The α particle based on modern nuclear forces

The Faddeev-Yakubovsky equations for the α particle are solved. Accurate results are obtained for several modern nucleon-nucleon $\mathrm{}\left(\mathrm{NN}\right)\mathrm{}$ interaction models, which include charge-symmetry breaking effects in the $\mathrm{NN}$ force, nucleon mass dependences as well as the Coulomb interaction. These models are augmented by three-nucleon forces of different types and adjusted to the $3N$ binding energy. Our results are close to the experimental binding energy with a slight overbinding. Thus there is only little room left for the contribution of possible $4N$ interactions to the α-particle binding energy. We also discuss model dependences of the binding energies and the wave functions.