16,793 research outputs found
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
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.
Nuclear three-body problem in the complex energy plane: Complex-Scaling-Slater method
The physics of open quantum systems is an interdisciplinary area of research.
The nuclear "openness" manifests itself through the presence of the many-body
continuum representing various decay, scattering, and reaction channels. As the
radioactive nuclear beam experimentation extends the known nuclear landscape
towards the particle drip lines, the coupling to the continuum space becomes
exceedingly more important. Of particular interest are weakly bound and unbound
nuclear states appearing around particle thresholds. Theories of such nuclei
must take into account their open quantum nature. To describe open quantum
systems, we introduce a Complex Scaling (CS) approach in the Slater basis. We
benchmark it with the complex-energy Gamow Shell Model (GSM) by studying
energies and wave functions of the bound and unbound states of the two-neutron
halo nucleus 6He viewed as an + n + n cluster system. In the CS
approach, we use the Slater basis, which exhibits the correct asymptotic
behavior at large distances. To extract particle densities from the
back-rotated CS solutions, we apply the Tikhonov regularization procedure,
which minimizes the ultraviolet numerical noise. While standard applications of
the inverse complex transformation to the complex-rotated solution provide
unstable results, the stabilization method fully reproduces the GSM benchmark.
We also propose a method to determine the smoothing parameter of the Tikhonov
regularization. The combined suite of CS-Slater and GSM techniques has many
attractive features when applied to nuclear problems involving weakly-bound and
unbound states. While both methods can describe energies, total widths, and
wave functions of nuclear states, the CS-Slater method, if it can be applied,
can provide an additional information about partial energy widths associated
with individual thresholds.Comment: 15 pages, 16 figure
Uniform WKB approximation of Coulomb wave functions for arbitrary partial wave
Coulomb wave functions are difficult to compute numerically for extremely low
energies, even with direct numerical integration. Hence, it is more convenient
to use asymptotic formulas in this region. It is the object of this paper to
derive analytical asymptotic formulas valid for arbitrary energies and partial
waves. Moreover, it is possible to extend these formulas for complex values of
parameters.Comment: 5 pages, 2 figure
Crystal Structures of Polymerized Fullerides AC60, A=K, Rb, Cs and Alkali-mediated Interactions
Starting from a model of rigid interacting C60 polymer chains on an
orthorhombic lattice, we study the mutual orientation of the chains and the
stability of the crystalline structures Pmnn and I2/m. We take into account i)
van der Waals interactions and electric quadrupole interactions between C60
monomers on different chains as well as ii) interactions of the monomers with
the surrounding alkali atoms. The direct interactions i) always lead to an
antiferrorotational structure Pmnn with alternate orientation of the C60 chains
in planes (001). The interactions ii) with the alkalis consist of two parts:
translation-rotation (TR) coupling where the orientations of the chains
interact with displacements of the alkalis, and quadrupolar electronic
polarizability (ep) coupling, where the electric quadrupoles on the C60
monomers interact with induced quadrupoles due to excited electronic d states
of the alkalis. Both interactions ii) lead to an effective
orientation-orientation interaction between the C60 chains and always favor the
ferrorotational structure I2/m where C60 chains have a same orientation. The
structures Pmnn for KC60 and I2/m for Rb- and CsC60 are the result of a
competition between the direct interaction i) and the alkali-mediated
interactions ii). In Rb- and CsC60 the latter are found to be dominant, the
preponderant role being played by the quadrupolar electronic polarizability of
the alkali ions.Comment: J.Chem.Phys., in press, 14 pages, 3 figures, 8 table
Access to improve the muon mass and magnetic moment anomaly via the bound-muon factor
A theoretical description of the factor of a muon bound in a nuclear
potential is presented. One-loop self-energy and multi-loop vacuum polarization
corrections are calculated, taking into account the interaction with the
binding potential exactly. Nuclear effects on the bound-muon factor are
also evaluated. We put forward the measurement of the bound-muon factor via
the continuous Stern-Gerlach effect as an independent means to determine the
free muons magnetic moment anomaly and mass. The scheme presented enables to
increase the accuracy of the mass by more than an order of magnitude
Accretion of Ghost Condensate by Black Holes
The intent of this letter is to point out that the accretion of a ghost
condensate by black holes could be extremely efficient. We analyze steady-state
spherically symmetric flows of the ghost fluid in the gravitational field of a
Schwarzschild black hole and calculate the accretion rate. Unlike minimally
coupled scalar field or quintessence, the accretion rate is set not by the
cosmological energy density of the field, but by the energy scale of the ghost
condensate theory. If hydrodynamical flow is established, it could be as high
as tenth of a solar mass per second for 10MeV-scale ghost condensate accreting
onto a stellar-sized black hole, which puts serious constraints on the
parameters of the ghost condensate model.Comment: 5 pages, 3 figures, REVTeX 4.0; discussion expande
Chaotic motion of charged particles in toroidal magnetic configurations
We study the motion of a charged particle in a tokamak magnetic field and
discuss its chaotic nature. Contrary to most of recent studies, we do not make
any assumption on any constant of the motion and solve numerically the
cyclotron gyration using Hamiltonian formalism. We take advantage of a
symplectic integrator allowing us to make long-time simulations. First
considering an idealized magnetic configuration, we add a non generic
perturbation corresponding to a magnetic ripple, breaking one of the invariant
of the motion. Chaotic motion is then observed and opens questions about the
link between chaos of magnetic field lines and chaos of particle trajectories.
Second, we return to a axi-symmetric configuration and tune the safety factor
(magnetic configuration) in order to recover chaotic motion. In this last
setting with two constants of the motion, the presence of chaos implies that no
third global constant exists, we highlight this fact by looking at variations
of the first order of the magnetic moment in this chaotic setting. We are
facing a mixed phase space with both regular and chaotic regions and point out
the difficulties in performing a global reduction such as gyrokinetics
A Methodology to Engineer and Validate Dynamic Multi-level Multi-agent Based Simulations
This article proposes a methodology to model and simulate complex systems,
based on IRM4MLS, a generic agent-based meta-model able to deal with
multi-level systems. This methodology permits the engineering of dynamic
multi-level agent-based models, to represent complex systems over several
scales and domains of interest. Its goal is to simulate a phenomenon using
dynamically the lightest representation to save computer resources without loss
of information. This methodology is based on two mechanisms: (1) the activation
or deactivation of agents representing different domain parts of the same
phenomenon and (2) the aggregation or disaggregation of agents representing the
same phenomenon at different scales.Comment: Presented at 3th International Workshop on Multi-Agent Based
Simulation, Valencia, Spain, 5th June 201
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