89 research outputs found
Numeric and symbolic evaluation of the pfaffian of general skew-symmetric matrices
Evaluation of pfaffians arises in a number of physics applications, and for
some of them a direct method is preferable to using the determinantal formula.
We discuss two methods for the numerical evaluation of pfaffians. The first is
tridiagonalization based on Householder transformations. The main advantage of
this method is its numerical stability that makes unnecessary the
implementation of a pivoting strategy. The second method considered is based on
Aitken's block diagonalization formula. It yields to a kind of LU (similar to
Cholesky's factorization) decomposition (under congruence) of arbitrary
skew-symmetric matrices that is well suited both for the numeric and symbolic
evaluations of the pfaffian. Fortran subroutines (FORTRAN 77 and 90)
implementing both methods are given. We also provide simple implementations in
Python and Mathematica for purpose of testing, or for exploratory studies of
methods that make use of pfaffians.Comment: 13 pages, Download links:
http://gamma.ft.uam.es/robledo/Downloads.html and
http://www.phys.washington.edu/users/bertsch/computer.htm
Coulomb exchange and pairing contributions in nuclear Hartree-Fock-Bogoliubov calculations with the Gogny force
We present exact Hartree-Fock-Bogoliubov calculations with the finite range
density dependent Gogny force using a triaxial basis. For the first time, all
contributions to the Pairing and Fock Fields arising from the Gogny and Coulomb
interactions as well as the two-body correction of the kinetic energy have been
calculated in this basis. We analyze the relevance of these terms in different
regions of the periodic table at zero and high angular momentum. The validity
of commonly used approximations that neglect different terms in the variational
equations is also checked. We find a decrease of the proton pairing energies
mainly due to a Coulomb antipairing effect.Comment: 32 pages, 12 figures. In press in Nucl. Physics
Mean-field Based Approaches to Pairing Correlations in Atomic Nuclei
The evolution of the pairing correlations from closed shell to middle shell
nuclei is analyzed with a Finite Range Density Dependent interaction in the Sn
isotopes. As theoretical approaches we use the Hartree-Fock-Bogoliubov, the
Lipkin-Nogami, their particle number projected counterparts and the full
variation after particle number projection method. We find that whereas all
approaches succeed rather well in the description of the total energy they
differ significantly in the pairing correlation content of the wave functions.
The description of the evolution from the weak to the strong pairing regime is
also approach dependent, specially at shell closure.Comment: 14 pages, 5 figure
Charge radii and structural evolution in Sr, Zr, and Mo isotopes
The evolution of the ground-state nuclear shapes in neutron-rich Sr, Zr, and
Mo isotopes, including both even-even and odd-A nuclei, is studied within a
self-consistent mean-field approximation based on the D1S Gogny interaction.
Neutron separation energies and charge radii are calculated and compared with
available data. A correlation between a shape transition and a discontinuity in
those observables is found microscopically. While in Sr and Zr isotopes the
steep behavior observed in the isotopic dependence of the charge radii is a
consequence of a sharp prolate-oblate transition, the smooth behavior found in
Mo isotopes has its origin in an emergent region of triaxiality.Comment: 6 pages, 7 figures, to be published in Phys. Lett.
Thermal shape fluctuation effects in the description of hot nuclei
The behavior of several nuclear properties with temperature is analyzed
within the framework of the Finite Temperature Hartree-Fock-Bogoliubov (FTHFB)
theory with the Gogny force and large configuration spaces. Thermal shape
fluctuations in the quadrupole degree of freedom, around the mean field
solution, are taken into account with the Landau prescription. As
representative examples the nuclei Er, Dy and Hg are
studied. Numerical results for the superfluid to normal and deformed to
spherical shape transitions are presented. We found a substantial effect of the
fluctuations on the average value of several observables. In particular, we get
a decrease in the critical temperature () for the shape transition as
compared with the plain FTHFB prediction as well as a washing out of the shape
transition signatures. The new values of are closer to the ones found in
Strutinsky calculations and with the Pairing Plus Quadrupole model Hamiltonian.Comment: 17 pages, 8 Figure
Particle number projection with effective forces
The particle number projection method is formulated for density dependent
forces and in particular for the finite range Gogny force. Detailed formula for
the projected energy and its gradient are provided. The problems arising from
the neglection of any exchange term, which may lead to divergences, are
throughly discussed and the possible inaccuracies estimated. Numericala results
for the projection after variation method are shown for the nucleus 164Er and
for the projection before variation approach for the nuclei 48-50Cr. We also
confirm the Coulomb antipairing effect found in mean field theories.Comment: 33 pages, 8 figures. Submit to Nuc. Phys.
Approximate particle number projection with density dependent forces: Superdeformed bands in the A=150 and A=190 regions
We derive the equations for approximate particle number projection based on
mean field wave functions with finite range density dependent forces. As an
application ground bands of even-A superdeformed nuclei in the A=150 and A=190
regions are calculated with the Gogny force.
We discuss nuclear properties such as quadrupole moments, moments of inertia
and quasiparticle spectra, among others, as a function of the angular momentum.
We obtain a good overall description.Comment: 31 pages, 10 figures, 3 appendices. In press in Nucl. Phy
Angular momentum projected analysis of Quadrupole Collectivity in \protect(^{30,32,34}Mg\protect) and \protect(^{32,34,36,38}Si\protect) with the Gogny interaction
A microscopic angular momentum projection after variation is used to describe
quadrupole collectivity in (^{30,32,34}Mg) and (^{32,34,36,38}Si). The
Hartree-Fock-Bogoliubov states obtained in the quadrupole constrained mean
field approach are taken as intrinsic states for the projection. Excitation
energies of the first (2^{+}) states and the (B(E2,0^{+}\to 2^{+})) transition
probabilities are given. A reasonable agreement with available experimental
data is obtained. It is also shown that the mean field picture of those nuclei
is strongly modified by the projection.Comment: 10 pages, 2 figures, to be published in Phys. Lett.
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
Cluster Interpretation of Properties of Alternating Parity Bands in Heavy Nuclei
The properties of the states of the alternating parity bands in actinides,
Ba, Ce and Nd isotopes are analyzed within a cluster model. The model is based
on the assumption that cluster type shapes are produced by the collective
motion of the nuclear system in the mass asymmetry coordinate. The calculated
spin dependences of the parity splitting and of the electric multipole
transition moments are in agreement with the experimental data.Comment: 29 pages, 10 figure
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