Few-nucleon systems in a 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 (HO) 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 (NN) potential in model spaces that include up to $34ħ\Omega$ and $16ħ\Omega$ HO excitations, respectively. 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 ${\mathrm{V}8\mathrm{}}^{\prime }$ NN potentials.