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 ͑HO͒ 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 ͑NN͒ potential in model spaces that include up to 34ប⍀ and 16ប⍀ 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 V8Ј NN potentials.

We present a very simple expression and a Fortran code for the fast and precise calculation of three-dimensional harmonic-oscillator transformation brackets. The complete system of symmetries for the brackets along with analytical expressions for sums, containing products of two and three brackets, is given.

The charge-dependent realistic nuclear Hamiltonian for a nucleus, composed of neutrons and protons, can be successfully approximated by a chargeindependent 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.

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