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We assume that the nuclear potential for distances larger than 2.5 fm is given just by the exchanges of one and two pions and, for the latter, we adopt a model based on chiral symmetry and subthreshold pion-nucleon amplitudes, which contains no free parameters. The predictions produced by this model for nucleon-nucleon observables are calculated and shown to agree well with both experiment and those due to phenomenological potentials. ͓S0556-2813͑98͒01503-9͔

Four-nucleon bound-state problems have been solved in the framework of the hyperspherical methods for various central N-N potentials, using the optimal subset expansion. The results are compared to variational ones. The convergence of the expansion for the binding energies is discussed 9There has been considerable work over the past ten years on trinucleon bound state calculations [11][12][13][14]. We have learnt that "realistic" N-N interactions do not yield "realistic" tri-nucleon wave functions because they leads to important discrepancies with the experimental data concerning both the static and dynamic properties. To understand these discrepancies and to improve this situation one considers such non conventional effects as a three-body forces and explicit mesonic degrees of freedom in the electron-nucleus interaction hamiltonian. However because of the phenomenological core of all the "realistic" N-N interactions these non conventional effects are not free from ambiguities. Few calculations exist to date on the 4He bound state using central interactions [19,22,6] or realistic potentials [15,17,20,21,23]. It is of interest to know whether the disagreement between calculated and experimental static and dynamic properties of 4He and 3He is very similar 9 For this purpose we should solve the non relativistic Schr6dinger equation for the four body problem exactly. The aim of this letter is to show that this purpose is possible in the framework of the hyperspherical method in using the optimal subset expansion [11]. For the sake of comparison with the results obtained by accurate variational calculations [9,16] we used a set of typical central potentials which are superpositions of Gaussians [1-3, 5, 6] and the potential of Bell and Delves which has a Yukawa shape [4]. The method used is based on the hyper-