Screening effects on ${}^1{S}_0$ pairing in neutron matter

The ${}^1{S}_0$ superfluidity of neutron matter is studied in the framework of the generalized Gorkov equation. Vertex corrections to the pairing interaction and the self-energy corrections are introduced and approximated on the same footing in the gap equation. A suppression of the pairing gap by more than $50\%$ with respect to the BCS prediction is found, which deeply changes the scenario for the dynamical and thermal evolution of neutron stars.