Isoscalar Hamiltonians for light atomic nuclei

The charge-dependent realistic nuclear Hamiltonian for a nucleus, composed of neutrons and protons, can be successfully approximated by a charge-independent one. The parameters of such a Hamiltonian, i.e., the nucleon mass and the NN potential, depend upon the mass number A, charge Z and isospin quantum number T of state of the studied nucleus.Comment: REVTeX, 22 pages, 3 eps figures, to appear in PR

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

Converging upper and lower bounds for ground-state energies of atomic nuclei

By expanding the wave function in terms of the translationally invariant basis of harmonic oscillator functions, we calculate the converging upper (variational) bound for the energy. It is shown that one can construct lower bounds using the reduced density matrix that corresponds to the upper bound. These lower bounds converge to an exact value with the expansion of the basis. We perform the calculations of both bounds with realistic nucleon-nucleon potential for ground states of the triton and the alpha-particle