We consider the modified Urca processess in the nucleon cores of neutron stars and focus on the impact of many-body effects on simplest "leg" diagram contribution. These include the treatment of the the nucleon interaction in the BHF framework utilizing the full Argonne v18 nucleon potential with addition of the Urbana XI three-body forces, and the modification of the in-medium proton propagator in the intermediate nucleon line. We obtain that the latter effect is dominant and increases the neutrino emissivity up to several orders of magnitude. This effect is most pronounced at the densities close to the direct Urca threshold, but it is also significant throughout the entire outer core. It is a consequence of the beta-stability condition in the neutron star core and it has been overlooked in all previous considerations (to the best of our knowledge). We also show that main modification of the modified Urca emissivities is well described by a universal analytical factor valid for any EOS of nucleon matter at the densities below the direct Urca threshold. The consequences of our results for the neutron star cooling theory are discussed.

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