50 research outputs found
Low energy n-\nuc{3}{H} scattering : a novel testground for nuclear interaction
The low energy n-\nuc{3}{H} elastic cross sections near the resonance peak
are calculated by solving the 4-nucleon problem with realistic NN interactions.
Three different methods -- Alt, Grassberger and Shandas (AGS), Hyperspherical
Harmonics and Faddeev-Yakubovsky -- have been used and their respective results
are compared. We conclude on a failure of the existing NN forces to reproduce
the n-\nuc{3}{H} total cross section.Comment: To be published in Phys. Rev.
The Four-Boson System with Short-Range Interactions
We consider the non-relativistic four-boson system with short-range forces
and large scattering length in an effective quantum mechanics approach. We
construct the effective interaction potential at leading order in the large
scattering length and compute the four-body binding energies using the
Yakubovsky equations. Cutoff independence of the four-body binding energies
does not require the introduction of a four-body force. This suggests that two-
and three-body interactions are sufficient to renormalize the four-body system.
We apply the equations to 4He atoms and calculate the binding energy of the 4He
tetramer. We observe a correlation between the trimer and tetramer binding
energies similar to the Tjon line in nuclear physics. Over the range of binding
energies relevant to 4He atoms, the correlation is approximately linear.Comment: 23 pages, revtex4, 5 PS figures, discussion expanded, results
unchange
Binding and structure of tetramers in the scaling limit
The momentum-space structure of the Faddeev-Yakubovsky (FY)components of
weakly-bound tetramers is investigated at the unitary limit using a
renormalized zero-range two-body interaction. The results, obtained by
considering a given trimer level with binding energy , provide further
support to a universal scaling function relating the binding energies of two
successive tetramer states. The correlated scaling between the tetramer
energies comes from the sensitivity of the four-boson system to a short-range
four-body scale. Each excited th tetramer energy moves as the
short-range four-body scale changes, while the trimer properties are kept
fixed, with the next excited tetramer emerging from the
atom-trimer threshold for a universal ratio , which does not depend on . We show that both
channels of the FY decomposition [atom-trimer (type) and dimer-dimer
(type)] present high momentum tails, which reflect the short-range
four-body scale. We also found that the channel is favored over channel
at low momentum when the four-body momentum scale largely overcomes the
three-body one.Comment: To appear in PR
Benchmark calculation of n-3H and p-3He scattering
The n-3H and p-3He elastic phase-shifts below the trinucleon disintegration
thresholds are calculated by solving the 4-nucleon problem with three different
realistic nucleon-nucleon interactions (the I-N3LO model by Entem and
Machleidt, the Argonne v18 potential model, and a low-k model derived from the
CD-Bonn potential). Three different methods -- Alt, Grassberger and Sandhas,
Hyperspherical Harmonics, and Faddeev-Yakubovsky -- have been used and their
respective results are compared. For both n-3H and p-3He we observe a rather
good agreement between the three different theoretical methods. We also compare
the theoretical predictions with the available experimental data, confirming
the large underprediction of the p-3He analyzing power.Comment: 18 pages, 9 figure
Spurious states in the Faddeev formalism for few-body systems
We discuss the appearance of spurious solutions of few-body equations for
Faddeev amplitudes. The identification of spurious states, i.e., states that
lack the symmetry required for solutions of the Schroedinger equation, as well
as the symmetrization of the Faddeev equations is investigated. As an example,
systems of three and four electrons, bound in a harmonic-oscillator potential
and interacting by the Coulomb potential, are presented.Comment: 11 pages. REVTE
Properties of C in the {\it ab initio} nuclear shell-model
We obtain properties of C in the {\it ab initio} no-core nuclear
shell-model. The effective Hamiltonians are derived microscopically from the
realistic CD-Bonn and the Argonne V8' nucleon-nucleon (NN) potentials as a
function of the finite harmonic oscillator basis space. Binding energies,
excitation spectra and electromagnetic properties are presented for model
spaces up to . The favorable comparison with available data is a
consequence of the underlying NN interaction rather than a phenomenological
fit.Comment: 9 pages, 2 figure
Few-nucleon systems in translationally invariant harmonic oscillator basis
We present a translationally invariant formulation of the no-core shell model
approach for few-nucleon systems. We discuss a general method of
antisymmetrization of the harmonic-oscillator basis depending on Jacobi
coordinates. The use of a translationally invariant basis allows us to employ
larger model spaces than in traditional shell-model calculations. Moreover, in
addition to two-body effective interactions, three- or higher-body effective
interactions as well as real three-body interactions can be utilized. In the
present study we apply the formalism to solve three and four nucleon systems
interacting by the CD-Bonn nucleon-nucleon potential. Results of ground-state
as well as excited-state energies, rms radii and magnetic moments are
discussed. In addition, we compare charge form factor results obtained using
the CD-Bonn and Argonne V8' NN potentials.Comment: 25 pages. RevTex. 13 Postscript figure
Four-nucleon shell-model calculations in a Faddeev-like approach
We use equations for Faddeev amplitudes to solve the shell-model problem for
four nucleons in the model space that includes up to 14 hbar Omega
harmonic-oscillator excitations above the unperturbed ground state. Two- and
three-body effective interactions derived from the Reid93 and Argonne V8'
nucleon-nucleon potentials are used in the calculations. Binding energies,
excitations energies, point-nucleon radii and electromagnetic and strangeness
charge form factors for 4He are studied. The structure of the Faddeev-like
equations is discussed and a formula for matrix elements of the permutation
operators in a harmonic-oscillator basis is given. The dependence on
harmonic-oscillator excitations allowed in the model space and on the
harmonic-oscillator frequency is investigated. It is demonstrated that the use
of the three-body effective interactions improves the convergence of the
results.Comment: 22 pages, 13 figures, REVTe
Two-body correlations in N-body boson systems
We formulate a method to study two-body correlations in a system of N
identical bosons interacting via central two-body potentials. We use the
adiabatic hyperspherical approach and assume a Faddeev-like decomposition of
the wave function. For a fixed hyperradius we derive variationally an optimal
integro-differential equation for hyperangular eigenvalue and wave function.
This equation reduces substantially by assuming the interaction range much
smaller than the size of the N-body system. At most one-dimensional integrals
then remain. We view a Bose-Einstein condensate pictorially as a structure in
the landscape of the potential given as a function of the one-dimensional
hyperradial coordinate. The quantum states of the condensate can be located in
one of the two potential minima. We derive and discuss properties of the
solutions and illustrate with numerical results. The correlations lower the
interaction energy substantially. The new multi-body Efimov states are
solutions independent of details of the two-body potential. We compare with
mean-field results and available experimental data.Comment: 19 pages (RevTeX4), 13 figures (latex). Journal-link:
http://pra.aps.org
Benchmark Test Calculation of a Four-Nucleon Bound State
In the past, several efficient methods have been developed to solve the
Schroedinger equation for four-nucleon bound states accurately. These are the
Faddeev-Yakubovsky, the coupled-rearrangement-channel Gaussian-basis
variational, the stochastic variational, the hyperspherical variational, the
Green's function Monte Carlo, the no-core shell model and the effective
interaction hyperspherical harmonic methods. In this article we compare the
energy eigenvalue results and some wave function properties using the realistic
AV8' NN interaction. The results of all schemes agree very well showing the
high accuracy of our present ability to calculate the four-nucleon bound state.Comment: 17 pages, 1 figure