4,086 research outputs found
Accuracy of BCS-based approximations for pairing in small Fermi systems
We analyze the accuracy of BCS-based approximations for calculating
correlation energies and odd-even energy differences in 2-component fermionic
systems with a small number of pairs. The analysis is focused on comparing BCS
and projected BCS treatments with the exact solution of the pairing
Hamiltonian, considering parameter ranges appropriate for nuclear pairing
energies. We find that the projected BCS is quite accurate over the entire
range of coupling strengths in spaces of up to about 20 doubly degenerate
orbitals. It is also quite accurate for two cases we considered with a more
realistic Hamiltonian, representing the nuclei around 117Sn and 207Pb. However,
the projected BCS significantly underestimates the energies for much larger
spaces when the pairing is weak.Comment: 10 pages; 14 figure
Application of the gradient method to Hartree-Fock-Bogoliubov theory
A computer code is presented for solving the equations of
Hartree-Fock-Bogoliubov (HFB) theory by the gradient method, motivated by the
need for efficient and robust codes to calculate the configurations required by
extensions of HFB such as the generator coordinate method. The code is
organized with a separation between the parts that are specific to the details
of the Hamiltonian and the parts that are generic to the gradient method. This
permits total flexibility in choosing the symmetries to be imposed on the HFB
solutions. The code solves for both even and odd particle number ground states,
the choice determined by the input data stream. Application is made to the
nuclei in the -shell using the USDB shell-model Hamiltonian.Comment: 20 pages, 5 figures, 3 table
Self-consistent description of multipole strength: systematic calculations
We use the quasiparticle random phase approximation with a few Skyrme density
functionals to calculate strength functions in the Jpi = 0+, 1-, and 2+
channels for even Ca, Ni, and Sn isotopes, from the proton drip line to the
neutron drip line. We show where and how low-lying strength begins to appear as
N increases. We also exhibit partial energy-weighted sums of the transition
strength as functions of N for all nuclei calculated, and transition densities
for many of the interesting peaks. We find that low-energy strength increases
with N in all multipoles, but with distinctive features in each. The low-lying
0+ strength near the neutron at large N barely involves protons at all, with
the strength coming primarily from a single two-quasineutron configuration with
very large spatial extent. The low-lying 1- strength is different, with protons
contributing to the transition density in the nuclear interior together with
neutrons at large radii. The low-lying 2+ transition strength goes largely to
more localized states. The three Skyrme interactions we test produce similar
results, differing most significantly in their predictions for the location of
the neutron drip line, the boundaries of deformed regions, energies of and
transition strengths to the lowest 2+ states between closed shells, and
isovector energy-weighted sum rules.Comment: 43 pages, 48 figures, 1 tabl
Electromagnetic transition strengths in soft deformed nuclei
Spectroscopic observables such as electromagnetic transitions strengths can
be related to the properties of the intrinsic mean-field wave function when the
latter are strongly deformed, but the standard rotational formulas break down
when the deformation decreases. Nevertheless there is a well-defined, non-zero,
spherical limit that can be evaluated in terms of overlaps of mean-field
intrinsic deformed wave functions. We examine the transition between the
spherical limit and strongly deformed one for a range of nuclei comparing the
two limiting formulas with exact projection results. We find a simple criterion
for the validity of the rotational formula depending on ,
the mean square fluctuation in the angular momentum of the intrinsic state. We
also propose an interpolation formula which describes the transition strengths
over the entire range of deformations, reducing to the two simple expressions
in the appropriate limits.Comment: 16 pages, 5 figures, supplemental material include
Mixed-Spin Pairing Condensates in Heavy Nuclei
We show that the Bogoliubov-de Gennes equations for nuclear ground-state wave
functions support solutions in which the condensate has a mixture of
spin-singlet and spin-triplet pairing. We find that such mixed-spin condensates
do not occur when there are equal numbers of neutrons and protons, but only
when there is an isospin imbalance. Using a phenomenological Hamiltonian, we
predict that such nuclei may occur in the physical region within the proton
dripline. We also solve the Bogoliubov-de Gennes equations with variable
constraints on the spin-singlet and spin-triplet pairing amplitudes. For nuclei
that exhibit this new pairing behavior, the resulting energy surface can be
rather soft, suggesting that there may be low-lying excitations associated with
the spin mixing.Comment: 4+ pages, 3 figures, 1 table; 1 reference added; v2 corresponds to
the published versio
Structure properties of Th and Fm fission fragments: mean field analysis with the Gogny force
The constrained Hartree-Fock-Bogoliubov method is used with the Gogny
interaction D1S to calculate potential energy surfaces of fissioning nuclei
Th and Fm up to very large deformations. The
constraints employed are the mass quadrupole and octupole moments. In this
subspace of collective coordinates, many scission configurations are identified
ranging from symmetric to highly asymmetric fragmentations. Corresponding
fragment properties at scission are derived yielding fragment deformations,
deformation energies, energy partitioning, neutron binding energies at
scission, neutron multiplicities, charge polarization and total fragment
kinetic energies.Comment: 15 pages, 23 figures, accepted for publication in Phys. Rev. C (2007
Spin-triplet pairing in large nuclei
The nuclear pairing condensate is expected to change character from
spin-singlet to spin-triplet when the nucleus is very large and the neutron and
proton numbers are equal. We investigate the transition between these two
phases within the framework of the Hartree-Fock-Bogoliubov equations, using a
zero-range interaction to generate the pairing. We confirm that extremely large
nucleus would indeed favor triplet pairing condensates, with the Hamiltonian
parameters taken from known systematics. The favored phase is found to depend
on the specific orbitals at the Fermi energy. The smallest nuclei with a
well-developed spin-triplet condensate are in the mass region A ~ 130-140.Comment: 8 pages, 2 figures, 2 table
Mean field and pairing properties in the crust of neutron stars
Properties of the matter in the inner crust of a neutron star are
investigated in a Hartree-Fock plus BCS approximation employing schematic
effective forces of the type of the Skyrme forces. Special attention is paid to
differences between a homogenous and inhomogeneous description of the matter
distribution. For that purpose self-consistent Hartree Fock calculations are
performed in a spherical Wigner-Seitz cell. The results are compared to
predictions of corresponding Thomas Fermi calculations. The influence of the
shell structure on the formation of pairing correlations in inhomogeneous
matter are discussed.Comment: 11 pages, 9 figure
Coupling of hydrodynamics and quasiparticle motion in collective modes of superfluid trapped Fermi gases
At finite temperature, the hydrodynamic collective modes of superfluid
trapped Fermi gases are coupled to the motion of the normal component, which in
the BCS limit behaves like a collisionless normal Fermi gas. The coupling
between the superfluid and the normal components is treated in the framework of
a semiclassical transport theory for the quasiparticle distribution function,
combined with a hydrodynamic equation for the collective motion of the
superfluid component. We develop a numerical test-particle method for solving
these equations in the linear response regime. As a first application we study
the temperature dependence of the collective quadrupole mode of a Fermi gas in
a spherical trap. The coupling between the superfluid collective motion and the
quasiparticles leads to a rather strong damping of the hydrodynamic mode
already at very low temperatures. At higher temperatures the spectrum has a
two-peak structure, the second peak corresponding to the quadrupole mode in the
normal phase.Comment: 14 pages; v2: major changes (effect of Hartree field included
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