13,703 research outputs found
From Microscales to Macroscales in 3D: Selfconsistent Equation of State for Supernova and Neutron Star Models
First results from a fully self-consistent, temperature-dependent equation of
state that spans the whole density range of neutron stars and supernova cores
are presented. The equation of state (EoS) is calculated using a mean-field
Hartree-Fock method in three dimensions (3D). The nuclear interaction is
represented by the phenomenological Skyrme model in this work, but the EoS can
be obtained in our framework for any suitable form of the nucleon-nucleon
effective interaction. The scheme we employ naturally allows effects such as
(i) neutron drip, which results in an external neutron gas, (ii) the variety of
exotic nuclear shapes expected for extremely neutron heavy nuclei, and (iii)
the subsequent dissolution of these nuclei into nuclear matter. In this way,
the equation of state is calculated across phase transitions without recourse
to interpolation techniques between density regimes described by different
physical models. EoS tables are calculated in the wide range of densities,
temperature and proton/neutron ratios on the ORNL NCCS XT3, using up to 2000
processors simultaneously.Comment: 6 pages, 11 figures. Published in conference proceedings Journal of
Physics: Conference Series 46 (2006) 408. Extended version to be submitted to
Phys. Rev.
Levinson's Theorem for Non-local Interactions in Two Dimensions
In the light of the Sturm-Liouville theorem, the Levinson theorem for the
Schr\"{o}dinger equation with both local and non-local cylindrically symmetric
potentials is studied. It is proved that the two-dimensional Levinson theorem
holds for the case with both local and non-local cylindrically symmetric cutoff
potentials, which is not necessarily separable. In addition, the problems
related to the positive-energy bound states and the physically redundant state
are also discussed in this paper.Comment: Latex 11 pages, no figure, submitted to J. Phys. A Email:
[email protected], [email protected]
Nilsson diagrams for light neutron-rich nuclei with weakly-bound neutrons
Using Woods-Saxon potentials and the eigenphase formalism for one-particle
resonances, one-particle bound and resonant levels for neutrons as a function
of quadrupole deformation are presented, which are supposed to be useful for
the interpretation of spectroscopic properties of some light neutron-rich
nuclei with weakly-bound neutrons. Compared with Nilsson diagrams in text books
which are constructed using modified oscillator potentials, we point out a
systematic change of the shell structure in connection with both weakly-bound
and resonant one-particle levels related to small orbital angular momenta
. Then, it is seen that weakly-bound neutrons in nuclei such as
C and Mg may prefer to being deformed as a result of
Jahn-Teller effect, due to the near degeneracy of the 1d-2s
levels and the 1f-2p levels in the spherical potential,
respectively. Furthermore, the absence of some one-particle resonant levels
compared with the Nilsson diagrams in text books is illustrated.Comment: 12 pages, 5 figure
Levinson's theorem for the Schr\"{o}dinger equation in two dimensions
Levinson's theorem for the Schr\"{o}dinger equation with a cylindrically
symmetric potential in two dimensions is re-established by the Sturm-Liouville
theorem. The critical case, where the Schr\"{o}dinger equation has a finite
zero-energy solution, is analyzed in detail. It is shown that, in comparison
with Levinson's theorem in non-critical case, the half bound state for
wave, in which the wave function for the zero-energy solution does not decay
fast enough at infinity to be square integrable, will cause the phase shift of
wave at zero energy to increase an additional .Comment: Latex 11 pages, no figure and accepted by P.R.A (in August); Email:
[email protected], [email protected]
On the number of particles which a curved quantum waveguide can bind
We discuss the discrete spectrum of N particles in a curved planar waveguide.
If they are neutral fermions, the maximum number of particles which the
waveguide can bind is given by a one-particle Birman-Schwinger bound in
combination with the Pauli principle. On the other hand, if they are charged,
e.g., electrons in a bent quantum wire, the Coulomb repulsion plays a crucial
role. We prove a sufficient condition under which the discrete spectrum of such
a system is empty.Comment: a LateX file, 12 page
The equation of state of neutron star matter and the symmetry energy
We present an overview of microscopical calculations of the Equation of State
(EOS) of neutron matter performed using Quantum Monte Carlo techniques. We
focus to the role of the model of the three-neutron force in the high-density
part of the EOS up to a few times the saturation density. We also discuss the
interplay between the symmetry energy and the neutron star mass-radius
relation.
The combination of theoretical models of the EOS with recent neutron stars
observations permits us to constrain the value of the symmetry energy and its
slope. We show that astrophysical observations are starting to provide
important insights into the properties of neutron star matter.Comment: 7 pages, 3 figure, talk given at the 11th International Conference on
Nucleus-Nucleus Collisions (NN2012), San Antonio, Texas, USA, May 27-June 1,
2012. To appear in the NN2012 Proceedings in Journal of Physics: Conference
Series (JPCS
The Relativistic Levinson Theorem in Two Dimensions
In the light of the generalized Sturm-Liouville theorem, the Levinson theorem
for the Dirac equation in two dimensions is established as a relation between
the total number of the bound states and the sum of the phase shifts
of the scattering states with the angular momentum :
\noindent The critical case, where the Dirac equation has a finite
zero-momentum solution, is analyzed in detail. A zero-momentum solution is
called a half bound state if its wave function is finite but does not decay
fast enough at infinity to be square integrable.Comment: Latex 14 pages, no figure, submitted to Phys.Rev.A; Email:
[email protected], [email protected]
Generalized Mean Field Approach to a Resonant Bose-Fermi Mixture
We formulate a generalized mean-field theory of a mixture of fermionic and
bosonic atoms, in which the fermion-boson interaction can be controlled by a
Feshbach resonance. The theory correctly accounts for molecular binding
energies of the molecules in the two-body limit, in contrast to the most
straightforward mean-field theory. Using this theory, we discuss the
equilibrium properties of fermionic molecules created from atom pairs in the
gas. We also address the formation of molecules when the magnetic field is
ramped across the resonance, and present a simple Landau-Zener result for this
process.Comment: 35 page
Viscous evolution of point vortex equilibria: The collinear state
When point vortex equilibria of the 2D Euler equations are used as initial
conditions for the corre- sponding Navier-Stokes equations (viscous), typically
an interesting dynamical process unfolds at short and intermediate time scales,
before the long time single peaked, self-similar Oseen vortex state dom-
inates. In this paper, we describe the viscous evolution of a collinear three
vortex structure that cor- responds to an inviscid point vortex fixed
equilibrium. Using a multi-Gaussian 'core-growth' type of model, we show that
the system immediately begins to rotate unsteadily, a mechanism we attribute to
a 'viscously induced' instability. We then examine in detail the qualitative
and quantitative evolution of the system as it evolves toward the long-time
asymptotic Lamb-Oseen state, showing the sequence of topological bifurcations
that occur both in a fixed reference frame, and in an appropriately chosen
rotating reference frame. The evolution of passive particles in this viscously
evolving flow is shown and interpreted in relation to these evolving streamline
patterns.Comment: 17 pages, 15 figure
- …