84 research outputs found
Particle-Number Projection and the Density Functional Theory
In the framework of the Density Functional Theory for superconductors, we
study the restoration of the particle number symmetry by means of the
projection technique. Conceptual problems are outlined and numerical
difficulties are discussed. Both are related to the fact that neither the
many-body Hamiltonian nor the wave function of the system appear explicitly in
the Density Functional Theory. Similar obstacles are encountered in
self-consistent theories utilizing density-dependent effective interactions.Comment: 18 RevTex pages, 12 figures, submitted to Physical Review
Variation after Particle-Number Projection for the HFB Method with the Skyrme Energy Density Functional
Variation after particle-number restoration is incorporated for the first
time into the Hartree-Fock-Bogoliubov framework employing the Skyrme energy
density functional with zero-range pairing. The resulting projected HFB
equations can be expressed in terms of the local gauge-angle-dependent
densities. Results of projected calculations are compared with those obtained
within the Lipkin-Nogami method in the standard version and with the
Lipkin-Nogami method followed by exact particle-number projection.Comment: 11 pages, 6 figure
Two-Body Density Matrix for Closed s-d Shell Nuclei
The two-body density matrix for and within the
Low-order approximation of the Jastrow correlation method is considered. Closed
analytical expressions for the two-body density matrix, the center of mass and
relative local densities and momentum distributions are presented. The effects
of the short-range correlations on the two-body nuclear characteristics are
investigated.Comment: 13 pages(LaTeX), 4 figures (ps
Correlation effects in single-particle overlap functions and one-nucleon removal reactions
Single-particle overlap functions and spectroscopic factors are calculated on
the basis of the one-body density matrices (ODM) obtained for the nucleus
employing different approaches to account for the effects of
correlations. The calculations use the relationship between the overlap
functions related to bound states of the (A-1)-particle system and the ODM for
the ground state of the A-particle system. The resulting bound-state overlap
functions are compared and tested in the description of the experimental data
from (p,d) reactions for which the shape of the overlap function is important.Comment: 11 pages, 4 figures include
Systematic study of deformed nuclei at the drip lines and beyond
An improved prescription for choosing a transformed harmonic oscillator (THO)
basis for use in configuration-space Hartree-Fock-Bogoliubov (HFB) calculations
is presented. The new HFB+THO framework that follows accurately reproduces the
results of coordinate-space HFB calculations for spherical nuclei, including
those that are weakly bound. Furthermore, it is fully automated, facilitating
its use in systematic investigations of large sets of nuclei throughout the
periodic table. As a first application, we have carried out calculations using
the Skyrme Force SLy4 and volume pairing, with exact particle number projection
following application of the Lipkin-Nogami prescription. Calculations were
performed for all even-even nuclei from the proton drip line to the neutron
drip line having proton numbers Z=2,4,...,108 and neutron numbers
N=2,4,...,188. We focus on nuclei near the neutron drip line and find that
there exist numerous particle-bound even-even nuclei (i.e., nuclei with
negative Fermi energies) that have at the same time negative two-neutron
separation energies. This phenomenon, which was earlier noted for light nuclei,
is attributed to bound shape isomers beyond the drip line.Comment: 12 ReVTeX4 pages, 6 EPS figures. See also
http://www.fuw.edu.pl/~dobaczew/thodri/thodri.htm
Solution of relativistic Hartree-Bogoliubov equations in configurational representation: spherical neutron halo nuclei
The scaled harmonic oscillator basis (SHO) is derived by a local scaling-point transformation of the spherical harmonic oscillator radial wave functions. The unitary scaling transformation produces a basis with improved asymptotic properties. The SHO basis is employed in the solution of the relativistic Hartree-Bogoliubov (RHB) equations in configurational space. The model is applied in the self-consistent mean-field approximation to the description of the neutron halo in Ne isotopes. It is shown that an expansion of nucleon spinors and mean-field potentials in the SHO basis reproduces the asymptotic properties of neutron densities calculated by finite element discretization in the coordinate space. In the RHB description of neutron skins and halos, SHO bases in two or three dimensions can be a useful alternative to technically complicated solutions on a mesh in coordinate space
Monopole giant resonances and nuclear compressibility in relativistic mean field theory
Isoscalar and isovector monopole oscillations that correspond to giant
resonances in spherical nuclei are described in the framework of time-dependent
relativistic mean-field (RMF) theory. Excitation energies and the structure of
eigenmodes are determined from a Fourier analysis of dynamical monopole moments
and densities. The generator coordinate method, with generating functions that
are solutions of constrained RMF calculations, is also used to calculate
excitation energies and transition densities of giant monopole states.
Calculations are performed with effective interactions which differ in their
prediction of the nuclear matter compression modulus K_nm. Both time-dependent
and constrained RMF results indicate that empirical GMR energies are best
reproduced by an effective force with K_nm \approx 270 MeV.Comment: 30 pages of LaTeX, 18 PS-figure
Odd-even mass differences from self-consistent mean-field theory
We survey odd-even nuclear binding energy staggering using density functional
theory with several treatments of the pairing interaction including the BCS,
Hartree-Fock-Bogoliubov, and the Hartree-Fock-Bogoliubov with the Lipkin-Nogami
approximation. We calculate the second difference of binding energies and
compare with 443 measured neutron energy differences in isotope chains and 418
measured proton energy differences in isotone chains. The particle-hole part of
the energy functional is taken as the SLy4 Skyrme parametrization and the
pairing part of the functional is based on a contact interaction with possible
density dependence. An important feature of the data, reproduced by the theory,
is the sharp gap quenching at magic numbers. With the strength of the
interaction as a free parameter, the theory can reproduce the data to an rms
accuracy of about 0.25 MeV. This is slightly better than a single-parameter
phenomenological description but slightly poorer than the usual two-parameter
phenomenological form C/A^alpha . The following conclusions can be made about
the performance of common parametrization of the pairing interaction: (i) there
is a weak preference for a surface-peaked neutron-neutron pairing, which might
be attributable to many-body effects; (ii) a larger strength is required in the
proton pairing channel than in the neutron pairing channel; (iii) pairing
strengths adjusted to the well-known spherical isotope chains are too weak to
give a good overall fit to the mass differences.Comment: 13 pages, 9 figure
Jastrow-type calculations of one-nucleon removal reactions on open - shell nuclei
Single-particle overlap functions and spectroscopic factors are calculated on
the basis of Jastrow-type one-body density matrices of open-shell nuclei
constructed by using a factor cluster expansion. The calculations use the
relationship between the overlap functions corresponding to bound states of the
-particle system and the one-body density matrix for the ground state of
the -particle system. In this work we extend our previous analyses of
reactions on closed-shell nuclei by using the resulting overlap functions for
the description of the cross sections of reactions on the open -
shell nuclei Mg, Si and S and of S
reaction. The relative role of both shell structure and short-range
correlations incorporated in the correlation approach on the spectroscopic
factors and the reaction cross sections is pointed out.Comment: 11 pages, 5 figures, to be published in Phys. Rev.
Two-proton overlap functions in the Jastrow correlation method and cross section of the OC reaction
Using the relationship between the two-particle overlap functions (TOF's) and
the two-body density matrix (TDM), the TOF's for the
OC reaction are calculated on the
basis of a TDM obtained within the Jastrow correlation method. The main
contributions of the removal of and pairs from O
are considered in the calculation of the cross section of the
OC reaction using the Jastrow TOF's
which include short-range correlations (SRC). The results are compared with the
cross sections calculated with different theoretical treatments of the TOF's.Comment: 10 pages, 8 figures, ReVTeX
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