Shell-model calculations for the three-nucleon system

We use Faddeev's decomposition to solve the shell-model problem for three nucleons. The dependence on harmonic-oscillator excitations allowed in the model space, up to $32 \hbar\Omega$ in the present calculations, and on the harmonic-oscillator frequency is studied. Effective interactions derived from Nijmegen II and Reid93 potentials are used in the calculations. The binding energies obtained are close to those calculated by other methods. The structure of the Faddeev equations is discussed and a simple formula for matrix elements of the permutation operators in a harmonic-oscillator basis is given. The Pauli principle is properly treated in the calculations.Comment: 11 pages. REVTEX. 6 PostScript figure

Second Order Darboux Displacements

The potentials for a one dimensional Schroedinger equation that are displaced along the x axis under second order Darboux transformations, called 2-SUSY invariant, are characterized in terms of a differential-difference equation. The solutions of the Schroedinger equation with such potentials are given analytically for any value of the energy. The method is illustrated by a two-soliton potential. It is proven that a particular case of the periodic Lame-Ince potential is 2-SUSY invariant. Both Bloch solutions of the corresponding Schroedinger equation equation are found for any value of the energy. A simple analytic expression for a family of two-gap potentials is derived

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

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

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

Supersymmetric partners for the associated Lame potentials

The general solution of the stationary Schrodinger equation for the associated Lame potentials with an arbitrary real energy is found. The supersymmetric partners are generated by employing seeds solutions for factorization energies inside the gaps.Comment: 13 pages, 4 figures, talk given at the XXVII ICGTMP, Yerevan (Armenia) August 200

Nonlocal supersymmetric deformations of periodic potentials

Irreducible second-order Darboux transformations are applied to the periodic Schrodinger's operators. It is shown that for the pairs of factorization energies inside of the same forbidden band they can create new non-singular potentials with periodicity defects and bound states embedded into the spectral gaps. The method is applied to the Lame and periodic piece-wise transparent potentials. An interesting phenomenon of translational Darboux invariance reveals nonlocal aspects of the supersymmetric deformations.Comment: 15 pages, latex, 9 postscript figure