205 research outputs found
Minimizing Effective Many-Body Interactions
A simple two-level model is developed and used to test the properties of
effective interactions for performing nuclear structure calculations in
truncated model spaces. It is shown that the effective many-body interactions
sensitively depend on the choice of the single-particle basis and they appear
to be minimized when a self- consistent Hartree-Fock basis is used.Comment: (15 pages of text and 1 postscript figure (Figure available upon
request), Preprint Number not assigned ye
Exact Solutions of Model Hamiltonian Problems with Effective Interactions
We demonstrate with soluble models how to employ the effective Hamiltonian
approach of Lee and Suzuki to obtain all the exact eigenvalues of the full
Hamiltonian. We propose a new iteration scheme to obtain the effective
Hamiltonian and demonstrate its convergence properties.Comment: 12 pages and 1 figur
Nuclear shell-model calculations for 6Li and 14N with different NN potentials
Two ``phase-shift equivalent'' local NN potentials with different
parametrizations, Reid93 and NijmII, which were found to give nearly identical
results for the triton by Friar et al, are shown to yield remarkably similar
results for 6Li and 14N in a (0+2)hw no-core space shell-model calculation. The
results are compared with those for the widely used Hamada-Johnson hard-core
and the original Reid soft-core potentials, which have larger deuteron D-state
percentages. The strong correlation between the tensor strength and the nuclear
binding energy is confirmed. However, many nuclear-structure properties seem to
be rather insensitive to the details of the NN potential and, therefore, cannot
be used to test various NN potentials. (Submitted to Phys. Rev. C on Nov. 9,
1993 as a Brief Report.)Comment: 12 text pages and 1 figure (Figure available upon request),
University of Arizona Physics Preprint (Number not yet assigned
Simple approximation for the starting-energy-independent two-body effective interaction with applications to 6Li
We apply the Lee-Suzuki iteration method to calculate the linked-folded
diagram series for a new Nijmegen local NN potential. We obtain an exact
starting-energy-independent effective two-body interaction for a multi-shell,
no-core, harmonic-oscillator model space. It is found that the resulting
effective-interaction matrix elements can be well approximated by the Brueckner
G-matrix elements evaluated at starting energies selected in a simple way.
These starting energies are closely related to the energies of the initial
two-particle states in the ladder diagrams. The ``exact'' and approximate
effective interactions are used to calculate the energy spectrum of 6Li in
order to test the utility of the approximate form.Comment: 15 text pages and 2 PostScript figures (available upon request).
University of Arizona preprint, Number unassigne
Auxiliary potential in no-core shell-model calculations
The Lee-Suzuki iteration method is used to include the folded diagrams in the
calculation of the two-body effective interaction between
two nucleons in a no-core model space. This effective interaction still depends
upon the choice of single-particle basis utilized in the shell-model
calculation. Using a harmonic-oscillator single-particle basis and the
Reid-soft-core {\it NN} potential, we find that overbinds
^4\mbox{He} in 0, 2, and model spaces. As the size of the
model space increases, the amount of overbinding decreases significantly. This
problem of overbinding in small model spaces is due to neglecting effective
three- and four-body forces. Contributions of effective many-body forces are
suppressed by using the Brueckner-Hartree-Fock single-particle Hamiltonian.Comment: 14 text pages and 4 figures (in postscript, available upon request).
AZ-PH-TH/94-2
The general harmonic-oscillator brackets: compact expression, symmetries, sums and Fortran code
We present a very simple expression and a Fortran code for the fast and
precise calculation of three-dimensional harmonic-oscillator transformation
brackets. The complete system of symmetries for the brackets along with
analytical expressions for sums, containing products of two and three brackets,
is given.Comment: 13 pages, accepted for publication in Nuclear Physics
Large-space shell-model calculations for light nuclei
An effective two-body interaction is constructed from a new Reid-like
potential for a large no-core space consisting of six major shells and is used
to generate the shell-model properties for light nuclei from =2 to 6. (For
practical reasons, the model space is partially truncated for =6.) Binding
energies and other physical observables are calculated and compare favorably
with experiment.Comment: prepared using LaTex, 21 manuscript pages, no figure
No-core shell model in an effective-field-theory framework
We present a new approach to the construction of effective interactions
suitable for many-body calculations by means of the no-core shell model (NCSM).
We consider an effective field theory (EFT) with only nucleon fields directly
in the NCSM model spaces. In leading order, we obtain the strengths of the
three contact terms from the condition that in each model space the
experimental ground-state energies of 2H, 3H and 4He be exactly reproduced. The
first (0^+;0) excited state of 4He and the ground state of 6Li are then
obtained by means of NCSM calculations in several spaces and frequencies. After
we remove the harmonic-oscillator frequency dependence, we predict for 4He an
energy level for the first (0^+;0) excited state in remarkable agreement with
the experimental value. The corresponding 6Li binding energy is about 70% of
the experimental value, consistent with the expansion parameter of the EFT.Comment: 4 pages, 3 figures, revtex
An effective field theory approach to two trapped particles
We discuss the problem of two particles interacting via short-range
interactions within a harmonic-oscillator trap. The interactions are organized
according to their number of derivatives and defined in truncated model spaces
made from a bound-state basis. Leading-order (LO) interactions are iterated to
all orders, while corrections are treated in perturbation theory. We show
explicitly that next-to-LO and next-to-next-to-LO interactions improve
convergence as the model space increases. In the large-model-space limit we
regain results from a pseudopotential. Arbitrary scattering lengths are
considered, as well as a generalization to include the non-vanishing range of
the interaction.Comment: 27 pages, 12 figure
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