Consistent nuclear matter calculations with local three-nucleon interactions

I calculate the energy per particle of symmetric nuclear matter and pure neutron matter in the framework of the microscopic Brueckner-Hartree-Fock approach using some recent interactions derived in chiral perturbation theory at next-to-next-to-next-to-leading order (N3LO) for the nucleon-nucleon (NN) force, and next-to-next-to-leading order (N2LO) for the nucleon-nucleon-nucleon (NNN) one. The interactions considered in the present work have been adjusted to properties of light nuclei with A=3, adopting local regulators for the NNN interaction. I performed several calculations using an effective density dependent two-body force obtained from the original NNN one keeping the same parameters and the same regularization scheme employed in finite light nuclei calculations; I then compared these results with other calculations obtained, retaining the same parameters of the NNN force fixed on light nuclei but using a nonlocal regulator. This second strategy has been often used in the literature due to the easier derivation of the effective NN force in this case. I found that in pure neutron matter the use of local or nonlocal regulators does not sensibly affect the calculation of the energy per particle while in symmetric nuclear matter the use of local or nonlocal regulators produces appreciable differences. Saturation properties of nuclear matter are discussed for the various models considered; the uncertainties on the reported calculations are also estimated.