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

The accurate computation of nuclear matter properties, such as its binding energy, is still a challenge to nuclear theory, largely because the quark substructure of nucleons creates a strong repulsion at short distances that renders a straightforward perturbative calculation impossible. In this work, the authors study the Brueckner-Bethe-Goldstone expansion of dense Fermi systems in terms of hole-line contributions, of the associated Goldstone diagrams, to the binding energy of nuclear matter. They use various modern nucleon-nucleon potentials of high precision. In all cases the three-hole-line contributions are sufficiently small suggesting that the expansion converges. Yet, the empirical saturation properties of nuclear matter are not reproduced for any potential. This means that very strong nuclear three-body forces are required in order to achieve satisfactory saturation properties of nuclear matter, and that such forces are essential for all considered potentials.