40 research outputs found
Self-Consistent Nuclear Shell-Model Calculation Starting from a Realistic NN Potential
First self-consistent realistic shell-model calculation for the light p-shell
nuclei is performed, starting from the high-precision nucleon-nucleon (NN)
CD-Bonn potential. This realistic potential is renormalized deriving a
low-momentum NN potential V-low-k that preserves exactly the two-nucleon
low-energy physics. This V-low-k is suitable to derive a self-consistent
Hartree-Fock basis that is employed to derive both effective single-particle
energies and residual two-body matrix elements for the shell-model hamiltonian.
Results obtained show the reliability of such a fundamental microscopic
approach.Comment: 4 pages, 1 figure, 8 tables, to be published on Physics Letters
Equivalence of model space techniques and the renormalization group for a separable model problem
Lee-Suzuki similarity transformations and Krencigowa-Kuo folded diagrams are
two common methods used to derive energy independent model space effective
interactions for nuclear many-body systems. We demonstrate that these methods
are equivalent to a Renormalization Group (RG) analysis of a separable
potential model. The effective low-momentum potentials V_{eff} are shown to
give the same scaling equation that RG arguments predict. We find the new
result that the different model space techniques considered in this paper yield
a unique low-momentum V_{eff} when applied to the toy model problem.Comment: 10 pages. Minor content and stylistic change
Convergence properties of the effective interaction
The convergence properties of two perturbative schemes to sum the so-called
folded diagrams are critically reviewed, with an emphasis on the intruder state
problem. The methods we study are the approaches of Kuo and co-workers and Lee
and Suzuki. The suitability of the two schemes for shell-model calculations are
discussed.Comment: 10 pages in revtex ver. 3.0. 3 figs can be obtained upon request.
Univerisity of Oslo report UiO/PHYS/93-2
Effective Interactions for the Three-Body Problem
The three-body energy-dependent effective interaction given by the
Bloch-Horowitz (BH) equation is evaluated for various shell-model oscillator
spaces. The results are applied to the test case of the three-body problem
(triton and He3), where it is shown that the interaction reproduces the exact
binding energy, regardless of the parameterization (number of oscillator quanta
or value of the oscillator parameter b) of the low-energy included space. We
demonstrate a non-perturbative technique for summing the excluded-space
three-body ladder diagrams, but also show that accurate results can be obtained
perturbatively by iterating the two-body ladders. We examine the evolution of
the effective two-body and induced three-body terms as b and the size of the
included space Lambda are varied, including the case of a single included
shell, Lambda hw=0 hw. For typical ranges of b, the induced effective
three-body interaction, essential for giving the exact three-body binding, is
found to contribute ~10% to the binding energy.Comment: 19 pages, 9 figures, submitted to PR
Comparison of the Effective Interaction to Various Orders in Different Mass Regions
The convergence of the perturbation expansion for the effective interaction
to be used in shell-model calculations is investigated as function of the mass
number , from to . As the mass number increases, there are more
intermediate states to sum over in each higher-order diagram which contributes
to the effective interaction. Together with the fact that the energy
denominators in each diagram are smaller for larger mass numbers, these two
effects could largely enhance higher-order contributions to the effective
interaction, thereby deteriorating the order-by-order convergence of the
effective interaction. This effect is counterbalanced by the short range of the
nucleon-nucleon interaction, which implies that its matrix elements are weaker
for valence single-particle states in ``large'' nuclei with large mass number
as compared to those in light nuclei. These effects are examined by comparing
various mean values of the matrix elements. It turns out that the contributions
from higher-order terms remain fairly stable as the mass number increases from
to . The implications for nuclear structure calculations are
discussed.Comment: Revtex, 20 pages, 1 figure not include
Novel Methods for Determining Effective Interactions for the Nuclear Shell Model
The Contractor Renormalization (CORE) method is applied in combination with
modern effective-theory techniques to the nuclear many-body problem. A
one-dimensional--yet ``realistic''--nucleon-nucleon potential is introduced to
test these novel ideas. It is found that the magnitude of ``model-space''
(CORE) corrections diminishes considerably when an effective potential that
eliminates the hard-momentum components of the potential is first introduced.
As a result, accurate predictions for the ground-state energy of the there-body
system are made with relatively little computational effort when both
techniques are used in a complementary fashion.Comment: 14 pages, 5 figures and 2 tabl
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
Unitary-model-operator approach to hypernuclei
A method is formulated for the description of lambda hypernuclei in the
framework of the unitary-model-operator approach (UMOA). The method is applied
to O. A lambda-nucleon effective interaction is derived,
taking the coupling of the sigma-nucleon channel into account. The lambda
single-particle energies are calculated for the 0s_{1/2}, 0p_{3/2} and 0p_{1/2}
states employing the Nijmegen soft-core (NSC), J\"ulich model-\~A (J\~A) and
model-\~B (J\~B) hyperon-nucleon potentials.Comment: LaTeX, 27 pages, 4 figures, uses elsart.cls, submitted to Nucl. Phys.
A, revised version, the words 'unitary-correlation-operator method' have been
changed to 'unitary-model-operator approach' in order to avoid unnecessary
confusion, and relevant sentences have been modifie
Realistic Shell-Model Calculations for Proton-Rich N=50 Isotones
The structure of the N=50 isotones 98Cd, 97Ag, and 96Pd is studied in terms
of shell model employing a realistic effective interaction derived from the
Bonn-A nucleon-nucleon potential. The single-hole energies are fixed by
resorting to an analysis of the low-energy spectra of the isotones with A>= 91.
Comparison shows that our results are in very satisfactory agreement with the
available experimental data. This supports confidence in the predictions of our
calculationsComment: 8 pages, 3 figures, to be published on Journal of Physics
Suppression of core polarization in halo nuclei
We present a microscopic study of halo nuclei, starting from the Paris and
Bonn potentials and employing a two-frequency shell model approach. It is found
that the core-polarization effect is dramatically suppressed in such nuclei.
Consequently the effective interaction for halo nucleons is almost entirely
given by the bare G-matrix alone, which presently can be evaluated with a high
degree of accuracy. The experimental pairing energies between the two halo
neutrons in He and Li nuclei are satisfactorily reproduced by our
calculation. It is suggested that the fundamental nucleon-nucleon interaction
can be probed in a clearer and more direct way in halo nuclei than in ordinary
nuclei.Comment: 11 pages, RevTex, 2 postscript figures; major revisions, matches
version to appear in Phys. Rev. Letter