The harmonic hyperspherical basis for identical particles without permutational symmetry

The hyperspherical harmonic basis is used to describe bound states in an $A$--body system. The approach presented here is based on the representation of the potential energy in terms of hyperspherical harmonic functions. Using this representation, the matrix elements between the basis elements are simple, and the potential energy is presented in a compact form, well suited for numerical implementation. The basis is neither symmetrized nor antisymmetrized, as required in the case of identical particles; however, after the diagonalization of the Hamiltonian matrix, the eigenvectors reflect the symmetries present in it, and the identification of the physical states is possible, as it will be shown in specific cases. We have in mind applications to atomic, molecular, and nuclear few-body systems in which symmetry breaking terms are present in the Hamiltonian; their inclusion is straightforward in the present method. As an example we solve the case of three and four particles interacting through a short-range central interaction and Coulomb potential

General integral relations for the description of scattering states using the hyperspherical adiabatic basis

In this work we investigate 1+2 reactions within the framework of the hyperspherical adiabatic expansion method. To this aim two integral relations, derived from the Kohn variational principle, are used. A detailed derivation of these relations is shown. The expressions derived are general, not restricted to relative $s$ partial waves, and with applicability in multichannel reactions. The convergence of the ${\cal K}$-matrix in terms of the adiabatic potentials is investigated. Together with a simple model case used as a test for the method, we show results for the collision of a $^4$He atom on a \dimer dimer (only the elastic channel open), and for collisions involving a $^6$Li and two $^4$He atoms (two channels open).Comment: Accepted for publication in Physical Review

Variational description of continuum states in terms of integral relations

Two integral relations derived from the Kohn Variational Principle (KVP) are used for describing scattering states. In usual applications the KVP requires the explicit form of the asymptotic behavior of the scattering wave function. This is not the case when the integral relations are applied since, due to their short range nature, the only condition for the scattering wave function $\Psi$ is that it be the solution of $(H-E)\Psi=0$ in the internal region. Several examples are analyzed for the computation of phase-shifts from bound state type wave functions or, in the case of the scattering of charged particles, it is possible to obtain phase-shifts using free asymptotic conditions. As a final example we discuss the use of the integral relations in the case of the Hyperspherical Adiabatic method.Comment: 34 pages, 7 figures, accepted in Phys. Rev.

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

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

Haptic guidance improves the visuo-manual tracking of trajectories

BACKGROUND: Learning to perform new movements is usually achieved by following visual demonstrations. Haptic guidance by a force feedback device is a recent and original technology which provides additional proprioceptive cues during visuo-motor learning tasks. The effects of two types of haptic guidances-control in position (HGP) or in force (HGF)-on visuo-manual tracking ("following") of trajectories are still under debate. METHODOLOGY/PRINCIPALS FINDINGS: Three training techniques of haptic guidance (HGP, HGF or control condition, NHG, without haptic guidance) were evaluated in two experiments. Movements produced by adults were assessed in terms of shapes (dynamic time warping) and kinematics criteria (number of velocity peaks and mean velocity) before and after the training sessions. CONCLUSION/SIGNIFICANCE: These results show that the addition of haptic information, probably encoded in force coordinates, play a crucial role on the visuo-manual tracking of new trajectories

Parameter-Free Calculation of the Solar Proton Fusion Rate in Effective Field Theory

Spurred by the recent complete determination of the weak currents in two-nucleon systems up to ${\cal O}(Q^3)$ in heavy-baryon chiral perturbation theory, we carry out a parameter-free calculation of the solar proton fusion rate in an effective field theory that combines the merits of the standard nuclear physics method and systematic chiral expansion. Using the tritium beta-decay rate as an input to fix the only unknown parameter in the effective Lagrangian, we can evaluate with drastically improved precision the ratio of the two-body contribution to the well established one-body contribution; the ratio is determined to be (0.86\pm 0.05) %. This result is essentially independent of the cutoff parameter for a wide range of its variation (500 MeV \le \Lambda \le 800 MeV), a feature that substantiates the consistency of the calculation.Comment: 10 pages. The argument is considerably more sharpened with a reduced error ba

Realistic Calculation of the hep Astrophysical Factor

The astrophysical factor for the proton weak capture on 3He is calculated with correlated-hyperspherical-harmonics bound and continuum wave functions corresponding to a realistic Hamiltonian consisting of the Argonne v18 two-nucleon and Urbana-IX three-nucleon interactions. The nuclear weak charge and current operators have vector and axial-vector components, that include one- and many-body terms. All possible multipole transitions connecting any of the p-3He S- and P-wave channels to the 4He bound state are considered. The S-factor at a p-3He center-of-mass energy of 10 keV, close to the Gamow-peak energy, is predicted to be 10.1 10^{-20} keV b, a factor of five larger than the standard-solar-model value. The P-wave transitions are found to be important, contributing about 40 % of the calculated S-factor.Comment: 8 pages RevTex file, submitted to Phys. Rev. Let

Comparison of experimental and numerical sloshing loads in partially filled tanks

Sloshing phenomenon consists in the movement of liquids inside partially filled tanks, whichgenerates dynamic loads on the tank structure. Resulting impact pressures are of great importance in assessingstructural strength, and their correct evaluation still represents a challenge for the designer due to the highnonlinearities involved, with complex free surface deformations, violent impact phenomena and influence of airtrapping. In the present paper a set of two-dimensional cases for which experimental results are available areconsidered to assess merits and shortcomings of different numerical methods for sloshing evaluation, namely twocommercial RANS solvers (FLOW-3D and LS-DYNA), and two own developed methods (Smoothed ParticleHydrodynamics and RANS). Impact pressures at different critical locations and global moment induced by watermotion for a partially filled tank with rectangular section having a rolling motion have been evaluated and resultsare compared with experiments