1,960 research outputs found
The harmonic hyperspherical basis for identical particles without permutational symmetry
The hyperspherical harmonic basis is used to describe bound states in an
--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 partial waves, and with applicability in multichannel
reactions. The convergence of the -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 He atom on a \dimer
dimer (only the elastic channel open), and for collisions involving a Li
and two 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
is that it be the solution of 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 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 He-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 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
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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
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