700 research outputs found
Configuration mixing within the energy density functional formalism: pathologies and cures
Configuration mixing calculations performed in terms of the Skyrme/Gogny
Energy Density Functional (EDF) rely on extending the Single-Reference energy
functional into non-diagonal EDF kernels. The standard way to do so, based on
an analogy with the pure Hamiltonian case and the use of the generalized Wick
theorem, is responsible for the recently observed divergences and steps in
Multi-Reference calculations. We summarize here the minimal solution to this
problem recently proposed [Lacroix et al, arXiv:0809.2041] and applied with
success to particle number restoration[Bender et al, arXiv:0809.2045]. Such a
regularization method provides suitable corrections of pathologies for EDF
depending on integer powers of the density. The specific case of fractional
powers of the density[Duguet et al, arXiv:0809.2049] is also discussed.Comment: 5 pages, Proceedings of the French-Japanese Symposium, September
2008. To be published in Int. J. of Mod. Phys.
Do halos exist on the dripline of deformed nuclei?
A study of the effect of deformation and pairing on the development of halo
nuclei is presented. Exploratory three-body calculations show that
both the NN interaction and the deformation/excitation of the core hinder the
formation of the halo. Preliminary self-consistent mean-field calculations are
used to search for regions in the nuclear chart where halos could potentially
develop. These are also briefly discussed.Comment: 5 pages and 3 figures, proceedings for CGS1
Skyrme functional from a three-body pseudo-potential of second-order in gradients. Formalism for central terms
In one way or the other, all modern parametrizations of the nuclear energy
density functional (EDF) do not respect the exchange symmetry associated with
Pauli's principle. It has been recently shown that this practice jeopardizes
multi-reference (MR) EDF calculations by contaminating the energy with spurious
self-interactions that, for example, lead to finite steps or even divergences
when plotting it as a function of collective coordinates. As of today, the only
viable option to bypass these pathologies is to rely on EDF kernels that
enforce Pauli's principle from the outset by strictly and exactly deriving from
a genuine, i.e. density-independent, Hamilton operator.
We wish to develop the most general Skyrme-like EDF parametrization
containing linear, bilinear and trilinear terms in the density matrices with up
to two gradients, under the key constraint that it derives strictly from an
effective Hamilton operator. The most general three-body Skyrme-like
pseudo-potential containing up to two gradient operators is constructed to
generate the trilinear part. The present study is limited to central terms.
Spin-orbit and tensor will be addressed in a forthcoming paper.
(See paper for full abstract)Comment: 38 pages revtex, no figur
Pairing correlations beyond the mean field
We discuss dynamical pairing correlations in the context of configuration
mixing of projected self-consistent mean-field states, and the origin of a
divergence that might appear when such calculations are done using an energy
functional in the spirit of a naive generalized density functional theory.Comment: Proceedings of the XIII Nuclear Physics Workshop ``Maria and Pierre
Curie'' on ``Pairing and beyond - 50 years of the BCS model'', held at
Kazimierz Dolny, Poland, September 27 - October 1, 2006. Int. J. Mod. Phys.
E, in prin
Particle-Number Restoration within the Energy Density Functional formalism: Nonviability of terms depending on noninteger powers of the density matrices
We discuss the origin of pathological behaviors that have been recently
identified in particle-number-restoration calculations performed within the
nuclear energy density functional framework. A regularization method that
removes the problematic terms from the multi-reference energy density
functional and which applies (i) to any symmetry restoration- and/or
generator-coordinate-method-based configuration mixing calculation and (ii) to
energy density functionals depending only on integer powers of the density
matrices, was proposed in [D. Lacroix, T. Duguet, M. Bender, arXiv:0809.2041]
and implemented for particle-number restoration calculations in [M. Bender, T.
Duguet, D. Lacroix, arXiv:0809.2045]. In the present paper, we address the
viability of non-integer powers of the density matrices in the nuclear energy
density functional. Our discussion builds upon the analysis already carried out
in [J. Dobaczewski \emph{et al.}, Phys. Rev. C \textbf{76}, 054315 (2007)].
First, we propose to reduce the pathological nature of terms depending on a
non-integer power of the density matrices by regularizing the fraction that
relates to the integer part of the exponent using the method proposed in [D.
