Effective theory for the two-nucleon system

We apply the method of unitary transformations to a model two-nucleon potential and construct from it an effective potential in a subspace of momenta below a given cut-off $\Lambda$. The S-matrices in the full space and in the subspace are shown to be identical. We solve numerically the Schr\"odinger equation in the small momentum space and recover exactly the bound and scattering states of the full theory. We then expand the heavy repulsive meson exchange of the effective potential in a series of local contact terms and discuss the question of naturalness of the corresponding coupling constants. Using our exact effective theory we address further issues related to the chiral perturbation theory approach of the two-nucleon system. The coordinate space representation of the effective potential is also considered.