22,983 research outputs found
A simple and efficient numerical scheme to integrate non-local potentials
As nuclear wave functions have to obey the Pauli principle, potentials issued
from reaction theory or Hartree-Fock formalism using finite-range interactions
contain a non-local part. Written in coordinate space representation, the
Schrodinger equation becomes integro-differential, which is difficult to solve,
contrary to the case of local potentials, where it is an ordinary differential
equation. A simple and powerful method has been proposed several years ago,
with the trivially equivalent potential method, where non-local potential is
replaced by an equivalent local potential, which is state-dependent and has to
be determined iteratively. Its main disadvantage, however, is the appearance of
divergences in potentials if the wave functions have nodes, which is generally
the case. We will show that divergences can be removed by a slight modification
of the trivially equivalent potential method, leading to a very simple, stable
and precise numerical technique to deal with non-local potentials. Examples
will be provided with the calculation of the Hartree-Fock potential and
associated wave functions of 16O using the finite-range N3LO realistic
interaction.Comment: 8 pages, 2 figures, submitted to Eur. Phys. J.
Density Matrix Renormalization Group study of Cr and Ni
We discuss the development of an angular-momentum-conserving variant of the
Density Matrix Renormalization Group (DMRG) method for use in large-scale
shell-model calculations of atomic nuclei and report a first application of the
method to the ground state of Ni and improved results for Cr. In
both cases, we see a high level of agreement with the exact results. A
comparison of the two shows a dramatic reduction in the fraction of the space
required to achieve accuracy as the size of the problem grows.Comment: 4 pages. Published in PRC Rapi
Gamow Shell-Model Description of Weakly Bound and Unbound Nuclear States
Recently, the shell model in the complex k-plane (the so-called Gamow Shell
Model) has been formulated using a complex Berggren ensemble representing bound
single-particle states, single-particle resonances, and non-resonant continuum
states. In this framework, we shall discuss binding energies and energy spectra
of neutron-rich helium and lithium isotopes. The single-particle basis used is
that of the Hartree-Fock potential generated self-consistently by the
finite-range residual interaction.Comment: 13 pages, 2 figures, presented by N. Michel at the XXVII Symposium On
Nuclear Physics, Taxco, Guerrero, Mexico, January 5-8 200
Approximate solution of the pairing Hamiltonian in the Berggren basis
We derive the approximate solution for the pairing Hamiltonian in the
Berggren ensemble of single particle states including bound, resonance and
non-resonant scattering states. We show that this solution is reliable in the
limit of a weak pairing interaction
The Functional Integral for a Free Particle on a Half-Plane
A free non-relativistic particle moving in two dimensions on a half-plane can
be described by self-adjoint Hamiltonians characterized by boundary conditions
imposed on the systems. The most general boundary condition is parameterized in
terms of the elements of an infinite-dimensional matrix. We construct the
Brownian functional integral for each of these self-adjoint Hamiltonians.
Non-local boundary conditions are implemented by allowing the paths striking
the boundary to jump to other locations on the boundary. Analytic continuation
in time results in the Green's functions of the Schrodinger equation satisfying
the boundary condition characterizing the self-adjoint Hamiltonian.Comment: 16 page
Isospin mixing and the continuum coupling in weakly bound nuclei
The isospin breaking effects due to the Coulomb interaction in weakly-bound
nuclei are studied using the Gamow Shell Model, a complex-energy configuration
interaction approach which simultaneously takes into account many-body
correlations between valence nucleons and continuum effects. We investigate the
near-threshold behavior of one-nucleon spectroscopic factors and the structure
of wave functions along an isomultiplet. Illustrative calculations are carried
out for the T=1 isobaric triplet. By using a shell-model Hamiltonian consisting
of an isoscalar nuclear interaction and the Coulomb term, we demonstrate that
for weakly bound or unbound systems the structure of isobaric analog states
varies within the isotriplet and impacts the energy dependence of spectroscopic
factors. We discuss the partial dynamical isospin symmetry present in
isospin-stretched systems, in spite of the Coulomb interaction that gives rise
to large mirror symmetry breaking effects.Comment: 10 pages, 5 figures ; published versio
Weakly bound systems, continuum effects, and reactions
Structure of weakly bound/unbound nuclei close to particle drip lines is
different from that around the valley of beta stability. A comprehensive
description of these systems goes beyond standard Shell Model and demands an
open quantum system description of the nuclear many-body system. We approach
this problem using the Gamow Shell Model which provides a fully microscopic
description of bound and unbound nuclear states, nuclear decays, and reactions.
We present in this paper the first application of the GSM for a description of
the elastic and inelastic scattering of protons on 6He.Comment: Proc. Int. Conf. "Horizons of Innovative Theories, Experiments and
Supercomputing in Nuclear Physics", June 4-7, 2012, New Orleans, Luisiana,
USA; 10 pages, 4 figure
Time resolved tracking of a sound scatterer in a turbulent flow: non-stationary signal analysis and applications
It is known that ultrasound techniques yield non-intrusive measurements of
hydrodynamic flows. For example, the study of the echoes produced by a large
number of particle insonified by pulsed wavetrains has led to a now standard
velocimetry technique. In this paper, we propose to extend the method to the
continuous tracking of one single particle embedded in a complex flow. This
gives a Lagrangian measurement of the fluid motion, which is of importance in
mixing and turbulence studies. The method relies on the ability to resolve in
time the Doppler shift of the sound scattered by the continuously insonfied
particle.
For this signal processing problem two classes of approaches are used:
time-frequency analysis and parametric high resolution methods. In the first
class we consider the spectrogram and reassigned spectrogram, and we apply it
to detect the motion of a small bead settling in a fluid at rest. In more
non-stationary turbulent flows where methods in the second class are more
robust, we have adapted an Approximated Maximum Likelihood technique coupled
with a generalized Kalman filter.Comment: 16 pages 9 figure
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