Lacroix, T. Duguet, M. Bender, arXiv:0809.2041]. Then, we discuss the spurious
features brought about by the remaining fractional power. Finally, we conclude
that non-integer powers of the density matrices are not viable and should be
avoided in the first place when constructing nuclear energy density functionals
that are eventually meant to be used in multi-reference calculations.Comment: 17 pages, 12 figures, accepted for publication in PR
Quasiparticle Coupled Cluster Theory for Pairing Interactions
We present an extension of the pair coupled cluster doubles (p-CCD) method to
quasiparticles and apply it to the attractive pairing Hamiltonian. Near the
transition point where number symmetry gets spontaneously broken, the proposed
BCS-based p-CCD method yields significantly better energies than existing
methods when compared to exact results obtained via solution of the Richardson
equations. The quasiparticle p-CCD method has a low computational cost of
as a function of system size. This together with the high
quality of results here demonstrated, points to considerable promise for the
accurate description of strongly correlated systems with more realistic pairing
interactions
The tensor part of the Skyrme energy density functional. I. Spherical nuclei
We perform a systematic study of the impact of the J^2 tensor term in the
Skyrme energy functional on properties of spherical nuclei. In the Skyrme
energy functional, the tensor terms originate both from zero-range central and
tensor forces. We build a set of 36 parameterizations, which covers a wide
range of the parameter space of the isoscalar and isovector tensor term
coupling constants, with a fit protocol very similar to that of the successful
SLy parameterizations. We analyze the impact of the tensor terms on a large
variety of observables in spherical mean-field calculations, such as the
spin-orbit splittings and single-particle spectra of doubly-magic nuclei, the
evolution of spin-orbit splittings along chains of semi-magic nuclei, mass
residuals of spherical nuclei, and known anomalies of charge radii. Our main
conclusion is that the currently used central and spin-orbit parts of the
Skyrme energy density functional are not flexible enough to allow for the
presence of large tensor terms.Comment: 38 pages, 36 figures; Minor correction
Shape Coexistence in Pb186: Beyond-mean-field description by configuration mixing of symmetry restored wave functions
We study shape coexistence in Pb186 using configuration mixing of
angular-momentum and particle-number projected self-consistent mean-field
states. The same Skyrme interaction SLy6 is used everywhere in connection with
a density-dependent zero-range pairing force. The model predicts coexisting
spherical, prolate and oblate 0+ states at low energy.Comment: 5 pages REVTEX4, 4 eps figures, accepted by Phys. Lett. B. Revised
version with some polishing of the text without changing its conten
Functional approach for pairing in finite systems: How to define restoration of broken symmetries in Energy Density Functional theory ?
The Multi-Reference Energy Density Functional (MR-EDF) approach (also called
configuration mixing or Generator Coordinate Method), that is commonly used to
treat pairing in finite nuclei and project onto particle number, is
re-analyzed. It is shown that, under certain conditions, the MR-EDF energy can
be interpreted as a functional of the one-body density matrix of the projected
state with good particle number. Based on this observation, we propose a new
approach, called Symmetry-Conserving EDF (SC-EDF), where the breaking and
restoration of symmetry are accounted for simultaneously. We show, that such an
approach is free from pathologies recently observed in MR-EDF and can be used
with a large flexibility on the density dependence of the functional.Comment: proceeding of the conference "Many body correlations from dilute to
dense Nuclear systems", Paris, February 201
New analysis method of the halo phenomenon in finite many-fermion systems. First applications to medium-mass atomic nuclei
A new analysis method to investigate halos in finite many-fermion systems is
designed, as existing characterization methods are proven to be
incomplete/inaccurate. A decomposition of the internal wave-function of the
{-body} system in terms of overlap functions allows a model-independent
analysis of medium-range and asymptotic properties of the internal one-body
density. The existence of a spatially decorrelated region in the density
profile is related to the existence of three typical energy scales in the
excitation spectrum of the {-body} system. A series of model-independent
measures, taking the internal density as the only input, are introduced. The
new measures allow a quantification of the potential halo in terms of the
average number of fermions participating to it and of its impact on the system
extension. Those new "halo factors" are validated through simulations and
applied to results obtained through energy density functional calculations of
medium-mass nuclei. Performing spherical Hartree-Fock-Bogoliubov calculations
with state-of-the-art Skyrme plus pairing functionals, a collective halo is
predicted in drip-line Cr isotopes, whereas no such effect is seen in Sn
isotopes.Comment: 27 Pages, 29 Figures. Accepted for publication in Phys. Rev. C
back-to-back with second part (arXiv:0711.1275
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