555 research outputs found
Description of two-electron atoms with correct cusp conditions
New sets of functions with arbitrary large finite cardinality are constructed
for two-electron atoms. Functions from these sets exactly satisfy the Kato's
cusp conditions. The new functions are special linear combinations of
Hylleraas- and/or Kinoshita-type terms. Standard variational calculation,
leading to matrix eigenvalue problem, can be carried out to calculate the
energies of the system. There is no need for optimization with constraints to
satisfy the cusp conditions. In the numerical examples the ground state energy
of the He atom is considered
Quasi-particle continuum and resonances in the Hartree-Fock-Bogoliubov theory
The quasi-particle energy spectrum of the Hartree-Fock-Bogoliubov (HFB)
equations contains discrete bound states, resonances, and non-resonant
continuum states. We study the structure of the unbound quasi-particle spectrum
of weakly bound nuclei within several methods that do not rely on imposing
scattering or outgoing boundary conditions. Various approximations are examined
to estimate resonance widths. It is shown that the stabilization method works
well for all HFB resonances except for very narrow ones.
The Thomas-Fermi approximation to the non-resonant continuum has been shown
to be very effective, especially for coordinate-space HFB calculations in large
boxes that involve huge amounts of discretized quasi-particle continuum states.Comment: 12 pages,11 figures,submitted to PR
Shell corrections for finite depth potentials: Particle continuum effects
Shell corrections of finite, spherical, one-body potentials are analyzed
using a smoothing procedure which properly accounts for the contribution from
the particle continuum, i.e., unbound states. Since the plateau condition for
the smoothed single-particle energy seldom holds, a new recipe is suggested for
the definition of the shell correction. The generalized Strutinsky smoothing
procedure is compared with the results of the semi-classical Wigner-Kirkwood
expansion. A good agreement has been found for weakly bound nuclei in the
vicinity of the proton drip line. However, some deviations remain for extremely
neutron-rich systems due to the pathological behavior of the semi-classical
level density around the particle threshold.Comment: 18 pages, 8 figure
Soft repulsive mixtures under gravity: brazil-nut effect, depletion bubbles, boundary layering, nonequilibrium shaking
A binary mixture of particles interacting via long-ranged repulsive forces is
studied in gravity by computer simulation and theory. The more repulsive
A-particles create a depletion zone of less repulsive B-particles around them
reminiscent to a bubble. Applying Archimedes' principle effectively to this
bubble, an A-particle can be lifted in a fluid background of B-particles. This
"depletion bubble" mechanism explains and predicts a brazil-nut effect where
the heavier A-particles float on top of the lighter B-particles. It also
implies an effective attraction of an A-particle towards a hard container
bottom wall which leads to boundary layering of A-particles. Additionally, we
have studied a periodic inversion of gravity causing perpetual mutual
penetration of the mixture in a slit geometry. In this nonequilibrium case of
time-dependent gravity, the boundary layering persists. Our results are based
on computer simulations and density functional theory of a two-dimensional
binary mixture of colloidal repulsive dipoles. The predicted effects also occur
for other long-ranged repulsive interactions and in three spatial dimensions.
They are therefore verifiable in settling experiments on dipolar or charged
colloidal mixtures as well as in charged granulates and dusty plasmas.Comment: 10 pages, 11 figure
Particle-unstable nuclei in the Hartree-Fock theory
Ground state energies and decay widths of particle unstable nuclei are
calculated within the Hartree-Fock approximation by performing a complex
scaling of the many-body Hamiltonian. Through this transformation, the wave
functions of the resonant states become square integrable. The method is
implemented with Skyrme effective interactions. Several Skyrme parametrizations
are tested on four unstable nuclei: 10He, 12O, 26O and 28O.Comment: 5 pages, LaTeX, submitted to Phys. Rev. Let
Entanglement and correlation in two-nucleon systems
We examine the mode entanglement and correlation of two fermionic particles.
We study the one- and two-mode entropy and a global characteristic, the
one-body entanglement entropy. We consider not only angular momentum coupled
states with single configuration but use the configuration interaction method.
With the help of the Slater decomposition, we derive analytical expressions for
the entanglement measures. We show that when the total angular momentum is zero
specific single configurations describe maximally entangled states. It turns
out that for a finite number of associated modes the one- and two-mode
entropies have identical values. In the shell model framework, we numerically
study two valence neutrons in the shell. The one-body entanglement entropy
of the ground state is close to the maximal value and the associated modes have
the largest mutual information.Comment: 20 pages, 1 figur
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