9 research outputs found
On the breaking and restoration of symmetries within the nuclear energy density functional formalism
We review the notion of symmetry breaking and restoration within the frame of
nuclear energy density functional methods. We focus on key differences between
wave-function- and energy-functional-based methods. In particular, we point to
difficulties encountered within the energy functional framework and discuss new
potential constraints on the underlying energy density functional that could
make the restoration of broken symmetries better formulated within such a
formalism. We refer to Ref.~\cite{duguet10a} for details.Comment: 5 pages, presented at the 17th nuclear physics conference "Marie and
Pierre Curie", September 2010, Kazimierz Dolny, Polan
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
Breaking and restoring symmetries within the nuclear energy density functional method
We review the notion of symmetry breaking and restoration within the frame of
nuclear energy density functional methods. We focus on key differences between
wave-function- and energy-functional-based methods. In particular, we point to
difficulties to formulate the restoration of symmetries within the energy
functional framework. The problems tackled recently in connection with
particle-number restoration serve as a baseline to the present discussion.
Reaching out to angular-momentum restoration, we identify an exact mathematical
property of the energy density that could be used to
constrain energy density functional kernels. Consequently, we suggest possible
routes towards a better formulation of symmetry restorations within energy
density functional methods.Comment: 16 pages, 3 figures, contribution to the "Focus issue on Open
Problems in Nuclear Structure", Journal of Physics
Ab initio derivation of model energy density functionals
I propose a simple and manageable method that allows for deriving coupling constants of model energy density functionals (EDFs) directly from ab initio calculations performed for finite fermion systems. A proof-of-principle application allows for linking properties of finite nuclei, determined by using the nuclear nonlocal Gogny functional, to the coupling constants of the quasilocal Skyrme functional. The method does not rely on properties of infinite fermion systems but on the ab initio calculations in finite systems. It also allows for quantifying merits of different model EDFs in describing the ab initio results
The nuclear energy density functional formalism
The present document focuses on the theoretical foundations of the nuclear
energy density functional (EDF) method. As such, it does not aim at reviewing
the status of the field, at covering all possible ramifications of the approach
or at presenting recent achievements and applications. The objective is to
provide a modern account of the nuclear EDF formalism that is at variance with
traditional presentations that rely, at one point or another, on a {\it
Hamiltonian-based} picture. The latter is not general enough to encompass what
the nuclear EDF method represents as of today. Specifically, the traditional
Hamiltonian-based picture does not allow one to grasp the difficulties
associated with the fact that currently available parametrizations of the
energy kernel at play in the method do not derive from a genuine
Hamilton operator, would the latter be effective. The method is formulated from
the outset through the most general multi-reference, i.e. beyond mean-field,
implementation such that the single-reference, i.e. "mean-field", derives as a
particular case. As such, a key point of the presentation provided here is to
demonstrate that the multi-reference EDF method can indeed be formulated in a
{\it mathematically} meaningful fashion even if does {\it not} derive
from a genuine Hamilton operator. In particular, the restoration of symmetries
can be entirely formulated without making {\it any} reference to a projected
state, i.e. within a genuine EDF framework. However, and as is illustrated in
the present document, a mathematically meaningful formulation does not
guarantee that the formalism is sound from a {\it physical} standpoint. The
price at which the latter can be enforced as well in the future is eventually
alluded to.Comment: 64 pages, 8 figures, submitted to Euroschool Lecture Notes in Physics
Vol.IV, Christoph Scheidenberger and Marek Pfutzner editor
Skyrme pseudo-potential-based EDF parametrisation for spuriousity-free MR-EDF calculations
First exploratory steps towards a pseudo-potential-based Skyrme energy density functional for spuriousity-free multi-reference calculations are presented. A qualitatively acceptable fit can be accomplished by adding simple three- and four-body contact terms to the standard central plus spin-orbit two-body terms. To achieve quantitative predictive power, higher-order terms, e.g.\ velocity-dependent three-body terms, will be required