282 research outputs found
Development of a Web-based software tool for predicting the occurrence and effect of air pollutants inside museum buildings
22-27 September 200
Precise Coulomb wave functions for a wide range of complex l, eta and z
A new algorithm to calculate Coulomb wave functions with all of its arguments
complex is proposed. For that purpose, standard methods such as continued
fractions and power/asymptotic series are combined with direct integrations of
the Schrodinger equation in order to provide very stable calculations, even for
large values of |eta| or |Im(l)|. Moreover, a simple analytic continuation for
Re(z) < 0 is introduced, so that this zone of the complex z-plane does not pose
any problem. This code is particularly well suited for low-energy calculations
and the calculation of resonances with extremely small widths. Numerical
instabilities appear, however, when both |eta| and |Im(l)| are large and
|Re(l)| comparable or smaller than |Im(l)|
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
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
Chaos and isospin symmetry breaking in rotational nuclei
For nuclei with N = Z, the isospin degree of freedom is important and, for
deformed systems, rotational bands of different isospin may be expected at low
excitation energies. We have investigated, in a simple model space, the
influence of the isospin-breaking Coulomb interaction on the degree of
chaoticity of these rotational bands. The statistical measures used rely on an
analysis of level-spacing distributions, which are extremely difficult to
measure experimentally. We show, however, that the overlap intergrals between
states of similar frequency reflect well the degree of chaoticity. This
quantity is closely related to the experimentally more accessible gamma-decay
``spreading width''.Comment: 13 pages, 9 figures, Elsevie
Effects of resonant single-particle states on pairing correlations
Effects of resonant single-particle (s.p.) states on the pairing correlations
are investigated by an exact treatment of the pairing Hamiltonian on the Gamow
shell model basis. We introduce the s.p. states with complex energies into the
Richardson equations. The solution shows the property that the resonant s.p.
states with large widths are less occupied. The importance of many-body
correlations between bound and resonant prticle pairs is shown.Comment: 4 pages, 3 figures, to be published in Phys. Rev.
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