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 $v^{(2)}_{\rm eff}$ 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 $v^{(2)}_{\rm eff}$ overbinds ^4\mbox{He} in 0, 2, and $4\hbar\Omega$ 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

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

Camera distortion self-calibration using the plumb-line constraint and minimal Hough entropy

In this paper we present a simple and robust method for self-correction of camera distortion using single images of scenes which contain straight lines. Since the most common distortion can be modelled as radial distortion, we illustrate the method using the Harris radial distortion model, but the method is applicable to any distortion model. The method is based on transforming the edgels of the distorted image to a 1-D angular Hough space, and optimizing the distortion correction parameters which minimize the entropy of the corresponding normalized histogram. Properly corrected imagery will have fewer curved lines, and therefore less spread in Hough space. Since the method does not rely on any image structure beyond the existence of edgels sharing some common orientations and does not use edge fitting, it is applicable to a wide variety of image types. For instance, it can be applied equally well to images of texture with weak but dominant orientations, or images with strong vanishing points. Finally, the method is performed on both synthetic and real data revealing that it is particularly robust to noise.Comment: 9 pages, 5 figures Corrected errors in equation 1

Two-dimensional limit of exchange-correlation energy functional approximations in density functional theory

We investigate the behavior of three-dimensional (3D) exchange-correlation energy functional approximations of density functional theory in anisotropic systems with two-dimensional (2D) character. Using two simple models, quasi-2D electron gas and two-electron quantum dot, we show a {\it fundamental limitation} of the local density approximation (LDA), and its semi-local extensions, generalized gradient approximation (GGA) and meta-GGA (MGGA), the most widely used forms of which are worse than the LDA in the strong 2D limit. The origin of these shortcomings is in the inability of the local (LDA) and semi-local (GGA/MGGA) approximations to describe systems with 2D character in which the nature of the exchange-correlation hole is very nonlocal. Nonlocal functionals provide an alternative approach, and explicitly the average density approximation (ADA) is shown to be remarkably accurate for the quasi-2D electron gas system. Our study is not only relevant for understanding of the functionals but also practical applications to semiconductor quantum structures and materials such as graphite and metal surfaces. We also comment on the implication of our findings to the practical device simulations based on the (semi-)local density functional method.Comment: 21 pages including 9 figures, to be published in Phys. Rev.

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

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