982 research outputs found
Number-conserving theory of nuclear pairing gaps: a global assessment
We study odd-even mass staggering of nuclei, also called pairing gaps, using
a Skyrme self-consistent mean-field theory and a numerically exact treatment of
the pairing Hamiltonian. We find that the configuration-space Monte Carlo
method proposed by Cerf and Martin offers a practical computational procedure
to carry out the numerical solutions in large-dimensional model spaces.
Refitting the global strength of the pairing interaction for 443 neutron
pairing gaps in our number-conserving treatment, we find the correction to the
pairing correlation energies and pairing gaps to have rms values of 0.6 MeV and
0.12 MeV, respectively. The exact treatment provides a significant improvement
in the fit to experimental gaps, although it is partially masked by a larger
rms error due to deficiencies in other aspects of the theory such as the
mean-field energy functional.Comment: 11 pages, 9 figure
Neutron width statistics using a realistic description of the neutron channel
A basic prediction of the statistical model of compound nucleus reactions is
that the partial widths for decay into any open channel channel fluctuate
according to the Porter-Thomas distribution (PTD). A recent experiment on -
and -wave neutron scattering from platinum isotopes found that the
experimental -wave partial neutron width distributions deviated
substantially from the PTD. Several explanations for this finding have been
proposed within the statistical model, but none has resolved this issue. Here,
we review the application of a realistic resonance-reaction model to -wave
neutron scattering from Pt. Our main conclusion is that the PTD
provides an excellent description of the partial neutron width distribution,
provided that the secular energy dependence of the average neutron width is
correctly described. Within a realistic range of model parameters, there can be
a near-threshold bound or virtual state of the neutron channel that changes
this secular dependence from the usual dependence, as proposed by
Weidenm\"uller [1]. In this case, the use of the dependence to
analyze the data will lead to apparent deviations from the PTD. We discuss the
limited parameter range where such a near threshold state can have a
significant effect.Comment: Proceedings of the 15th Varenna Conference on Nuclear Reaction
Mechanisms. 7 pages, 4 figures, 1 tabl
Unitary Fermi Gas in a Harmonic Trap
We present an {\it ab initio} calculation of small numbers of trapped,
strongly interacting fermions using the Green's Function Monte Carlo method
(GFMC). The ground state energy, density profile and pairing gap are calculated
for particle numbers using the parameter-free "unitary"
interaction. Trial wave functions are taken of the form of correlated pairs in
a harmonic oscillator basis. We find that the lowest energies are obtained with
a minimum explicit pair correlation beyond that needed to exploit the
degeneracy of oscillator states. We find that energies can be well fitted by
the expression where is the
Thomas-Fermi energy of a noninteracting gas in the trap and is a
pairing gap. There is no evidence of a shell correction energy in the
systematics, but the density distributions show pronounced shell effects. We
find the value for the pairing gap. This is smaller
than the value found for the uniform gas at a density corresponding to the
central density of the trapped gas.Comment: 2 figures, 2 table
A new effective interaction for the trapped Fermi gas
We apply the configuration-interaction method to calculate the spectra of
two-component Fermi systems in a harmonic trap, studying the convergence of the
method at the unitary interaction limit. We find that for a fixed
regularization of the two-body interaction the convergence is exponential or
better in the truncation parameter of the many-body space. However, the
conventional regularization is found to have poor convergence in the
regularization parameter, with an error that scales as a low negative power of
this parameter. We propose a new regularization of the two-body interaction
that produces exponential convergence for systems of three and four particles.
From the systematics, we estimate the ground-state energy of the
four-particle system to be (5.05 +- 0.024)hbar omega.Comment: 4 pages, 3 figure
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
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