41 research outputs found
Generator Coordinate Truncations
We investigate the accuracy of several schemes to calculate ground-state
correlation energies using the generator coordinate technique. Our test-bed for
the study is the interacting boson model, equivalent to a 6-level
Lipkin-type model. We find that the simplified projection of a triaxial
generator coordinate state using the subgroup of the rotation group is
not very accurate in the parameter space of the Hamiltonian of interest. On the
other hand, a full rotational projection of an axial generator coordinate state
gives remarkable accuracy. We also discuss the validity of the simplified
treatment using the extended Gaussian overlap approximation (top-GOA), and show
that it works reasonably well when the number of boson is four or larger.Comment: 19 pages, 6 eps figure
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