational principle and the (correlated) Hyperspherical Harmonics technique with full treatment of the Coulomb force. The inclusion of the three-nucleon interaction does not improve the agreement with the experimental data.Comment: Latex file, 4 pages, 2 figures, to be published on Phys. Rev. Let

A small parameter approach for few-body problems

A procedure to solve few-body problems is developed which is based on an expansion over a small parameter. The parameter is the ratio of potential energy to kinetic energy for states having not small hyperspherical quantum numbers, K>K_0. Dynamic equations are reduced perturbatively to equations in the finite-dimension subspace with K\le K_0. Contributions from states with K>K_0 are taken into account in a closed form, i.e. without an expansion over basis functions. Estimates on efficiency of the approach are presented.Comment: 17 pages, 1 figur

Reenacting sensorimotor features of drawing movements from friction sounds

International audienceEven though we generally don't pay attention to the friction sounds produced when we are writing or drawing, these sounds are recordable, and can even evoke the underlying gesture. In this paper, auditory perception of such sounds, and the internal representations they evoke when we listen to them, is considered from the sensorimotor learning point of view. The use of synthesis processes of friction sounds makes it possible to investigate the perceptual influence of each gestures parameter separately. Here, the influence of the velocity profile on the mental representation of the gesture induced by a friction sound was investigated through 3 experiments. The results reveal the perceptual relevance of this parameter, and particularly a specific morphology corresponding to biological movements, the so-called 1/3-power law. The experiments are discussed according to the sensorimotor theory and the invariant taxonomy of the ecological approach