314 research outputs found
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
Chemotactic predator-prey dynamics
A discrete chemotactic predator-prey model is proposed in which the prey
secrets a diffusing chemical which is sensed by the predator and vice versa.
Two dynamical states corresponding to catching and escaping are identified and
it is shown that steady hunting is unstable. For the escape process, the
predator-prey distance is diffusive for short times but exhibits a transient
subdiffusive behavior which scales as a power law with time and
ultimately crosses over to diffusion again. This allows to classify the
motility and dynamics of various predatory bacteria and phagocytes. In
particular, there is a distinct region in the parameter space where they prove
to be infallible predators.Comment: 4 pages, 4 figure
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
Shell Corrections for Finite-Depth Deformed Potentials: Green's Function Oscillator Expansion Method
Shell corrections of the finite deformed Woods-Saxon potential are calculated
using the Green's function method and the generalized Strutinsky smoothing
procedure. They are compared with the results of the standard prescription
which are affected by the spurious contribution from the unphysical particle
gas. In the new method, the shell correction approaches the exact limit
provided that the dimension of the single-particle (harmonic oscillator) basis
is sufficiently large. For spherical potentials, the present method is faster
than the exact one in which the contribution from the particle continuum states
is explicitly calculated. For deformed potentials, the Green's function method
offers a practical and reliable way of calculating shell corrections for weakly
bound nuclei.Comment: submitted to Phys. Rev. C, 12 pages, 7 figure
Modified two-potential approach to tunneling problems
One-body quantum tunneling to continuum is treated via the two-potential
approach, dividing the tunneling potential into external and internal parts. We
show that corrections to this approach can be minimized by taking the
separation radius inside the interval determined by simple expressions. The
resulting two-potential approach reproduces the resonance energy and its width,
both for narrow and wide resonances. We also demonstrate that, without losing
its accuracy, the two-potential approach can be modified to a form resembling
the R-matrix theory, yet without any uncertainties of the latter related to the
choice of the matching radius.Comment: 7 two-column pages, 3 figures, extra-explanation added, Phys. Rev. A,
in pres
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
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