Convergence of the hole-line expansion with modern nucleon-nucleon potentials

We calculate the three-hole-line contributions to the binding energy of symmetric nuclear matter in the Brueckner-Bethe-Goldstone expansion using various modern nucleon-nucleon potentials of high precision. The relation with the correlation parameter kappa = rho V-core is examined. In all cases the three-hole-line contributions turn out to be sufficiently small, but no satisfactory saturation is obtained. This means that three-nucleon forces are essential for all considered potentials.