The nuclear shell model has enjoyed a remarkable success in explaining a wide variety of detailed nuclear features. This proves that it is often convenient to describe the nuclear dynamics as a movement of independent nucleons in (single particle) central potentials, which are function of the nucleonic space, spin and charge co-ordinates. An effective residual interaction is then added and treated perturbatively. The validity of this model depends, of course, on its detailed formulation and, specifically, on the assumptions made on the central potentials. Calculations in which these potentials are assumed to be harmonic oscillators (HOSM) have the clear advantage of a great formal and numerical simplicity. The parabolic central potentials can be introduced through the arbitrary addition of a strongly attractive nuclear potential :