Four-nucleon shell-model calculations in a Faddeev-like approach

We use equations for Faddeev amplitudes to solve the shell-model problem fo r four nucleons in a model space that includes up to 14h Omega harmonic-osc illator excitations above the unperturbed ground state. Two- and three-body effective interactions derived from the Reid93 and Argonne V8' nucleon-nuc leon potentials are used in the calculations. Binding energies, excitation energies, point-nucleon radii, and electromagnetic and strangeness charge f orm factors for He-4 are studied. The structure of the Faddeev-like equatio ns is discussed and a formula for the matrix elements of the permutation op erators in a harmonic-oscillator basis is given. The dependence on harmonic -oscillator excitations allowed in the model space and on the harmonic-osci llator frequency is investigated. It is demonstrated that the use of three- body effective interactions improves the convergence of the results. [S0556 -2813(99)03004-6].